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‡ɋɨɮɢʁɚɁɚɪɭɩɫɤɢ‡Ȼɨɲɤɨȼɥɚɯɨɜɢʄ‡

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ɆȺɌȿɆȺɌɂɄȺ ED

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ɍʇɛɟɧɢɤɡɚɬɪɟʄɢɪɚɡɪɟɞɨɫɧɨɜɧɟɲɤɨɥɟ


ɋɨɮɢʁɚɁɚɪɭɩɫɤɢ Ȼɨɲɤɨȼɥɚɯɨɜɢʄ Ɇɚɬɟɦɚɬɢɤɚɛ ɍʇɛɟɧɢɤɡɚɬɪɟʄɢɪɚɡɪɟɞɨɫɧɨɜɧɟɲɤɨɥɟ ȽɅȺȼɇɂɍɊȿȾɇɂɄ ɉɪɨɮɞɪȻɨɲɤɨȼɥɚɯɨɜɢʄ

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ɈȾȽɈȼɈɊɇɂɍɊȿȾɇɂɄ ȾɨɰɞɪɇɚɬɚɲɚɎɢɥɢɩɨɜɢʄ

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ȾɂɁȺȳɇɂɉɊȿɅɈɆ ɋɨɮɢʁɚɁɚɪɭɩɫɤɢ

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ɊȿɐȿɇɁȿɇɌɂ ȺɧɞɪɢʁɚɧɚȻɚʁɢʄɩɪɨɮɟɫɨɪɪɚɡɪɟɞɧɟɧɚɫɬɚɜɟɈɒÄȾɭɲɤɨɊɚɞɨɜɢʄ³Ȼɟɨɝɪɚɞ ɌɚʃɚɆɚɪɬɢʄɧɚɫɬɚɜɧɢɤɦɚɬɟɦɚɬɢɤɟɈɒÄɂɜɚɧȽɭɧɞɭɥɢʄ³ɇɨɜɢɋɚɞ ɌɚɬʁɚɧɚȽɪɝɭɪɨɜɧɚɫɬɚɜɧɢɤɦɚɬɟɦɚɬɢɤɟɈɒÄɂɜɚɧȽɭɧɞɭɥɢʄ³ɇɨɜɢɋɚɞ

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ɅȿɄɌɍɊȺɂɄɈɊȿɄɌɍɊȺ ȳɨɜɚɧɤɚȼɥɚɱɢʄ

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ɂɁȾȺȼȺɑ ȿȾɍɄȺɞɨɨȻɟɨɝɪɚɞ ɍɥɁɦɚʁɚɨɞɇɨʄɚʁɚɛɪ Ɍɟɥɮɚɤɫ ɋɚʁɬZZZHGXNDUVɢɦɟʁɥHGXND#HGXNDUV ɁȺɂɁȾȺȼȺɑȺ ɉɪɨɮɞɪȻɨɲɤɨȼɥɚɯɨɜɢʄɞɢɪɟɤɬɨɪ ɒɌȺɆɉȺ

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ɂɡɞɚʃɟɛɪ ɌɂɊȺɀ


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ɉɨɧɚɜʂɚɦɨ: Ɇɧɨɠɟʃɟɞɨ 100 ........................................................................................................ ɉɨɧɚɜʂɚɦɨ: Ⱦɟʂɟʃɟ ɞɨ 100 ........................................................................................................... Ɇɧɨɠɟʃɟɫɚ 10 ɢɫɚ 100 .................................................................................................................. ȼȿɀȻȺɆɈ: Ɇɧɨɠɟʃɟɫɚ 10 ɢɫɚ 100 ............................................................................................ Ⱦɟʂɟʃɟɫɚ 10 ɢɫɚ 100 .................................................................................................................. ȼȿɀȻȺɆɈ: Ⱦɟʂɟʃɟ ɫɚ 10 ɢɫɚ 100 .............................................................................................. Ɂɚɦɟɧɚ ɦɟɫɬɚ ɢ ɡɞɪɭɠɢɜɚʃɟɱɢɧɢɥɚɰɚ .......................................................................................... ȼȿɀȻȺɆɈ: Ɂɚɦɟɧɚ ɦɟɫɬɚ ɢ ɡɞɪɭɠɢɜɚʃɟɱɢɧɢɥɚɰɚ ..................................................................... Ɇɧɨɠɟʃɟɞɟɫɟɬɢɰɚʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ .................................................................................. ȼȿɀȻȺɆɈ:Ɇɧɨɠɟʃɟɞɟɫɟɬɢɰɚʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ ............................................................. Ɇɧɨɠɟʃɟ ɡɛɢɪɚ ɢ ɪɚɡɥɢɤɟɛɪɨʁɟɦ .................................................................................................. ȼȿɀȻȺɆɈ: Ɇɧɨɠɟʃɟ ɡɛɢɪɚ ɢ ɪɚɡɥɢɤɟ ɛɪɨʁɟɦ .............................................................................. Ⱦɟʂɟʃɟɫɚ ɨɫɬɚɬɤɨɦ........................................................................................................................ ȼȿɀȻȺɆɈ: Ⱦɟʂɟʃɟ ɫɚ ɨɫɬɚɬɤɨɦ ................................................................................................... Ⱦɟʂɟʃɟɞɟɫɟɬɢɰɚʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ .................................................................................... ȼȿɀȻȺɆɈ: Ⱦɟʂɟʃɟ ɞɟɫɟɬɢɰɚʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ ............................................................... Ⱦɟʂɟʃɟ ɡɛɢɪɚ ɢ ɪɚɡɥɢɤɟɛɪoʁɟɦ .......................................................................... ......................... ȼȿɀȻȺɆɈ: Ⱦɟʂɟʃɟ ɡɛɢɪɚ ɢ ɪɚɡɥɢɤɟɛɪoʁɟɦ ................................................................................ Ɇɧɨɠɟʃɟɞɜɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ .................................................................. ȼȿɀȻȺɆɈ:Ɇɧɨɠɟʃɟɞɜɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ .............................................. Ɇɧɨɠɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ ................................................................... ȼȿɀȻȺɆɈ:Ɇɧɨɠɟʃɟɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ .............................................. Ⱦɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ .................................................................... ȼȿɀȻȺɆɈ: Ⱦɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ ............................................... ɋɚɞɚ ɡɧɚɦ ɦɧɨɝɨɜɢɲɟ ..................................................................................................................... ɉɪɨɜɟɪɚɜɚɦɨɧɚɭɱɟɧɨ ......................................................................................................................

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 33 34

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ɆɇɈɀȿȵȿ ɂȾȿȴȿȵȿȾɈ 1000 – ɩɪɜɢ ɞɟɨ ...................................................................

35 36 37 38 39 40 41 43 44 45 46 47 48 49 50

ɋȺȻɂɊȺȵȿ ɂ ɈȾɍɁɂɆȺȵȿȾɈ1000 – ɞɪɭɝɢ ɞɟɨ .................................................... ɉɢɫɦɟɧɨ ɫɚɛɢɪɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ: 437 + 352 .................................................................. ɉɢɫɦɟɧɨ ɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ: 698 352 ................................................................ ȼȿɀȻȺɆɈ ɉɢɫɦɟɧɨ ɫɚɛɢɪɚʃɟ ɢ ɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ: 437 + 352; 698 352 ... ɉɢɫɦɟɧɨ ɫɚɛɢɪɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ: 538 + 245 ..................................................................

51 52 53 54 55

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ȽȿɈɆȿɌɊɂȳɋɄȿ ɎɂȽɍɊȿ ɞɪɭɝɢ ɞɟɨ .......................................................................... ɍɝɚɨ ................................................................................................................................................... ȼȿɀȻȺɆɈ ɍɝɚɨ .............................................................................................................................. ȼɪɫɬɟ ɭɝɥɨɜɚ ..................................................................................................................................... ȼȿɀȻȺɆɈ ȼɪɫɬɟ ɭɝɥɨɜɚ ................................................................................................................ ɐɪɬɚʃɟ ɩɪɚɜɨɝɭɝɥɚ ......................................................................................................................... ȼȿɀȻȺɆɈ ȼɪɫɬɟ ɭɝɥɨɜɚ ................................................................................................................ ɍɡɚʁɚɦɧɢɩɨɥɨɠɚʁɞɜɟɩɪɚɜɟ .......................................................................................................... ɐɪɬɚʃɟ ɩɚɪɚɥɟɥɧɢɯ ɩɪɚɜɢɯ ........................................................................................................... ȼȿɀȻȺɆɈ ɐɪɬɚʃɟ ɩɚɪɚɥɟɥɧɢɯɩɪɚɜɢɯ ...................................................................................... ɐɪɬɚʃɟɧɨɪɦɚɥɧɢɯɩɪɚɜɢɯ ............................................................................................................. ȼȿɀȻȺɆɈ ɐɪɬɚʃɟ ɧɨɪɦɚɥɧɢɯɩɪɚɜɢɯ ........................................................................................ ȼȿɀȻȺɆɈ: ɍɡɚʁɚɦɧɢɩɨɥɨɠɚʁɞɜɟ ɩɪɚɜɟ....................................................................................... ɋɚɞɚ ɡɧɚɦ ɦɧɨɝɨɜɢɲɟ ................................................................................................................... ɉɪɨɜɟɪɚɜɚɦɨɧɚɭɱɟɧɨ .....................................................................................................................

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ȼȿɀȻȺɆɈ ɉɢɫɦɟɧɨ ɫɚɛɢɪɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ 538 + 245 ........................................... ɉɢɫɦɟɧɨ ɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ 674 238 .............................................................. ȼȿɀȻȺɆɈ ɉɢɫɦɟɧɨ ɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ 674 238.......................................... ɉɢɫɦɟɧɨ ɫɚɛɢɪɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ185 + 163 ................................................................ ȼȿɀȻȺɆɈ ɉɢɫɦɟɧɨ ɫɚɛɢɪɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ 185 + 163 ........................................... ɉɢɫɦɟɧɨ ɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ 358 185 .............................................................. ȼȿɀȻȺɆɈ ɉɢɫɦɟɧɨ ɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ 358 185 ......................................... ɉɢɫɦɟɧɨ ɫɚɛɢɪɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ359 + 364 ................................................................ ȼȿɀȻȺɆɈ ɉɢɫɦɟɧɨ ɫɚɛɢɪɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ 359 + 364 ........................................... ɉɢɫɦɟɧɨ ɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ 934 796; 500 385; 1000 738 ........................ ȼȿɀȻȺɆɈ ɉɢɫɦɟɧɨ ɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ 934 796; 500 385; 1000 738 .... ɋɚɛɢɪɚʃɟɜɢɲɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ ........................................................................................ ȼȿɀȻȺɆɈɋɚɛɢɪɚʃɟɜɢɲɟ ɬɪɨɰɢɮɪɟɧɢɯɛɪɨʁɟɜɚ ................................................................... Ɂɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ (ɫɚɛɢɪɚʃɟ ɢ ɨɞɭɡɢɦɚʃɟ) ................................................................... ȼȿɀȻȺɆɈ Ɂɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ (ɫɚɛɢɪɚʃɟ ɢ ɨɞɭɡɢɦɚʃɟ) .............................................. ɋɚɞɚ ɡɧɚɦ ɦɧɨɝɨɜɢɲɟ ................................................................................................................. ɉɪɨɜɟɪɚɜɚɦɨɧɚɭɱɟɧɨ ...................................................................................................................

56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

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ȽȿɈɆȿɌɊɂȳɋɄȿ ɎɂȽɍɊȿ ɬɪɟʄɢ ɞɟɨ .................................................................. 73 ɉɨɧɚɜʂɚɦɨ ɉɪɚɜɨɭɝɚɨɧɢɤɢ ɤɜɚɞɪɚɬ ɢ ɬɪɨɭɝɚɨ ......................................................................... 74 ɉɪɚɜɨɭɝɚɨɧɢɤɢ ɤɜɚɞɪɚɬ ................................................................................................................ 75 ȼȿɀȻȺɆɈ ɉɪɚɜɨɭɝɚɨɧɢɤɢ ɤɜɚɞɪɚɬ .......................................................................................... 76 ɍɩɨɪɟɻɢɜɚʃɟɞɭɠɢ Ƚɪɚɮɢɱɤɨɧɚɞɨɜɟɡɢɜɚʃɟɞɭɠɢ ɩɨɦɨʄɭɲɟɫɬɚɪɚ ..................................... 77 ɐɪɬɚʃɟ ɩɪɚɜɨɭɝɚɨɧɢɤɚ ɢ ɤɜɚɞɪɚɬɚ ɬɪɨɭɝɚɨɧɢɤɨɦ ɢ ɥɟʃɢɪɨɦ .................................................... 78 ɐɪɬɚʃɟ ɩɪɚɜɨɭɝɚɨɧɢɤɚ ɢ ɤɜɚɞɪɚɬɚɲɟɫɬɚɪɨɦ ɢ ɬɪɨɭɝɚɨɧɢɤɨɦ ................................................... 79 ȼȿɀȻȺɆɈ ɐɪɬɚʃɟ ɩɪɚɜɨɭɝɚɨɧɢɤɚ ɢ ɤɜɚɞɪɚɬɚ ........................................................................... 80 Ɉɛɢɦ ɩɪɚɜɨɭɝɚɨɧɢɤɚ ....................................................................................................................... 81 ȼȿɀȻȺɆɈ Ɉɛɢɦ ɩɪɚɜɨɭɝɚɨɧɢɤɚ .................................................................................................. 82 Ɉɛɢɦ ɤɜɚɞɪɚɬɚ ................................................................................................................................ 84 ȼȿɀȻȺɆɈ Ɉɛɢɦ ɤɜɚɞɪɚɬɚ .......................................................................................................... 85 ɆȺɌȿɆȺɌɂɑɄȺ ɉȺɅɂȾɊȼɐȺ ...................................................................................................... 86 Ɍɪɨɭɝɚɨ ȼɪɫɬɟ ɬɪɨɭɝɥɨɜɚ ............................................................................................................ 87 ȼȿɀȻȺɆɈ Ɍɪɨɭɝɚɨ ȼɪɫɬɟ ɬɪɨɭɝɥɨɜɚ ....................................................................................... 88 ɐɪɬɚʃɟ ɬɪɨɭɝɥɨɜɚ .......................................................................................................................... 89 ȼȿɀȻȺɆɈ ɐɪɬɚʃɟ ɬɪɨɭɝɥɨɜɚ ..................................................................................................... 90 Ɉɛɢɦ ɬɪɨɭɝɥɚ ................................................................................................................................. 91 ȼȿɀȻȺɆɈ Ɉɛɢɦ ɬɪɨɭɝɥɚ ............................................................................................................. 92 ɉɪɟɫɥɢɤɚɜɚʃɟ ɝɟɨɦɟɬɪɢʁɫɤɢɯɮɢɝɭɪɚɧɚ ɤɜɚɞɪɚɬɧɨʁɦɪɟɠɢ ....................................................... 93 ȼȿɀȻȺɆɈ ɉɪɟɫɥɢɤɚɜɚʃɟ ɝɟɨɦɟɬɪɢʁɫɤɢɯɮɢɝɭɪɚɧɚ ɤɜɚɞɪɚɬɧɨʁ ɦɪɟɠɢ .................................. 94 ɋɚɞɚ ɡɧɚɦ ɦɧɨɝɨɜɢɲɟ .................................................................................................................. 95 ɉɪɨɜɟɪɚɜɚɦɨɧɚɭɱɟɧɨ ................................................................................................................... 96 ɆɇɈɀȿȵȿ ɂȾȿȴȿȵȿȾɈ 1000 – ɞɪɭɝɢɞɟɨ ...................................................... 97 ɉɢɫɦɟɧɨ ɦɧɨɠɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ 243 2; 216 3 ................... 98 ȼȿɀȻȺɆɈ ɉɢɫɦɟɧɨ ɦɧɨɠɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ 243 2; 216 3 ... 99 ɉɢɫɦɟɧɨ ɦɧɨɠɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ 241 4; 165 5 ...................... 100 ȼȿɀȻȺɆɈ ɉɢɫɦɟɧɨ ɦɧɨɠɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ 241 4; 165 5 .. 101 Ɂɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ ɦɧɨɠɟʃɟ ɢ ɫɚɛɢɪɚʃɟ) ..................................................................... 102 ȼȿɀȻȺɆɈ Ɂɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ ɦɧɨɠɟʃɟ ɢ ɫɚɛɢɪɚʃɟ) ................................................ 103 Ɂɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ ɦɧɨɠɟʃɟɢ ɨɞɭɡɢɦɚʃɟ) ................................................................... 104 ȼȿɀȻȺɆɈ Ɂɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ ɦɧɨɠɟʃɟɢ ɨɞɭɡɢɦɚʃɟ) .............................................. 105

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ɉɢɫɦɟɧɨ ɞɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ: 693 : 3; 456 : 3 ....................... ȼȿɀȻȺɆɈ ɉɢɫɦɟɧɨ ɞɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ: 693 : 3; 456 : 3 .. ɉɢɫɦɟɧɨ ɞɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ: 850 : 2; 672 : 4 ....................... ȼȿɀȻȺɆɈ: ɉɢɫɦɟɧɨ ɞɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ: 850 : 2; 672 : 4 .. ɉɢɫɦɟɧɨ ɞɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ: 415 : 5; 459 : 9 ....................... ȼȿɀȻȺɆɈ: ɉɢɫɦɟɧɨ ɞɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ: 415 : 5; 459 : 9 .. Ɂɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ (ɞɟʂɟʃɟ ɢ ɫɚɛɢɪɚʃɟ) ....................................................................... ȼȿɀȻȺɆɈ:Ɂɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ (ɞɟʂɟʃɟ ɢɫɚɛɢɪɚʃɟ) .................................................. Ɂɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ (ɞɟʂɟʃɟ ɢ ɨɞɭɡɢɦɚʃɟ) ..................................................................... ȼȿɀȻȺɆɈ:Ɂɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ (ɞɟʂɟʃɟ ɢ ɨɞɭɡɢɦɚʃɟ) ................................................ Ɋɟɞɨɫɥɟɞ ɢɡɜɨɻɟʃɚ ɪɚɱɭɧɫɤɢɯ ɨɩɟɪɚɰɢʁɚ .................................................................................. ȼȿɀȻȺɆɈ Ɋɟɞɨɫɥɟɞ ɢɡɜɨɻɟʃɚ ɪɚɱɭɧɫɤɢɯ ɨɩɟɪɚɰɢʁɚ ............................................................. Ɂɚɜɢɫɧɨɫɬɩɪɨɢɡɜɨɞɚ ɨɞɱɢɧɢɥɚɰɚ;ɋɬɚɥɧɨɫɬ ɩɪɨɢɡɜɨɞɚ ......................................................... ȼȿɀȻȺɆɈ: Ɂɚɜɢɫɧɨɫɬ ɩɪɨɢɡɜɨɞɚ ɨɞɱɢɧɢɥɚɰɚ; ɋɬɚɥɧɨɫɬ ɩɪɨɢɡɜɨɞɚ .................................... Ɂɚɜɢɫɧɨɫɬ ɤɨɥɢɱɧɢɤɚ ɨɞɞɟʂɟɧɢɤɚ ɢɞɟɥɢɨɰɚ; ɋɬɚɥɧɨɫɬ ɤɨɥɢɱɧɢɤɚ ....................................... ȼȿɀȻȺɆɈ Ɂɚɜɢɫɧɨɫɬ ɤɨɥɢɱɧɢɤɚ ɨɞɞɟʂɟɧɢɤɚ ɢɞɟɥɢɨɰɚ; ɋɬɚɥɧɨɫɬ ɤɨɥɢɱɧɢɤɚ ................. ȳɟɞɧɚɱɢɧɟɫɚɧɟɩɨɡɧɚɬɢɦ ɱɢɧɢɨɰɟɦ ........................................................................................... ȼȿɀȻȺɆɈ ȳɟɞɧɚɱɢɧɟɫɚɧɟɩɨɡɧɚɬɢɦɱɢɧɢɨɰɟɦ ...................................................................... ɋɚɞɚ ɡɧɚɦ ɦɧɨɝɨɜɢɲɟ ................................................................................................................. ɉɪɨɜɟɪɚɜɚɦɨɧɚɭɱɟɧɨ ..................................................................................................................

ED

U KA

-P

O

ɊȺɁɅɈɆɐɂ .................................................................................................................. ɉɨɧɚɜʂɚɦɨ: Ɋɚɡɥɨɦɰɢ ................................................................................................................. Ɋɚɡɥɨɦɰɢ ....................................................................................................................................... ȼȿɀȻȺɆɈ: Ɋɚɡɥɨɦɰɢ .................................................................................................................. ɍɩɨɪɟɻɢɜɚʃɟ ɪɚɡɥɨɦɚɤɚʁɟɞɧɚɤɢɯ ɢɦɟɧɢɥɚɰɚ ........................................................................... ȼȿɀȻȺɆɈ: ɍɩɨɪɟɻɢɜɚʃɟ ɪɚɡɥɨɦɚɤɚ ʁɟɞɧɚɤɢɯ ɢɦɟɧɢɥɚɰɚ ...................................................... Ⱦɟɰɢɦɚɥɧɢɡɚɩɢɫɛɪɨʁɚ ɫɚʁɟɞɧɨɦɞɟɰɢɦɚɥɨɦ ........................................................................... ȼɟɠɛɚɦɨ: Ⱦɟɰɢɦɚɥɧɢ ɡɚɩɢɫɛɪɨʁɚɫɚ ʁɟɞɧɨɦɞɟɰɢɦɚɥɨɦ ......................................................... ɋɚɞɚ ɡɧɚɦ ɦɧɨɝɨɜɢɲɟ ................................................................................................................. ɉɪɨɜɟɪɚɜɚɦɨɧɚɭɱɟɧɨ ..................................................................................................................

Ɉɜɞɟ ɫɟɧɚɥɚɡɟ ɡɚɞɚɰɢ ɤɨʁɢ ʄɟ ɬɢ ɩɨɦɨʄɢ ɞɚ ɨɛɧɨɜɢɲɪɚɧɢʁɟɫɬɟɱɟɧɚ ɡɧɚʃɚ.

ɇɚ ɨɜɢɦ ɫɬɪɚɧɚɦɚ ɫɟ ɧɚɥɚɡɢɩɪɟɝɥɟɞɫɚɞɪɠɚʁɚ ɜɟʄɟɰɟɥɢɧɟ ɤɨʁɚ ɫɥɟɞɢ

Ɉɜɨɫɭɫɬɪɚɧɟ ɧɚ ɤɨʁɢɦɚ ɭɫɜɚʁɚɲɧɨɜɚ ɡɧɚʃɚ.

Ɉɜɞɟ ɫɟɧɚɥɚɡɟ ɡɚɞɚɰɢ ɤɨʁɢʄɟ ɬɢ ɩɨɦɨʄɢ ɞɚ ɭɫɜɨʁɢɲɢ ɭɬɜɪɞɢɲɡɧɚʃɚ ɢɡɩɪɟɬɯɨɞɧɟ ɥɟɤɰɢʁɟ

ɉɊɈȼȿɊȺȼȺɆɈ ɇȺɍɑȿɇɈ

ɋȺȾȺɁɇȺɆɆɇɈȽɈ ȼɂɒȿ

Ɉɜɞɟɫɟɧɚɥɚɡɟ ɡɚɞɚɰɢ ɩɨɦɨʄɭ ɤɨʁɢɯɩɪɨɜɟɪɚɜɚɲɫɜɨʁɚ ɫɬɟɱɟɧɚ ɡɧɚʃɚ.

ɇɚ ɨɜɢɦ ɫɬɪɚɧɚɦɚ ɫɟɧɚɥɚɡɟɫɜɚɜɚɠɧɚ ɩɪɚɜɢɥɚ ɢɩɨɫɬɭɩɰɢ ɤɨʁɟ ɬɪɟɛɚɞɚ ɡɧɚɲ

5

106 107 108 109 110 111 112 113 114 115 116 118 119 120 121 122 123 124 126 127 128 129 132 133 134 135 137 138 139 140


ɨɫɧɨɜɧɢ ɧɢɜɨ

Ɉɡɧɚɤɚ ɡɚ ɪɚɞ ɭ ɝɪɭɩɢɢɥɢɬɢɦɭ

ɫɪɟɞʃɢɧɢɜɨ ɧɚɩɪɟɞɧɢ ɧɢɜɨ Ɉɜɚɤɨɫɭ ɨɡɧɚɱɟɧɢ ɡɚɞɚɰɢ ɩɪɟɦɚɧɢɜɨɢɦɚ ɩɨɫɬɢɝɧɭʄɚ.

ȻɊɈȳȿȼɂ ɉɊȼȿ ɏɂȴȺȾȿ ɂ ɊȺɑɍɇɋɄȿ ɈɉȿɊȺɐɂȳȿ ɋȺȵɂɆȺ

-P

ȽȿɈɆȿɌɊɂȳɋɄȿɎɂȽɍɊȿ

R

Ɂɚɧɢɦʂɢɜɢ ɡɚɞɚɰɢ

O

Ɋɚɞ ɭɫɜɟɫɰɢ

TA

L

ɉɪɨɧɚɻɢɨɞɝɨɜɨɪ ɭɡ ɩɨɦɨʄ ɩɪɟɬɪɚɠɢɜɚɱɚ ɧɚ ɪɚɱɭɧɚɪɭ.

U KA

Ɉɜɨɫɭ ɨɡɧɚɤɟ ɡɚ ɫɚɞɪɠɚʁɟ ɜɟʄɢɯ ɰɟɥɢɧɚ ɢɧɚɥɚɡɟ ɫɟ ɭ ɝɨɪʃɟɦ ɭɝɥɭ ɫɜɚɤɟɫɬɪɚɧɟ.ɋɥɭɠɟ ɡɚɛɪɠɟ ɩɪɨɧɚɥɚɠɟʃɟ ɫɬɪɚɧɚ ɫɜɚɤɢ ɩɭɬ ɤɚɞɚ ɨɬɜɨɪɢɲɭʇɛɟɧɢɤ

ED

ɅȿȽȿɇȾȺ ʁɟ ɨɛʁɚɲʃɟʃɟ ɡɚ ɩɨɞɚɬɤɟ ɤɨʁɢ ɫɟ ɧɚɥɚɡɟɧɚ ɰɪɬɟɠɭ ɢɥɢ ɫɥɢɰɢ.

Ɂɚɞɚɬɚɤ ɭ ɤɨɦɟ ɤɨɪɢɫɬɢɲ ɨɥɚɤɲɢɰɟ ɩɪɢ ɪɚɱɭɧɚʃɭ

Ɂɚɞɚɬɚɤ ɭ ɤɨɦɟʁɟɩɨɤɚɡɚɧ ɩɨɫɬɭɩɚɤ ɢɥɢ ɧɚɱɢɧɧɚ ɤɨʁɢ ɫɟɞɨɥɚɡɢɞɨ ɪɟɲɟʃɚ.

ɂɧɬɟɪɧɟɬ ɚɞɪɟɫɚ

ɅȿȽȿɇȾȺ

ɋɚɞɪɠɢ ɜɚɠɧɟ ɩɨɞɚɬɤɟ ɤɨʁɢɫɟ ɧɚɥɚɡɢɧɚɫɥɢɰɢ ɢɥɢ ɰɪɬɟɠɭ.

ɝɞɟ ɦɨɠɟɲɞɚ ɭɜɟɠɛɚɲ ɫɚɞɪɠɚʁɟ ɤɨʁɟ ɭɱɢɲ

Ɇɨʁɢɞɪɭɝɚɪɢɢ ʁɚ ʄɟɦɨ ɫɟɩɨɬɪɭɞɢɬɢ ɞɚ ɫɟɞɨɛɪɨ ɡɚɛɚɜɢɬɟ.

6


TA

L

МНОЖЕЊЕ И ДЕЉЕЊЕ ДО 1000 

O

R

ŘřŋőōŎŗ

U KA

-P

ŖʼnŜŠőŅŎš ŷźūŷƐźŻūűŵũŷŸŮŹũſűƐũŵŶŷůŮƒũűŭŮƑŮƒũ

ED

ŭũŵŶŷůűƁűŭŮŴűƁŭūŷſűŽŹŮŶŮŪŹŷƐŮūŮ ƐŮŭŶŷſűŽŹŮŶűŵŪŹŷƐŮŵ ŭũŵŶŷůűƁŻŹŷſűŽŹŮŶŮŪŹŷƐŮūŮƐŮŭŶŷſűŽŹŮŶűŵŪŹŷƐŮŵ ŭũŭŮŴűƁŻŹŷſűŽŹŮŶŮŪŹŷƐŮūŮƐŮŭŶŷſűŽŹŮŶűŵŪŹŷƐŮŵ źũűŪŮŰŷźŻũŻũųũ ŭũŸŹŷſŮŶűƁūŹŮŭŶŷźŻűŰŹũŰũźũƐŮŭŶŷŵ ŹũƀżŶźųŷŵŷŸŮŹũſűƐŷŵ ŭũŸŹűŵŮŶűƁźūŷƐŮŰŶũƒŮŸŹűŹŮƁũūũƒż ŹũŰŴűƀűŻűžŰũŭũŻũųũ


ɆɇɈɀȿȵȿ ȾɈ Ʉʂɭɱɧɟɪɟɱɢ: ɭɫɦɟɧɨ ɦɧɨɠɟʃɟ ɞɨ0, ɩɨɧɚɜʂɚʃɟ ɝɪɚɞɢɜɚ ɞɪɭɝɨɝɪɚɡɪɟɞɚ

1. ɂɡɪɚɱɭɧɚʁɭɤɭɩɚɧɛɪɨʁʁɚɛɭɤɚ ɤɨʁɟ ɫɟɧɚɥɚɡɟɧɚɫɥɢɰɢ Ɇɨɝɭ ɞɚ ɢɡɪɚɱɭɧɚɦɩɨɦɨʄɭɞɜɟ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ. ɋɚɛɢɪɚʃɟɦ ɢɥɢʁɨɲɤɪɚʄɟ, ɦɧɨɠɟʃɟɦ

4

ɡɛɢɪ

 3

=

ɱɢɧɢɨɰɢ

12

L

ɫɚɛɢɪɰɢ

=

ɩɪɨɢɡɜɨɞ

TA

3 + 3 + 3 + 3 = 12

t ɍɱɟɬɢɪɢ ɩɨɫɭɞɟ ɢɦɚ ɭɤɭɩɧɨ __ ʁɚɛɭɤɚ.

R

4 · 3 = 12 ɑɢɬɚɦɨ: ɩɪɨɢɡɜɨɞɛɪɨʁɟɜɚ 4 ɢ __ ʁɟɫɬɟɛɪɨʁ 12. 2. ɉɨɩɭɧɢɬɚɛɥɢɰɭ ɦɧɨɠɟʃɚ. 3

4

5

6

7 14

16

8

O

2

9 10

ɚ) 5ɩɭɬɚɜɟʄɢ ɨɞɛɪɨʁɚ 2; ________

-P

1 1

ɛ) 8ɩɭɬɚɜɟʄɢɨɞɛɪɨʁɚ 4; ________

U KA

· 1 2 3 4 5 6 7 8 9 10

3. Ɉɞɪɟɞɢ ɛɪɨʁɤɨʁɢʁɟ:

ɜ) 4ɩɭɬɚɜɟʄɢɨɞɛɪɨʁɚ 9; ________ ɝ) 7ɩɭɬɚɜɟʄɢɨɞ ɛɪɨʁɚ 6.

________

4. Ⱥɰɚʁɟɧɚɞɭɜɚɨ 7 ɛɚɥɨɧɚ, ɚ ȼɢɤɬɨɪ 3ɩɭɬɚɜɢɲɟ. Ʉɨɥɢɤɨɛɚɥɨɧɚ ʁɟ ɧɚɞɭɜɚɨ ȼɢɤɬɨɪ" ____________

72

ȼɢɤɬɨɪʁɟɧɚɞɭɜɚɨ ________________

ED

ɉɨɞɫɟɬɢɫɟ ɤɚɤɨɫɦɨ ɞɜɨɰɢɮɪɟɧɢɛɪɨʁɦɧɨɠɢɥɢʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ 3 · 18 = 3 · (10 + 8) = (3 · 10) + (3 · 8) = 30 + 24 = 54 6. Ʉɨʁɢɛɪɨʁɧɟɞɨɫɬɚʁɟ?

5. ɇɚɫɬɚɜɢɞɚ ɪɚɱɭɧɚɲɤɚɤɨʁɟ ɡɚɩɨɱɟɬɨ:

Ɂɚɨɤɪɭɠɢɫɥɨɜɨ ɢɫɩɪɟɞɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ.

4 · 15 = 4 · (10 + 5) = (4 · 10) + (4 · 5) = __ + __ = 60 6 ·14 = ____________________________________________

+

3 · 18 = ____________________________________________ 7 · 12 = ____________________________________________ 4 · 16 = ____________________________________________ 5 · 17 = ____________________________________________ 2 · 16 = ____________________________________________

8

(

+

+

= 27

·

= 90

·

= 45

=?

ɚ) 70 ɛ) 75 ɜ 80 ɝ) 85 ɞ) 95


Ⱦȿȴȿȵȿ ȾɈ Ʉʂɭɱɧɟɪɟɱɢ: ɭɫɦɟɧɨ ɞɟʂɟʃɟ ɞɨ0, ɩɨɧɚɜʂɚʃɟ ɝɪɚɞɢɜɚ ɞɪɭɝɨɝɪɚɡɪɟɞɚ

1. Ɉɥɝɚʁɟ 32 ɤɨɥɚɱɚ ɪɚɫɩɨɪɟɞɢɥɚ ɧɚ 4 ɬɚʃɢɪɚ, ɬɚɤɨɞɚ ɢɯ ɧɚ ɫɜɚɤɨɦ ɬɚʃɢɪɭɢɦɚ ʁɟɞɧɚɤ ɛɪɨʁ Ʉɨɥɢɤɨ ɤɨɥɚɱɚ ɢɦɚɧɚɫɜɚɤɨɦ ɬɚʃɢɪɭ?

L

Ɇɨɝɭ ɞɚ ɢɡɪɚɱɭɧɚɦɩɨɦɨʄɭ ʁɟɞɧɟ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ ɞɟʂɟʃɟɦ

t ɇɚ ɫɜɚɤɨɦ ɬɚʃɢɪɭ ɢɦɚ ɩɨ __ ɤɨɥɚɱɚ

TA

ɞɟʂɟɧɢɤĸ 32 : 4 = 8 ĺ ɤɨɥɢɱɧɢɤ ɞɟɥɢɥɚɰ

R

32 : 4 = 8 ɑɢɬɚɦɨ: ɤɨɥɢɱɧɢɤ ɛɪɨʁɟɜɚ 32 ɢ 4ʁɟɫɬɟ ɛɪɨʁ__. 2. ɉɨɞɟɥɢ ɛɪɨʁɟɜɟ ɢ ɩɨɩɭɧɢɬɚɛɟɥɭ.

m:2 m:4 ɚ:8

O

12 18 24 30 36 60

Ⴋ 8ɩɭɬɚ ɦɚʃɢ ɨɞɛɪɨʁɚ 40; ___________

Ⴋ9ɩɭɬɚ ɦɚʃɢ ɨɞɛɪɨʁɚ 81; ___________

-P

m

6

Ⴋ 3ɩɭɬɚ ɦɚʃɢ ɨɞɛɪɨʁɚ 27; ___________

Ⴋ 7ɩɭɬɚ ɦɚʃɢ ɨɞɛɪɨʁɚ 56; ___________

16 24 32 40 48 56 80

U KA

ɚ ɚ:2 ɚ:3 ɚ:6

3. Ɉɞɪɟɞɢ ɛɪɨʁɤɨʁɢʁɟ:

Ⴋ 4ɩɭɬɚ ɦɚʃɢ ɨɞɛɪɨʁɚ 32; ___________ Ⴋ 5ɩɭɬɚ ɦɚʃɢ ɨɞɛɪɨʁɚ 50; ___________ Ⴋ 6 ɩɭɬɚ ɦɚʃɢ ɨɞɛɪɨʁɚ36. ___________

ED

ɉɨɞɫɟɬɢ ɫɟ ɤɚɤɨɫɦɨɞɜɨɰɢɮɪɟɧɢ ɛɪɨʁɞɟɥɢɥɢʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ 78 : 6 = (60 + 18) : 6 = (60 : 6) + (18 : 6) = 10 + 3 = 13 5. ɍɩɢɲɢ ɭɩɪɚɡɧɚ ɩɨʂɚ ɨɞɝɨɜɚɪɚʁɭʄɟɛɪɨʁɟɜɟ

4. ɇɚɫɬɚɜɢɞɚ ɪɚɱɭɧɚɲɤɚɤɨ ʁɟ ɡɚɩɨɱɟɬɨ: 60 : 5 = (50 + 10) : 5 = (50 : 5) + (10 : 5) = __ + __ = 12 72 : 6 = (60 + __) : 6 = (__ : 6) + (12 : __) = __ + __ = __ 52 : 4 = ______________________________________________

:

= (60 + 24) : = (60 : 6) + (24 : 6)

96 : 8 = ______________________________________________ 42 : 3 = ______________________________________________

=

76 : 2 = ______________________________________________

=

60 : 4 = ______________________________________________

9

+


ɆɇɈɀȿȵȿ ɋȺ 10 ɂ ɋȺ 100 Ʉʂɭɱɧɟɪɟɱɢ: ɭɫɦɟɧɨ ɦɧɨɠɟʃɟ ɞɨ0, ɦɧɨɠɟʃɟ ɫɚ 10 ɢ ɫɚ0, ɩɪɨɢɡɜɨɞ ɛɪɨʁɟɜɚ, ɬɨɥɢɤɨ ɩɭɬɚ ɜɟʄɢɛɪɨʁ

1. ɉɨɫɦɚɬɪɚʁ ɫɥɢɤɭ ɢɞɨɩɭɧɢɲɬɚʁɟɩɨɬɪɟɛɧɨ. ɚ) Ʉɨɥɢɤɨ ɞɢɧɚɪɚ ɢɦɚ Ⱦɭʃɚ"

t Ʉɨɥɢɤɨɞɢɧɚɪɚ ɢɦɚɋɚɲɚ"

100 + ___ + ___ + ___ = 400 4 w 100 = 400

TA

4 w 10 = 40 Ⱦɭʃɚ ɢɦɚ ___ɞɢɧɚɪɚ.

ɋɚɲɚ ɢɦɚ ___ ɞɢɧɚɪɚ.

Ȼɪɨʁɫɟ ɦɧɨɠɢɫɚ 100 ɬɚɤɨɲɬɨ ɦɭ ɫɟ ɫɚɞɟɫɧɟɫɬɪɚɧɟ ɞɨɩɢɲɭɞɜɟ ɧɭɥɟ.

17 w 10 = 170

30 w 10 = 300

24 w 10

10 w 10

32 w 10

20 w 10

68 w 10 73 w 10

ED

85 w 10 99 w 10

4 w 100 = 400

3. ɐɟɧɚʁɟɞɧɨɝɛɚɥɨɧɚ ʁɟ 18 ɞɢɧɚɪɚ. Ɇɢɥɨɲʁɟ ɤɭɩɢɨ 10 ɛɚɥɨɧɚ. Ʉɨɥɢɤɢ ʁɟ ɛɢɨ ɪɚɱɭɧɡɚ ɤɭɩʂɟɧɟ ɛɚɥɨɧɟ"

1 w 100

U KA

56 w 10

-P

2. ɉɪɨɭɱɢ ɞɚɬɟɩɪɢɦɟɪɟ ɢ ɢɡɪɚɱɭɧɚʁ ɭɫɦɟɧɨ:

O

R

Ȼɪɨʁɫɟ ɦɧɨɠɢɫɚ 10 ɬɚɤɨɲɬɨ ɦɭ ɫɟɫɚɞɟɫɧɟɫɬɪɚɧɟ ɞɨɩɢɲɟ ʁɟɞɧɚɧɭɥɚ.

17 w 10

L

10 + __ + __ + __ = 40

_____________________

2 w 100

40 w 10

3 w 100

Ɉɞɝɨɜɨɪ: __________________

60 w 10

5 100

___________________________

70 w 10

8 w 100

50 w 10

6 w 100

80 w 10

7 w 100

90 w 10

· 8 = 32

9 w 100

·

4. Ʉɨʁɢɛɪɨʁɫɟ ɤɪɢʁɟ ɢɫɩɨɞ ɫɦɟɲɤɚ ɭɞɚɬɨɦ ɡɚɩɢɫɭ" = 400 Ɣ Ɍɨʁɟɛɪɨʁ ___.

5. Ɍɪɢ ɞɪɭɝɚ ɠɟɥɟ ɡɚʁɟɞɧɨɞɚ ɤɭɩɟ ɥɨɩɬɭ. ɋɜɚɤɢ ɨɞʃɢɯ ɞɚʄɟɩɨ 300ɞɢɧɚɪɚ. Ʉɨɥɢɤɚʁɟɰɟɧɚ ɬɟɥɨɩɬɟ" Ɉɞɝɨɜɨɪ: ____________________________________________

______________________

6. ɆɚɦɚʁɟɎɢɥɢɩɭ ɞɚɥɚ 3ɧɨɜɱɚɧɢɰɟɩɨ 100ɞɢɧɚɪɚ, ɚ ɏɟɥɟɧɢ 30ɧɨɜɱɚɧɢɰɚ ɩɨ 10ɞɢɧɚɪɚ. Ʉɨɥɢɤɨɞɢɧɚɪɚ ʁɟɞɚɥɚ Ɏɢɥɢɩɭ, ɚ ɤɨɥɢɤɨ ɏɟɥɟɧɢ" Ɉɞɝɨɜɨɪ: ____________________________________________

________________________

7. ɂɡɪɚɱɭɧɚʁɩɪɨɢɡɜɨɞɛɪɨʁɟɜɚ: t 12 · ɚ, t ɚ · 48, t t

4 · b, t

b · 7, t

10

60 · ɚ, ɚɤɨʁɟ ɚ = 10; 9 · b,

ɚɤɨʁɟ b = 100.


ɆɇɈɀȿȵȿ ɋȺ 10 ɂ ɋȺ 100 Ʉʂɭɱɧɟɪɟɱɢ: ɭɫɦɟɧɨ ɦɧɨɠɟʃɟ ɞɨ0, ɦɧɨɠɟʃɟ ɫɚ 10 ɢ ɫɚ0, ɩɪɨɢɡɜɨɞ ɛɪɨʁɟɜɚ, ɬɨɥɢɤɨ ɩɭɬɚ ɜɟʄɢɛɪɨʁ

Ɣ 60 w ___ = 600

Ɣ ___ w 10 = 590

Ɣ ___ w 100 = 700

Ɣ ___ w 10 = 200

Ɣ 17 w ___ = 170

Ɣ 9 w ___ = 900

Ɣ 80 w ___ = 800

Ɣ 68 w 10 = ___

Ɣ ___ w 100 = 300

Ɣ ___ w 10 = 900

Ɣ ___ w 10 = 820

Ɣ 6 w ___ = 600

Ɣ 50 w ___ = 500 3.

ȾɟɞɚɆɪɚɡʁɟ ɭʁɟɞɧɨɦɞɚɧɭ ɩɨɞɟɥɢɨ ɩɚɤɟɬɢʄɟ ɭɱɟɬɢɪɢɜɪɬɢʄɚ. ɍɫɜɚɤɨɦ ɜɪɬɢʄɭɛɢɥɨʁɟɩɨ 100ɞɟɰɟ. ɄɨɥɢɤɨɩɚɤɟɬɢʄɚʁɟȾɟɞɚɆɪɚɡ ɩɨɞɟɥɢɨ ɬɨɝɚɞɚɧɚ? ______________________ ȾɟɞɚɆɪɚɡʁɟɩɨɞɟɥɢɨ ___ɩɚɤɟɬɢʄɚ.

ɚ) 10ɩɭɬɚ ɜɟʄɢɨɞɛɪɨʁɚ 25;

ɍʁɟɞɧɨɦɩɚɤɟɬɭɫɟɧɚɥɚɡɢ 10ɱɨɤɨɥɚɞɢɰɚ Ʉɨɥɢɤɨɫɟɱɨɤɨɥɚɞɚ ɧɚɥɚɡɢ ɭ 27 ɬɚɤɜɢɯɩɚɤɟɬɚ? ______________________ Ɉɞɝɨɜɨɪ: _________________________

O

_________________________________

-P

4. Ɉɞɪɟɞɢɛɪɨʁɤɨʁɢʁɟ:

TA

Ɣ 4 w ___ = 400

R

2.

Ɣ 34 w ___ = 340

ɛ) 100ɩɭɬɚɜɟʄɢ ɨɞɛɪɨʁɚ 7; _____________________

U KA

_____________________

L

1. ɍɩɢɲɢ ɧɚ ɥɢɧɢʁɭ ɨɞɝɨɜɚɪɚʁɭʄɢ ɛɪɨʁ

ɜ) 10ɩɭɬɚɜɟʄɢ ɨɞɛɪɨʁɚ 64. _____________________

5. ȳɨɜɚɧɢɦɚ 5ɞɢɧɚɪɚ, ɚ Ⱥɰɚ 10 ɩɭɬɚɜɢɲɟ ɨɞʃɟɝɚ. ȼɨʁɚ ɢɦɚ 10ɩɭɬɚɜɢɲɟɞɢɧɚɪɚ ɨɞ Ⱥɰɟ, ɚ ɇɟɦɚʃɚ 100ɩɭɬɚɜɢɲɟ ɨɞȳɨɜɚɧɚ. Ʉɨɥɢɤɨɞɢɧɚɪɚ ɢɦɚɫɜɚɤɢɞɟɱɚɤ? ȼɨʁɚ ɢɦɚ ______________

Ⱥɰɚ ɢɦɚ ______________

ɇɟɦɚʃɚ ɢɦɚ ______________

ED

ȳɨɜɚɧɢɦɚ ______________

Ɉɞɝɨɜɨɪ: ___________________________________________________________

6. Ⱦɜɚ ɚɭɬɨɛɭɫɚɫɭ ɤɪɟɧɭɥɚ ɭ ɢɫɬɨɜɪɟɦɟ, ɚɥɢ ɭɫɭɩɪɨɬɧɨɦ ɫɦɟɪɭ. ɋɜɚɤɢ ɚɭɬɨɛɭɫʁɟ ɡɚ ʁɟɞɚɧɱɚɫ ɩɪɟɥɚɡɢɨ 100 ɤɢɥɨɦɟɬɚɪɚ. ɇɚ ɤɨʁɨʁɭɞɚʂɟɧɨɫɬɢ ɫɭɫɟɧɚɥɚɡɢɥɢ ɩɨɫɥɟ ɬɪɢ ɱɚɫɚ ɜɨɠʃɟ? ɚ) ɇɚɰɪɬɚʁ ɫɤɢɰɭɫɚ ɨɞɝɨɜɚɪɚʁɭʄɢɦɩɨɞɚɰɢɦɚ ɢɡ ɬɟɤɫɬɚ. ɛ Ɋɟɲɢɡɚɞɚɬɚɤ. ɜ) Ɉɞɝɨɜɨɪɢ ɧɚ ɩɢɬɚʃɟ.

_____________________________ Ɉɞɝɨɜɨɪ: ______________________________________________________________

11


Ⱦȿȴȿȵȿ ɋȺ 10 ɂ ɋȺ 100 Ʉʂɭɱɧɟɪɟɱɢ: ɭɫɦɟɧɨ ɞɟʂɟʃɟ ɞɨ1000, ɞɟʂɟʃɟ ɫɚ 10 ɢ ɫɚ0, ɤɨɥɢɱɧɢɤ ɛɪɨʁɟɜɚ, ɬɨɥɢɤɨ ɩɭɬɚ ɦɚʃɢ ɛɪɨʁ

ɉɨɞɫɟɬɢɦɨ ɫɟ ɭɡɚʁɚɦɧɟ ɜɟɡɟ ɦɧɨɠɟʃɚ ɢɞɟʂɟʃɚ. Ɣ Ɂɚ ɫɜɚɤɨ ɦɧɨɠɟʃɟ ɡɚɩɢɫɭʁɟɦɨ ɩɨ ɞɜɚ ɞɟʂɟʃɚ: 4 · 5 = 20 6 · 8 = 48 9 · 7 = 63 8 · 10 = 80 20 : 4 = 5 48 : 6 = 8 63 : 9 = 7 80 : 8 = 10 20 : 5 = 4 48 : 8 = 6 63 : 7 = 9 80 : 10 = 8

Ʉɚɤɨʁɟ 3 · 6 = 18, ɬɨʁɟ 18 : 3 = 6 ɢ 18 : 6 = 3

150 : 10 = 15

TA

Æ

15Ⱦ : 1Ⱦ = 15

L

Ɣ ɍɮɚɛɪɢɰɢ ɢɝɪɚɱɚɤɚɧɟɞɟʂɧɨ ɫɟɧɚɩɪɚɜɢ 150ɥɭɬɚɤɚ. Ʉɨɥɢɤɨʁɟɩɨɬɪɟɛɧɨ ɤɭɬɢʁɚ ɞɚɫɟ ɨɧɟ ɪɚɫɩɨɪɟɞɟ, ɚɤɨ ɫɟ ɭʁɟɞɧɭ ɤɭɬɢʁɭɫɬɚɜʂɚ ɩɨ 10ɥɭɬɚɤɚ?

Æ

R

 Ⱦɚɫɟ 150ɥɭɬɚɤɚ ɪɚɫɩɨɪɟɞɢɭ ɤɭɬɢʁɟ ɩɨ 10ɥɭɬɚɤɚ,ɩɨɬɪɟɛɧɨ ʁɟ 15 ɤɭɬɢʁɚ. 1. ɉɨɜɟɠɢ ɦɧɨɠɟʃɟ ɢɞɟʂɟʃɟ ɢɧɚɫɬɚɜɢɞɚ ɪɚɱɭɧɚɲɤɚɤɨʁɟ ɡɚɩɨɱɟɬɨ. Æ 130 : 10 = 13 Æ 190 : 10 = __ Æ 460 : 10 = __ Æ 720 : 10 = __

Ɣ 50 · Ɣ 70 · Ɣ 90 · Ɣ 40 ·

10 = 500 10 = ___ 10 = ___ 10 = ___

Æ 500 : 10 = 50

O

10 = 130 10 = ___ 10 = ___ 10 = ___

-P

Ɣ 13 · Ɣ 19 · Ɣ 46 · Ɣ 72 ·

Æ 700 : 10 = ___ Æ 900 : 10 = ___ Æ 400 : 10 = ___

U KA

Ȼɪɨʁ ɤɨʁɢɫɟ ɡɚɜɪɲɚɜɚ ɧɭɥɨɦ (ɧɭɥɚɦɚ), ɞɟɥɢ ɫɟɛɪɨʁɟɦ 10 ɬɚɤɨɲɬɨ ɦɭɫɟ ɫɚ ɞɟɫɧɟ ɫɬɪɚɧɟ ɢɡɨɫɬɚɜɢʁɟɞɧɚ ɧɭɥɚ. Ɣ ɇɚɫɥɢɱɚɧɧɚɱɢɧ ɢ ɫɬɨɬɢɧɟ ɞɟɥɢɲ ɛɪɨʁɟɦ 100,ɫɚɦɨ ɲɬɨɫɚɞɚɫɜɚɤɨʁɫɬɨɬɢɧɢɫɚɞɟɫɧɟ ɫɬɪɚɧɟ ɢɡɨɫɬɚɜɢɲɞɜɟ ɧɭɥɟ. 2. ɇɚɫɬɚɜɢɞɚɪɚɱɭɧɚɲɤɚɤɨʁɟ ɡɚɩɨɱɟɬɨ.

ED

Ɣ 100 : 100 = 1

9ɋ : 1ɋ= 9

Æ

900 : 100 = 9

Ɣ 600 : 100 = __

Ɣ 200 : 100 = 2

Ɣ 700 : 100 = __

Ɣ 300 : 100 = __

Ɣ 800 : 100 = __

Ɣ 400 : 100 = __

Ɣ 900 : 100 = __

Ɣ 500 : 100 = __

Ɣ 1000 : 100 = 10

Ȼɪɨʁ ɤɨʁɢɫɟ ɡɚɜɪɲɚɜɚ ɫɚɞɜɟ ɧɭɥɟ, ɞɟɥɢ ɫɟ ɛɪɨʁɟɦ 100 ɬɚɤɨɲɬɨ ɦɭɫɟ ɫɚɞɟɫɧɟ ɫɬɪɚɧɟ ɢɡɨɫɬɚɜɟɞɜɟ ɧɭɥɟ. 3. ɂɡ ɫɤɭɩɚ Ⱥ ɩɪɟɩɢɲɢ ɛɪɨʁɟɜɟ ɤɨʁɟ ɦɨɠɟɲɩɨɞɟɥɢɬɢ ɚ) ɫɚ 10; _________________________________ _________________________________ ɛ ɫɚ 100. _____________________________

12


ȾȿȴȿȵȿɋȺ 10 ɂ ɋȺ 100 Ʉʂɭɱɧɟɪɟɱɢ: ɭɫɦɟɧɨ ɞɟʂɟʃɟ ɞɨ0, ɞɟʂɟʃɟ ɫɚ 10 ɢ ɫɚ0, ɤɨɥɢɱɧɢɤ ɛɪɨʁɟɜɚ, ɬɨɥɢɤɨ ɩɭɬɚ ɦɚʃɢ ɛɪɨʁ

1. ɂɡɪɚɱɭɧɚʁɫɥɟɞɟʄɟ ɤɨɥɢɱɧɢɤɟ: 600 : 10 = ___

300 : 10 = ___

900 : 10 = ____

400 : 100 = ___

600 : 100 = ___

300 : 100 = ___

900 : 100 = ____

70 : 10 = ___

50 : 10 = ___

80 : 10 = ___

30 : 10 = ___

470 : 10 = ___

350 : 10 = ___

880 : 10 = ___

930 : 10 = ___

700 : 100 = ___

500 : 100 = ____

800 : 100 = ____

300 : 100 = ____

TA

L

400 : 10 = ___

2. ɍɩɢɲɢ ɧɚ ɛɚɥɨɧɞɟɫɟɬɢɧɭɛɪɨʁɚ ɤɨʁɢ ɫɟ ɧɚɥɚɡɢ ɢɫɩɨɞ ʃɟɝɚ.

_______________

O

R

3. ɐɟɧɚ ɤɭɬɢʁɟ ɨɞ 100 ɤɪɟɞɚ ɢɡɧɨɫɢ 500 ɞɢɧɚɪɚ. Ⱥɧɻɟɥɚ ʁɟ ɤɭɩɢɥɚ 10 ɤɪɟɞɚ. Ʉɨɥɢɤɢ ʁɟ ɛɢɨʃɟɧ ɪɚɱɭɧ"

-P

Ɉɞɝɨɜɨɪ: _________________________ _________________________________

Ɇɢɥɢɰɚ ɢ ʃɟɧɟ ɞɪɭɝɚɪɢɰɟɫɭ ɭɱɟɫɬɜɨɜɚɥɟ ɭ ɯɭɦɚɧɢɬɚɪɧɨʁ ɚɤɰɢʁɢȳȿȾȺɇɉȺɄȿɌɂȶ-ɆɇɈȽɈȴɍȻȺȼɂ. Ɇɟɻɭɫɚɤɭɩʂɟɧɢɦ ɥɭɬɤɚɦɚ, ɫɜɚɤɚɞɟɫɟɬɚʁɟɛɢɥɚ Ɏɪɨɡɟɧ. Ʉɨɥɢɤɨɫɭɥɭɬɤɢ Ɇɢɥɢɰɚ ɢʃɟɧɟ ɞɪɭɝɚɪɢɰɟɫɚɤɭɩɢɥɟ, ɚɤɨɫɟ ɭɩɚɤɟɬɭɧɚɥɚɡɢɥɨɩɟɬɧɚɟɫɬ Ɏɪɨɡɟɧɥɭɬɚɤɚ?

U KA

4.

___________________________

ED

Ɉɞɝɨɜɨɪ: _______________________________________

6. ɇɚ ɢɦɚʃɭɫɟɧɚɥɚɡɢ ɭɤɭɩɧɨ 340 ɤɨɤɨɲɚɤɚ ɢɩɟɬɥɨɜɚ. Ⱦɟɫɟɬɢɧɭ ɬɨɝ ɛɪɨʁɚ ɱɢɧɟɩɟɬɥɨɜɢ ɚ ɨɫɬɚɥɨɫɭ ɤɨɤɨɲɤɟ.Ʉɨɥɢɤɨ ɢɦɚɩɟɬɥɨɜɚ, ɚ ɤɨɥɢɤɨ ɤɨɤɨɲɚɤɚ?

5. Ɉɞɪɟɞɢ ɛɪɨʁɤɨʁɢʁɟ:

ɚ) 10ɩɭɬɚ ɦɚʃɢɨɞ ɛɪɨʁɚ 70; ________________

Ɍɨʁɟɛɪɨʁ___.

ɛ) 10ɩɭɬɚ ɦɚʃɢ ɨɞɛɪɨʁɚ 840; ________________

______________________

Ɍɨʁɟɛɪɨʁ___.

ɜ) 10ɩɭɬɚ ɦɚʃɢ ɨɞɛɪɨʁɚ 400. ________________

Ɍɨʁɟɛɪɨʁ___.

Ɉɞɨɜɨɪ: ____________________________ ____________________________________

13


ɁȺɆȿɇȺ ɆȿɋɌȺ ɂ ɁȾɊɍɀɂȼȺȵȿ ɑɂɇɂɅȺɐȺ Ʉʂɭɱɧɟɪɟɱɢ: ɫɜɨʁɫɬɜɚ ɦɧɨɠɟʃɚ, ɡɚɦɟɧɚ ɦɟɫɬɚɢɡɞɪɭɠɢɜɚʃɟ ɱɢɧɢɥɚɰɚ

ƔɄɨɥɢɤɨɧɚɥɟɩɧɢɰɚ ɫɟɧɚɥɚɡɢɧɚɫɥɢɰɢ" Ɇɢɥɟɧɚʁɟ ɪɚɱɭɧɚɥɚ ɨɜɚɤɨ: ɇɚɥɟɩɧɢɰɟ ɫɭ ɪɚɫɩɨɪɟɻɟɧɟ ɭ 3 ɤɨɥɨɧɟ. ɍɫɜɚɤɨʁ ɤɨɥɨɧɢ ɧɚɥɚɡɢɫɟɩɨ 5 ɧɚɥɟɩɧɢɰɚ. ɍɤɭɩɧɨ ɢɯ ɢɦɚ: 3 w 5 = 15

Ɣ ɍɨɱɚɜɚɦɨɞɚʁɟ 3 w 5 = 5 w 3.

TA

L

ɇɢɤɨɥɚʁɟ ɪɚɱɭɧɚɨ ɨɜɚɤɨ: ɇɚɥɟɩɧɢɰɟɫɭ ɪɚɫɩɨɪɟɻɟɧɟ ɭ 5 ɪɟɞɨɜɚ. ɍɫɜɚɤɨɦ ɪɟɞɭ ɧɚɥɚɡɟɫɟ ɩɨ 3 ɧɚɥɟɩɧɢɰɟ. ɍɤɭɩɧɨ ɢɯ ɢɦɚ: 5 w 3 = 15

R

Ⱥɤɨɱɢɧɢɨɰɢɦɚ ɡɚɦɟɧɢɦɨ ɦɟɫɬɚ ɩɪɨɢɡɜɨɞɫɟɧɟʄɟɩɪɨɦɟɧɢɬɢ Ɉɜɨɜɚɠɧɨɫɜɨʁɫɬɜɨ ɫɟɧɚɡɢɜɚɡɚɦɟɧɚ ɦɟɫɬɚɱɢɧɢɥɚɰɚ.

-P

O

 ɇɚ ʁɟɞɧɨʁɜɪɬɟɲɰɢ ɢɦɚ 6 ɤɚɛɢɧɚ. ɍɫɜɚɤɨʁ ɤɚɛɢɧɢɧɚɥɚɡɟ ɫɟ ɩɨɞɜɚɞɟɬɟɬɚ. Ʉɨɥɢɤɨɞɟɰɟ ɢɦɚɧɚ ɬɪɢ ɬɚɤɜɟ ɜɪɬɟɲɤɟ" Ȼɪɨʁɞɟɰɟ ɦɨɠɟɦɨ ɢɡɪɚɱɭɧɚɬɢ ɧɚ ɞɜɚ ɧɚɱɢɧɚ:

ɂɦɚɬɪɢ ɜɪɬɟɲɤɟ ɢɧɚ ɫɜɚɤɨʁɩɨ 6 ɤɚɛɢɧɚ. Ɍɨʁɟ 3 w 6 = 18 ɤɚɛɢɧɚ.ɍɫɜɚɤɨʁɤɚɛɢɧɢ ʁɟ ɩɨ ɞɜɚ ɞɟɬɟɬɚ.Ɍɨ ʁɟ 2 w 18 = 36ɞɟɰɟ.

U KA

ɇɚ ʁɟɞɧɨʁɜɪɬɟɲɰɢ ɢɦɚ 6 ɤɚɛɢɧɚ ɢ ɭɫɜɚɤɨʁ ɤɚɛɢɧɢɩɨ 2ɞɟɬɟɬɚ. Ɍɨʁɟ 6 w 2 = 12ɞɟɰɟ. ɇɚ ɬɪɢ ɜɪɬɟɲɤɟ ɢɦɚ 3 w 12 = 36ɞɟɰɟ. 3 w (6 w 2) = 3 w 12 = 36

(3 w 6) w 2 = 18 w 2 = 36

ɉɪɨɢɡɜɨɞɢ ɫɭʁɟɞɧɚɤɢ.

ED

ɉɪɨɢɡɜɨɞɬɪɢ ɱɢɧɢɨɰɚɫɟɧɟʄɟ ɩɪɨɦɟɧɢɬɢ ɚɤɨ ɡɞɪɭɠɢɦɨɞɜɚɱɢɧɢɨɰɚ, ɩɚ ɬɚɤɨɞɨɛɢʁɟɧɢ ɩɪɨɢɡɜɨɞɩɨɦɧɨɠɢɦɨ ɬɪɟʄɢɦ ɱɢɧɢɨɰɟɦ. Ɉɜɨɜɚɠɧɨɫɜɨʁɫɬɜɨ ɫɟ ɧɚɡɢɜɚɡɞɪɭɠɢɜɚʃɟɱɢɧɢɥɚɰɚ.

1. ɂɡɪɚɱɭɧɚʁɭɫɦɟɧɨ

ɚ) (3 w 5) w 2 Æ 3 w (5 w 2); ɛ) (8 w 10) w 10 Æ 8 w (10 w 10); ɜ) (2 w 4) w 10 Æ 2 w (4 w 10). 2. ɉɪɢɦɟɧɢɫɜɨʁɫɬɜɨ ɡɚɦɟɧɟ ɦɟɫɬɚ ɢ ɡɞɪɭɠɢɜɚʃɚɱɢɧɢɥɚɰɚ ɢ ɢɡɪɚɱɭɧɚʁɩɪɨɢɡɜɨɞɟ: 2 w 3 w 5 = 2 w 5 w 3 = (2 w 5) w 3 = 10 w 3 = 30 ɡɚɦɟɧɚ ɦɟɫɬɚ ɡɞɪɭɠɢɜɚʃɟ ɱɢɧɢɥɚɰɚ ɱɢɧɢɥɚɰɚ

M5w3w2 O3w6w2

N3w4w2 P5w4w2

ɉɪɨɢɡɜɨɞ ɬɪɢ ɱɢɧɢɨɰɚ ɦɨɠɟɦɨ ɢɡɪɚɱɭɧɚɬɢ ɢ ɧɚ ɬɪɟʄɢ ɧɚɱɢɧ ɩɪɢɦɟɧɨɦ ɫɜɨʁɫɬɜɚ ɡɚɦɟɧɟ ɦɟɫɬɚ ɢ ɡɞɪɭɠɢɜɚʃɚɱɢɧɢɥɚɰɚ

14


ɁȺɆȿɇȺ ɆȿɋɌȺ ɂ ɁȾɊɍɀɂȼȺȵȿ ɑɂɇɂɅȺɐȺ Ʉʂɭɱɧɟɪɟɱɢ: ɫɜɨʁɫɬɜɚ ɦɧɨɠɟʃɚ, ɡɚɦɟɧɚ ɦɟɫɬɚɢɡɞɪɭɠɢɜɚʃɟ ɱɢɧɢɥɚɰɚ

1. ɇɚɩɢɲɢ ɛɪɨʁɤɨʁɢɧɟɞɨɫɬɚʁɟ, ɬɚɤɨ ɞɚɫɟɞɨɛɢʁɟ ɬɚɱɧɚʁɟɞɧɚɤɨɫɬ ɚ) (10 w 2) w 5 = __ w (2 w 5);

ɛ) 4 w (3 w 2) = (4 w 3) w __;

ɜ) (__ w 5) w 3 = 4 w (5 w 3);

ɝ) 3 w (15 w 2) = (__ w 15) w 2.

2. ȳɟɞɚɧɜɨɡɢʄ ɢɦɚ 3ɜɚɝɨɧɚ. ɍɫɜɚɤɨɦ ɜɚɝɨɧɭ ɢɦɚɩɨ 8 ɤɥɭɩɚ ɚ ɧɚɫɜɚɤɨʁɤɥɭɩɢɫɟɞɢ ɩɨ ɬɪɨʁɟ ɞɟɰɟ. Ʉɨɥɢɤɨ ɢɦɚ ɞɟɰɟ ɭɬɨɦ ɜɨɡɢʄɭ?

TA

3 w 8 w 3 = _______________________________________

L

ɉɪɢɦɟɧɢɫɜɨʁɫɬɜɚ ɡɚɦɟɧɟ ɦɟɫɬɚ ɢ ɡɞɪɭɠɢɜɚʃɚɱɢɧɢɥɚɰɚ ɢ ɢɡɪɚɱɭɧɚʁɛɪɨʁɞɟɰɟ.

ɉɪɢɦɟɧɢɫɜɨʁɫɬɜɚ ɡɚɦɟɧɟ ɦɟɫɬɚ ɢ ɡɞɪɭɠɢɜɚʃɚɱɢɧɢɥɚɰɚ ɢɡɪɚɱɭɧɚʁɛɪɨʁɧɚɰɪɬɚɧɢɯʁɟɥɤɢ.

O

3.

R

Ɉɞɝɨɜɨɪ: __________________________________________________________

3 w 6 w 2 = (__ w __) w __

-P

= __ w __ = ___

U KA

3w6

3w6

4. Ɂɚɦɟɧɢɞɜɚɱɢɧɢɨɰɚʃɢɯɨɜɢɦ ɩɪɨɢɡɜɨɞɨɦ, ɤɚɤɨʁɟ ɡɚɩɨɱɟɬɨ. ɚ) 5 w 2 w 3 = 5 w 2 w 3 5 w __

__

30

ED

10 w 3

ɛ) 3 w 4 w 2 = 3 w 4 w 2 __ w 2

__ w 8

__

__

ɜ) 6 w 5 w 2 = 6 w 5 w 2 __ w __

__ w __

__

__

Ɣ Ɂɚɲɬɨ ɨɜɚɤɜɚ ɡɚɦɟɧɚ ɧɢʁɟ ɭɬɢɰɚɥɚɧɚɩɪɨɦɟɧɭ ɪɟɡɭɥɬɚɬɚ? Ɉɛʁɚɫɧɢ __________________________________________________________________________ ___________________________________________________________________________ 5. ɉɨɜɟɠɢ ɥɢɧɢʁɨɦʁɟɞɧɚɤɟ ɩɪɨɢɡɜɨɞɟ. 3 w 10 w 4

9w7

3w7w3

8w5

8 w 10 w 2

12 w 10

4w2w5

16 w 10

15

3 w 10 w 5

15 w 10


ɆɇɈɀȿȵȿȾȿɋȿɌɂɐȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɨ 1000 ɦɧɨɠɟʃɟ ɞɟɫɟɬɢɰɚʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ

t ɐɟɧɚʁɟɞɧɨɝ ɤɨɥɚɱɚʁɟ 50ɞɢɧɚɪɚ.Ʉɨɥɢɤɢ ʄɟɛɢɬɢ ɪɚɱɭɧɡɚ 3 ɬɚɤɜɚ ɤɨɥɚɱɚ"

Ɇɨɠɟɲɞɚ ɪɚɱɭɧɚɲɢɨɜɚɤɨ:

3 w Ⱦ

=

15Ⱦ

3 w 50

=

150

L

15Ⱦ

3 w 50 = 3 w (5 w 10) = (3 w 5) w 10 = 15 w 10 = 150

TA

Ⱦ Ⱦ Ⱦ =

5 w 10

Ɂɞɪɭɠɢɲ ɱɢɧɢɨɰɟ 3 ɢ 5.

R

t Ɋɚɱɭɧɡɚ ɬɪɢ ɤɨɥɚɱɚ ʄɟ ɛɢɬɢ 150ɞɢɧɚɪɚ. 1. ɇɚɫɬɚɜɢɞɚ ɪɚɱɭɧɚɲɤɚɤɨ ʁɟ ɡɚɩɨɱɟɬɨ: 7 w 80 = 560 3 w 40 = ____

5 w 6 = ___ ĺ

5 w 60 = ____

2 w 9 = ___ ĺ

2 w 90 = ____

8 w 9 = ___ ĺ

8 w 90 = ____

U KA

3 w 4 = ___ ĺ

7 w 30 = ___;

9 w 50 = ___;

6 w 70 = ___;

8 w 20 = ___;

3 w 50 = ___;

4 w 90 = ___;

4 w 60 = ___;

7 w 40 = ___;

6 w 60 = ___;

9 w 40 = ___;

5 w 90 = ___;

9 w 80 = ___;

6 w 80 = ___;

9 w 90 = ___;

7 w 50 = ___;

9 w 30 = ___;

8 w 70 = ___;

5 w 40 = ___.

O

ĺ

2. Ɉɞɪɟɞɢ ɩɪɨɢɡɜɨɞɟ:

-P

7 w 8 = 56

ɉɪɨɢɡɜɨɞɭɛɪɨʁɟɜɚ 3 ɢ 5ɞɨɩɢɲɟɲɧɭɥɭ ɫɚɞɟɫɧɟ ɫɬɪɚɧɟ

3 w 5 = 15 3 w 50 = 150

Ä

3. ɂɡɪɚɱɭɧɚʁɩɪɨɢɡɜɨɞɟ ɢɩɨɩɭɧɢɬɚɛɟɥɟ.

5 7

30

50

ED

.

70

80

90

.

40

50

70

70

80

4 9

4. ɐɟɧɚ ʁɟɞɧɟ ɱɨɤɨɥɚɞɟ ɢɡɧɨɫɢ90 ɞɢɧɚɪɚ. Ƚɨɪɚɧ ɠɟɥɢ ɞɚ ɤɭɩɢ8 ɬɚɤɜɢɯɱɨɤɨɥɚɞɚ. Ʉɨɥɢɤɢʄɟɛɢɬɢʃɟɝɨɜɪɚɱɭɧ" _________________

Ɉɞɝɨɜɨɪ: _______________________________________________

5. Ɇɢɧɚʁɟ ɤɭɩɢɥɚ 7ɲɧɚɥɢɰɚɩɨ ɢɫɬɨʁɰɟɧɢɄɨɥɢɤɢ ʁɟɛɢɨʃɟɧɪɚɱɭɧɚɤɨ ʁɟɰɟɧɚ ʁɟɞɧɟ ɲɧɚɥɢɰɟ 40 ɞɢɧɚɪɚ" _________________

Ɉɞɝɨɜɨɪ: _______________________________________________

6. ɇɚɩɢɲɢɨɞɝɨɜɚɪɚʁɭʄɢ ɛɪɨʁɬɚɤɨ ɞɚɫɟɞɨɛɢʁɟ ɬɚɱɧɚʁɟɞɧɚɤɨɫɬ. ɚ) 3 w 80 = __ w 60;

ɛ) 2 w 80 = 4 w __;

ɜ) 5 w 30 = 3 w __;

ɝ) 4 w 60 = __ w 80;

ɞ) 5 w 90 = 9 w __;

ɻ) 6 w 60 = 4 w __.

16


ɆɇɈɀȿȵȿȾȿɋȿɌɂɐȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ Ʉʂɭɱɧɟɪɟɱɢ ɦɧɨɠɟʃɟ ɞɨ 1000, ɦɧɨɠɟʃɟ ɞɟɫɟɬɢɰɚʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ

1. Ʉɨʁɢʁɟɛɪɨʁ

2. ɉɨɩɭɧɢɬɚɛɟɥɟ.

t 3ɩɭɬɚɜɟʄɢ ɨɞɛɪɨʁɚ 80? ___________ Ɍɨ ʁɟ ɛɪɨʁ____.

.

20

50

.

30

60

ɚ)

80

40

90

80

50

4

t 4ɩɭɬɚɜɟʄɢ ɨɞɛɪɨʁɚ 70? ___________ Ɍɨ ʁɟɛɪɨʁ____.

ɛ)

70

ɜ)

20

60

90

70

80

R

t 7ɩɭɬɚɜɟʄɢ ɨɞɛɪɨʁɚ 90? ___________ Ɍɨ ʁɟɛɪɨʁ____.

. 9

TA

t 5ɩɭɬɚɜɟʄɢ ɨɞɛɪɨʁɚ 60? ___________ Ɍɨ ʁɟɛɪɨʁ____.

L

7

O

3. Ɂɚɲɢɜɟʃɟʁɟɞɧɟ ɯɚʂɢɧɟɩɨɬɪɟɛɧɨ ʁɟ 30 cm ɱɢɩɤɟ ɛɟɥɟɛɨʁɟ ɢ 20 cm ɱɢɩɤɟ ɩɥɚɜɟ ɛɨʁɟ. Ʉɨɥɢɤɨʁɟɩɨɬɪɟɛɧɨɰɟɧɬɢɦɟɬɚɪɚɱɢɩɤɟ ɫɜɚɤɟɛɨʁɟɞɚɛɢɫɟ ɫɚɲɢɥɨ ɨɫɚɦ ɬɚɤɜɢɯ ɯɚʂɢɧɚ? ____________________________________________________________

-P

Ɉɞɝɨɜɨɪ ___________________________________________________________

U KA

___________________________________________________________________ 4. ɍʁɟɞɧɨɦ ɛɭɤɟɬɭ ɬɪɟɛɚɞɚɛɭɞɟ 30ɥɚɥɚ. Ʉɨɥɢɤɨʁɟɥɚɥɚɩɨɬɪɟɛɧɨ ɞɚɫɟɧɚɩɪɚɜɢ y 10 ɬɚɤɜɢɯ ɛɭɤɟɬɚ?

ɚ) 100

ɛ) 200

ɜ) 300

ɝ) 400

y 7 ɬɚɤɜɢɯɛɭɤɟɬɚ?

ɚ) 140

ɛ) 210

ɜ) 240

ɝ) 280

y 9 ɬɚɤɜɢɯɛɭɤɟɬɚ?

ɚ) 90

ɛ) 210

ɜ) 240

ɝ) 270

ED

Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ.

5. ɍɨɱɢɩɪɚɜɢɥɨ ɢɧɚɫɬɚɜɢ ɡɚɩɨɱɟɬɢɧɢɡ 40, 80, ____, ____, ____, ____, ____, ____, ____, 400. 6.

Ɇɢɥɚɧɚ ɢ ɂɜɚɧ ɤɭɩɭʁɭ ɢɝɪɚɱɤɟ. Ɇɢɥɚɧɚʁɟ ɡɚɫɜɨʁɭ ɢɝɪɚɱɤɭ ɬɪɝɨɜɤɢʃɢ ɞɚɥɚ 9ɧɨɜɱɚɧɢɰɚ ɩɨ 50ɞɢɧɚɪɚ ɢ ɞɨɛɢɥɚ ɤɭɫɭɪ 2ɧɨɜɱɚɧɢɰɟ ɩɨ 10ɞɢɧɚɪɚ. ɂɜɚɧʁɟ ɞɚɨ 5 ɧɨɜɱɚɧɢɰɚ ɩɨ 100 ɞɢɧɚɪɚ ɢɞɨɛɢɨ ɤɭɫɭɪ 4ɧɨɜɱɚɧɢɰɟ ɩɨ 20ɞɢɧɚɪɚ. ɑɢʁɚ ɢɝɪɚɱɤɚʁɟɛɢɥɚɫɤɭɩʂɚ ɢ ɡɚ ɤɨɥɢɤɨ? ________________________________________________ ________________________________________________ Ɉɞɝɨɜɨɪ _____________________________________________________________

7. ɇɚɩɢɲɢɧɚɥɢɧɢʁɭ ɨɞɝɨɜɚɪɚʁɭʄɢɛɪɨʁɬɚɤɨɞɚ ɞɚɬɢ ɡɚɩɢɫɛɭɞɟ ɬɚɱɚɧ. ɚ) 5 w __ = 8 w 40 – 20;

ɛ) 9 w __ = 7 w 50 + 10;

17

ɜ) 4 w __ = 5 w 60 + 20.


ɆɇɈɀȿȵȿ ɁȻɂɊȺ ɂ ɊȺɁɅɂɄȿ ȻɊɈȳȿɆ Ʉʂɭɱɧɟɪɟɱɢ: ɫɜɨʁɫɬɜɚ ɦɧɨɠɟʃɚ, ɦɧɨɠɟʃɟ ɡɛɢɪɚ ɛɪɨʁɟɦ, ɦɧɨɠɟʃɟ ɪɚɡɥɢɤɟɛɪɨʁɟɦ

Ž Ⱥɧɚʁɟɫɜɨʁɟ ɮɨɬɨɝɪɚɮɢʁɟ ʁɟɞɧɚɤɨ ɪɚɫɩɨɪɟɞɢɥɚ ɭ 3 ɚɥɛɭɦɚ.ɍʁɟɞɚɧ ɬɚɤɚɜ ɚɥɛɭɦ ɫɬɚɜɢɥɚʁɟ 40ɮɨɬɨɝɪɚɮɢʁɚ ɫɚɥɟɬɨɜɚʃɚ ɢ 30 ɫɚ ɡɢɦɨɜɚʃɚ. Ʉɨɥɢɤɨ Ⱥɧɚ ɢɦɚ ɭɤɭɩɧɨɮɨɬɨɝɪɚɮɢʁɚ? ȻɪɨʁȺɧɢɧɢɯɮɨɬɨɝɪɚɮɢʁɚ ɦɨɠɟɦɨɞɚ ɢɡɪɚɱɭɧɚɦɨɧɚ ɞɜɚ ɧɚɱɢɧɚ. 1. ɧɚɱɢɧ ɂɡɪɚɱɭɧɚɦɨ ɤɨɥɢɤɨɮɨɬɨɝɪɚɮɢʁɚ ɢɦɚ ɭʁɟɞɧɨɦ ɚɥɛɭɦɭ ɢ ɬɚʁɛɪɨʁɩɨɦɧɨɠɢɦɨɫɚ 3. 3 w (40 + 30) = 3 w 70 = 210

TA

L

2. ɧɚɱɢɧ ɍɤɭɩɧɨɦ ɛɪɨʁɭɮɨɬɨɝɪɚɮɢʁɚ ɫɚ ɡɢɦɨɜɚʃɚɞɨɞɚɦɨ ɭɤɭɩɚɧɛɪɨʁɮɨɬɨɝɪɚɮɢʁɚ ɫɚɥɟɬɨɜɚʃɚ. (3 w 40) + (3 w 30) = 120 + 90 = 210 t Ɋɚɱɭɧɚʁɭʄɢ ɧɚ ɨɛɚ ɧɚɱɢɧɚ,ɞɨɛɢɥɢɫɦɨʁɟɞɧɚɤɟ ɪɟɡɭɥɬɚɬɟ. Ⱥɧɚ ɢɦɚ 210 ɮɨɬɨɝɪɚɮɢʁɚ Ɂɧɚɱɢ ɞɚ ʁɟ: 3 w (40 + 30) = (3 w 40) + (3 w 30) = 210

O

R

Ɂɛɢɪ ɦɧɨɠɢɦɨɛɪɨʁɟɦ ɬɚɤɨɲɬɨ ɫɜɚɤɢɫɚɛɢɪɚɤ ɩɨɦɧɨɠɢɦɨɞɚɬɢɦ ɛɪɨʁɟɦ ɩɚɞɨɛɢʁɟɧɟ ɩɪɨɢɡɜɨɞɟ ɫɚɛɟɪɟɦɨ. Ɉɜɨɜɚɠɧɨɫɜɨʁɫɬɜɨ ɫɟ ɧɚɡɢɜɚɦɧɨɠɟʃɟ ɡɛɢɪɚɛɪɨʁɟɦ. 1. ɂɡɪɚɱɭɧɚʁɩɪɢɡɜɨɞɟ ɧɚɩɪɢɤɚɡɚɧ ɧɚɱɢɧ 75 w 8 = (70 + 5) w 8 = (70 w 8) + (5 w 8) = 560 + 40 = 600

-P

ɚ) 63 w 4 = _____________________________________________________________________ ɛ) 216 w 2 = (200 + 10 + 6) w 2 = (200 w 2) + ( __ w 2) + (__ w 2) = ____ + ___ + 12 = _____

U KA

Ž ɍʁɟɞɧɨɦ ɪɚɫɚɞɧɢɤɭ ɡɚɫɚɻɟɧɨʁɟ 5ɪɟɞɨɜɚ ɪɭɠɚ, ɭɫɜɚɤɨɦ ɪɟɞɭɩɨ 70 ɫɚɞɧɢɰɚ. ɉɨɫɥɟ ɢɡɜɟɫɧɨɝɜɪɟɦɟɧɚ, ɭɬɜɪɻɟɧɨ ʁɟ ɞɚ je ɭɫɜɚɤɨɦ ɪɟɞɭɭɜɟɧɭɥɨɩɨ 10 ɫɚɞɧɢɰɚ. ɂɡɪɚɱɭɧɚʁɛɪɨʁɫɚɞɧɢɰɚ ɪɭɠɚ ɤɨʁɟɫɭɫɟɩɪɢɦɢɥɟ. Ȼɪɨʁɫɚɞɧɢɰɚ ɪɭɠɚ ɤɨʁɟɫɭɫɟɩɪɢɦɢɥɟ ɦɨɠɟɦɨɞɚ ɢɡɪɚɱɭɧɚɦɨɧɚɞɜɚ ɧɚɱɢɧɚ. 1.ɧɚɱɢɧ ɂɡɪɚɱɭɧɚɦɨ ɤɨɥɢɤɨɫɟ ɪɭɠɚɩɪɢɦɢɥɨ ɭʁɟɞɧɨɦ ɪɟɞɭ ɢ ɬɚʁɛɪɨʁɩɨɦɧɨɠɢɦɨ ɫɚ 5.

ED

(70 – 10) w 5 = 60 w 5 = 300 2.ɧɚɱɢɧ Ɉɞɭɤɭɩɧɨɝɛɪɨʁɚ ɡɚɫɚɻɟɧɢɯ ɪɭɠɚ ɭ 5 ɪɟɞɨɜɚ, ɨɞɭɡɦɟɦɨ ɭɤɭɩɚɧɛɪɨʁɭɜɟɧɭɥɢɯ ɪɭɠɚ ɭ 5 ɪɟɞɨɜɚ (70 w 5) – (10 w 5) = 350 – 50 = 300

.

y Ɋɚɱɭɧɚʁɭʄɢ ɧɚ ɨɛɚ ɧɚɱɢɧɚ, ɞɨɛɢɥɢɫɦɨʁɟɞɧɚɤɟ ɪɟɡɭɥɬɚɬɟ. ɍɤɭɩɚɧɛɪɨʁɩɪɢɦʂɟɧɢɯ ɪɭɠɚʁɟ 300. Ɂɧɚɱɢ ɞɚ ʁɟ: (70 – 10) w 5 = (70 w 5) – (10 w 5) = 300 Ɋɚɡɥɢɤɭ ɦɧɨɠɢɦɨ ɛɪɨʁɟɦ, ɬɚɤɨ ɲɬɨɭɦɚʃɟɧɢɤɢ ɭɦɚʃɢɥɚɰɩɨɦɧɨɠɢɦɨɞɚɬɢɦɛɪɨʁɟɦ, ɩɚɞɨɛɢʁɟɧɟ ɩɪɨɢɡɜɨɞɟ ɨɞɭɡɦɟɦɨ. Ɉɜɨɜɚɠɧɨɫɜɨʁɫɬɜɨɫɟɧɚɡɢɜɚɦɧɨɠɟʃɟ ɪɚɡɥɢɤɟ ɛɪɨʁɟɦ. ɋɜɨʁɫɬɜɚ ɦɧɨɠɟʃɟ ɡɛɢɪɚ ɢ ɪɚɡɥɢɤɟɛɪɨʁɟɦ ɩɪɢɦɟʃɭʁɟɦɨ ɤɚɞɚɞɜɨɰɢɮɪɟɧɟɢ ɬɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɟ ɦɧɨɠɢɦɨʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ. 2. ɂɡɪɚɱɭɧɚʁɤɨɥɢɱɧɢɤɟɧɚɩɪɢɤɚɡɚɧɧɚɱɢɧ 75 w 8 = (80 í 5) w 8 = (80 w 8) í (5 w 8) = 640 í 40 = 600 ɚ) 98 w 5 = ___________________________________________________________________ ɛ) 199 w 3 = (200 – 1) w 3 = (200 w 3) – (__ w 3) = ___ – ___ = ___

18


ɆɇɈɀȿȵȿ ɁȻɂɊȺ ɂ ɊȺɁɅɂɄȿ ȻɊɈȳȿɆ Ʉʂɭɱɧɟɪɟɱɢ: ɫɜɨʁɫɬɜɚ ɦɧɨɠɟʃɚ, ɦɧɨɠɟʃɟ ɡɛɢɪɚ ɛɪɨʁɟɦ, ɦɧɨɠɟʃɟ ɪɚɡɥɢɤɟ ɛɪɨʁɟɦ

1. ɂɡɪɚɱɭɧɚʁɫɥɟɞɟʄɟɩɪɨɢɡɜɨɞɟ ɩɪɢɦɟɧɨɦ ɫɜɨʁɫɬɜɚ ɦɧɨɠɟʃɚ ɡɛɢɪɚɛɪɨʁɟɦ. 350 w 2 =

204 w 4 =

= (0 + __) w 7 =

= (300 + 50) w 2 =

= (___ + __) w __ =

= (__ w 7) + (__ w 7) =

= (___ w __) + (__ w __) =

= (___ w __) + (__ w __) =

= ____ + ___ =

= ____ + ___ =

= ____ + ___ =

= ____

= ____

= ____

L

 w 7 =

TA

2. Ɇɢɥɨɲɡɚ ɭɠɢɧɭ ɫɜɚɤɢ ɞɚɧɩɨɬɪɨɲɢ5 ɞɢɧɚɪɚ. ɄɨɥɢɤɨɞɢɧɚɪɚʁɟɆɢɥɨɲɭ ɩɨɬɪɟɛɧɨ ɡɚ ɭɠɢɧɭ ɡɚ 5ɞɚɧɚ? (___ + ___) w __ = ___________________________________________________

Ɉɞɝɨɜɨɪ: __________________________________________________________

R

3. ɉɪɢɦɟɧɢɫɜɨʁɫɬɜɨ ɦɧɨɠɟʃɚ ɡɛɢɪɚɛɪɨʁɟɦ ɢ ɢɡɪɚɱɭɧɚʁɩɪɨɢɡɜɨɞɟ.

O

15 w 30 = (10 + 5) w 30 = __________________________________________________ 17 w 40 = (___ + __) w 40 = ________________________________________________

-P

 w 50 = (___ + __) w ___ = _______________________________________________ 12 w 20 = ______________________________________________________________

U KA

4. ɋɥɟɞɟʄɟ ɩɪɨɢɡɜɨɞɟ ɢɡɪɚɱɭɧɚʁɩɪɢɦɟɧɨɦɫɜɨʁɫɬɜɚ ɦɧɨɠɟʃɚ ɪɚɡɥɢɤɟɛɪɨʁɟɦ. 38 w 4 = (40 – 2) w 4 = (___ w __) – (__w __) = ____ – ___ = ____  w 7 = (100 – 1) w 7 = (___ w __) – (__w __) = ____ – ___ = ____ 10 w 4 = (200 – 10) w 4 = (___ w __) – (__w __) = ____ – ___ = ____ 25 w 3 = (300 – 5) w 3 = (___ w __) – (__w __) = ____ – ___ = ____

ED

5. ɇɚ 3ɩɨɥɢɰɟɧɚɥɚɡɢ ɫɟɩɨ 40 ɤʃɢɝɚ. Ȼɢɛɥɢɨɬɟɤɚɪɤɚʁɟɫɚɫɜɚɤɟɩɨɥɢɰɟ ɭɡɟɥɚ ɩɨ 2 ɤʃɢɝɟ. ɂɡɪɚɱɭɧɚʁɭɤɭɩɚɧɛɪɨʁɤʃɢɝɚ ɤɨʁɢʁɟ ɨɫɬɚɨɧɚɩɨɥɢɰɚɦɚ. ɉɪɢɦɟɧɢɫɜɨʁɫɬɜɨ ɦɧɨɠɟʃɚ ɪɚɡɥɢɤɟɛɪɨʁɟɦ __________________________________________________________ Ɉɞɝɨɜɨɪ: _________________________________________________ 6. ɍ Ɇɚɪɤɨɜɨʁɲɤɨɥɢ ɢɦɚ 3 ɨɞɟʂɟʃɚ. Ɂɚɫɜɚɤɨ ɨɞɟʂɟʃɟɩɨɪɭɱɟɧɨʁɟɩɨ 5 ɤɭɬɢʁɚ ɤɪɟɞɚ. Ʉɨɥɢɤɨ ɤɭɬɢʁɚ ɤɪɟɞɚʁɟɩɨɪɭɱɟɧɨ? __________________________________________________________ Ɉɞɝɨɜɨɪ: ____________________________________________________________ 7. ɇɚ ɲɤɨɥɫɤɨɦ ɮɭɞɛɚɥɫɤɨɦ ɬɭɪɧɢɪɭɭɱɟɫɬɜɭʁɟ 6 ɬɢɦɨɜɚ.ɍɫɜɚɤɨɦ ɬɢɦɭ ɢɦɚ 15 ɢɝɪɚɱɚ. Ʉɨɥɢɤɨ ɭɱɟɧɢɤɚ ɭɱɟɫɬɜɭʁɟ ɧɚ ɬɭɪɧɢɪɭ? ___________________________ Ɉɞɝɨɜɨɪ: ________________________________________

19


Ⱦȿȴȿȵȿ ɋȺ ɈɋɌȺɌɄɈɆ Ʉʂɭɱɧɟɪɟɱɢ ɞɟʂɟʃɟ ɫɚɨɫɬɚɬɤɨɦ, ɤɨɥɢɱɧɢɤ ɛɪɨʁɟɜɚ, ɞɟʂɟɧɢɤ, ɞɟɥɢɥɚɰ

1. Ⱥɧɚ ɢɦɚ ɤɭɬɢʁɟ ɭ ɤɨʁɟ ɦɨɠɟɞɚ ɫɬɚɜɢ ɩɨ 6ʁɚʁɚ ɉɨɝɥɟɞɚʁɫɥɢɤɭ ɢ ɨɞɝɨɜɨɪɢ ƔɄɨɥɢɤɨʁɟ Ⱥɧɚ ɢɦɚɥɚʁɚʁɚ" Ɉɞɝɨɜɨɪ __________________________________ ƔɄɨɥɢɤɨʁɚʁɚ ʁɟɫɬɚɥɨ ɭ 3 ɤɭɬɢʁɟ" Ɉɞɝɨɜɨɪ __________________________________ ƔɄɨɥɢɤɨʁɚʁɚ ʁɟɛɢɥɨɜɢɲɚɤ" Ɉɞɝɨɜɨɪ __________________________________

L

Ɂɚɩɢɫɭʁɟɦɨ 20  6 = 3 (ɨɫɬɚɬɚɤ 2) ɑɢɬɚɦɨ 20ɩɨɞɟʂɟɧɨɫɚ 6ʁɟɫɬɟ 3 ɢ ɨɫɬɚɬɚɤ 2. ɉɪɨɜɟɪɚɜɚɦɨ 6 · 3 + 2 = 20

TA

ɉɪɢ ɞɟʂɟʃɭɧɟɤɢɯɛɪɨʁɟɜɚ ɦɨɠɟɞɚɫɟʁɚɜɢ ɨɫɬɚɬɚɤ. Ɍɚɤɜɨɞɟʂɟʃɟ ɡɨɜɟɦɨ ɞɟʂɟʃɟɫɚ ɨɫɬɚɬɤɨɦ.

23  5 = 4 (ɨɫɬɚɬɚɤ __)

__  __ = __ (ɨɫɬɚɬɚɤ __)

Ɣ

__  __ = __ (ɨɫɬɚɬɚɤ __)

U KA

3. ɉɨɩɭɧɢɬɚɛɟɥɭ ɤɚɤɨʁɟ ɡɚɩɨɱɟɬɨ. Ⱦɟʂɟʃɟ Ʉɨɥɢɱɧɢɤ Ɉɫɬɚɬɚɤ ɉɪɨɜɟɪɚ

-P

O

R

2. ɉɪɟɦɚɞɚɬɨɦ ɰɪɬɟɠɭ, ɧɚɩɢɲɢʁɟɞɧɚɤɨɫɬ

32  5 44  8 19  2 6 2 6 · 5 + 2 = 32 __· __+ __ = __ ____________

__  __ = __ (ɨɫɬɚɬɚɤ __)

37  7

____________

76  9

____________

ɍɫɜɚɤɨɦɩɪɢɦɟɪɭ ɭɩɨɪɟɞɢ ɭɦɚʃɢɥɚɰɢ ɨɫɬɚɬɚɤ. ɒɬɚ ɭɨɱɚɜɚɲ"

ED

Ɉɫɬɚɬɚɤ ɩɪɢ ɞɟʂɟʃɭʁɟ ɭɜɟɤ ɦɚʃɢ ɨɞ ɞɟɥɢɨɰɚ.

4. ɉɪɟɰɪɬɚʁɛɪɨʁɟɜɟ ɤɨʁɢ ɧɟ ɦɨɝɭɛɢɬɢ ɨɫɬɚɰɢ ɩɪɢ ɞɟʂɟʃɭ Ɣ ɫɚ 2 Ɣ ɫɚ 3 Ɣ ɫɚ 4 Ɣ ɫɚ 5 Ɣ ɫɚ

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Ɣ ɫɚ Ɣ ɫɚ Ɣ ɫɚ Ɣ ɫɚ

7 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 8 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 9 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Ⱥɤɨ ʁɟ ɨɫɬɚɬɚɤ ɧɭɥɚ, ɞɟʂɟɧɢɤʁɟɞɟʂɢɜɞɟɥɢɨɰɟɦ

5. ɂɡɪɚɱɭɧɚʁɤɨɥɢɱɧɢɤɢ ɨɫɬɚɬɚɤ,ɚ ɡɚɬɢɦ ɩɪɨɜɟɪɢ ɬɚɱɧɨɫɬ ɞɟʂɟʃɚ. ɚ) 275  10 = __ (ɨɫɬɚɬɚɤ __)

ɉɪɨɜɟɪɚ __________

ɛ) 631  10 = __ (ɨɫɬɚɬɚɤ __)

ɉɪɨɜɟɪɚ __________

ɜ) 946  10 = __ (ɨɫɬɚɬɚɤ __) ɉɪɨɜɟɪɚ __________

20

6. Ɏɢɥɢɩʁɟ ɡɚɦɢɫɥɢɨʁɟɞɚɧɛɪɨʁ Ʉɚɞɚ ɝɚʁɟɩɨɞɟɥɢɨ ɫɚ 10, ɞɨɛɢɨ ʁɟ ɤɨɥɢɱɧɢɤ35 ɢ ɨɫɬɚɬɚɤ 3. Ʉɨʁɢɛɪɨʁʁɟ Ɏɢɥɢɩ ɡɚɦɢɫɥɢɨ" Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞ ɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ

ɚ) 350 ɛ) 355 ɜ) 353 ɝ) 453 ɞ) 335


Ⱦȿȴȿȵȿ ɋȺ ɈɋɌȺɌɄɈɆ Ʉʂɭɱɧɟɪɟɱɢ: ɞɟʂɟʃɟ ɫɚɨɫɬɚɬɤɨɦ, ɤɨɥɢɱɧɢɤ ɛɪɨʁɟɜɚ, ɞɟʂɟɧɢɤ, ɞɟɥɢɥɚɰ

1. ɉɨɩɭɧɢɬɚɛɟɥɭ. 49 : 2

68 : 5

__ · __ + __ = __

76 : 7

___________ ___________

___________

TA

2. ȳɚɧɤɨ ɢɦɚ 235 kg ɦɚɥɢɧɚ. Ɉɧɠɟɥɢ ɫɜɟ ɦɚɥɢɧɟɞɚɫɩɚɤɭʁɟ ɭ ɝɚʁɛɟ ɭ ɤɨʁɟ ɦɨɠɟ ɞɚɫɬɚɧɟ 10 kg ɨɜɨɝɜɨʄɚ. Ʉɨɥɢɤɨ ɝɚʁɛɢʄɟɛɢɬɢ ɧɚɩɭʃɟɧɨ? Ʉɨɥɢɤɨ ɤɢɥɨɝɪɚɦɚ ɦɚɥɢɧɚ ʄɟ ɨɫɬɚɬɢɜɢɲɚɤ"

90 : 8

L

Ⱦɟʂɟʃɟ 75 : 9 Ʉɨɥɢɱɧɢɤ Ɉɫɬɚɬɚɤ 3 ɉɪɨɜɟɪɚ __ · __ + __ = __

____________________________

R

Ɉɞɝɨɜɨɪ: _______________________________________________

3. ɑɟɬɢɪɢ ɞɪɭɝɚ ɠɟɥɟɞɚɩɨɞɟɥɟ 83 ɤɥɢɤɟɪɚ, ɬɚɤɨ ɞɚɫɜɚɤɢɞɨɛɢʁɟ ʁɟɞɧɚɤ ɛɪɨʁ. Ʉɨɥɢɤɨ ʄɟɤɥɢɤɟɪɚɞɨɛɢɬɢ ɫɜɚɤɢ ɞɟɱɚɤ?Ʉɨɥɢɤɨ ɤɥɢɤɟɪɚ ʄɟ ɨɫɬɚɬɢɧɟɩɨɞɟʂɟɧɨ"

O

____________________________

-P

Ɉɞɝɨɜɨɪ: _______________________________________________

U KA

4. ɋɚʃɚ, ɂɜɚɧɚ, Ⱦɭʃɚ ɢɆɢɥɢɰɚ ɠɟɥɟɞɚ ɤɭɩɟ ɥɨɩɬɭ. Ⱥɤɨɫɜɚɤɚ ɨɞʃɢɯɞɚɩɨ 100ɞɢɧɚɪɚ, ɧɟɞɨɫɬɚʁɚʄɟ ɢɦ ʁɨɲ89ɞɢɧɚɪɚ. Ʉɨɥɢɤɚʁɟɰɟɧɚ ɥɨɩɬɟ ɤɨʁɭ ɠɟɥɟɞɚ ɤɭɩɟ" ɉɪɨɰɟɧɢɰɟɧɭ ɥɨɩɬɟ, ɚ ɡɚɬɢɦ ɪɚɱɭɧɚʃɟɦ ɭɬɜɪɞɢ ɬɚɱɧɨɫɬ ɩɪɨɰɟɧɟ Ɉɛɨʁɛɚɥɨɧ ɫɚ ɬɚɱɧɢɦ ɨɞɝɨɜɨɪɨɦ

ED

_________________________________________

5. ɂɡ ɱɟɬɢɪɢ ɤɨɪɩɟ ɩɚɤɭʁɭɫɟʁɚʁɚ ɭ ɤɭɬɢʁɟ. ɍɫɜɚɤɭ ɤɭɬɢʁɭ ɫɬɚɜʂɚ ɫɟɩɨ 10 ʁɚʁɚ. Ʉɨɪɢɫɬɢ ɞɚɬɟɩɨɞɚɬɤɟ ɢɩɨɩɭɧɢɬɚɛɟɥɭ. 1. ɤɨɪɩɚ

Ȼɪɨʁ ʁɚʁɚɭ ɤɨɪɩɢ Ȼɪɨʁɧɚɩɭʃɟɧɢɯ ɤɭɬɢʁɚ Ȼɪɨʁɩɪɟɨɫɬɚɥɢɯ ʁɚʁɚ

2. ɤɨɪɩɚ

350

0

3. ɤɨɪɩɚ

4. ɤɨɪɩɚ

317 28

43

3

8

6. Ɉɞɪɟɞɢ ɞɟʂɟɧɢɤ, ɚɤɨʁɟ: ɚ) ɞɟɥɢɥɚɰ10, ɤɨɥɢɱɧɢɤ 78 ɢɨɫɬɚɬɚɤ 8;

ɛ) ɞɟɥɢɥɚɰ10, ɤɨɥɢɱɧɢɤ55 ɢ ɨɫɬɚɬɚɤ 3.

______________________________ Ⱦɟʂɟɧɢɤ ʁɟ ___.

______________________________ Ⱦɟʂɟɧɢɤ ʁɟ ___.

21


ȾȿȴȿȵȿȾȿɋȿɌɂɐȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ Ʉʂɭɱɧɟɪɟɱɢ: ɞɟʂɟʃɟ ɞɨ0, ɞɟʂɟʃɟ ɞɟɫɟɬɢɰɚʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

ƒ ȻɚɤɚɆɢɥɢɰɚ ɬɪɟɛɚ 150 ɤɨɥɚɱɚɞɚ ɪɚɫɩɨɪɟɞɢ ɭ 3 ɤɭɬɢʁɟ ɫɚʁɟɞɧɚɤɢɦ ɛɪɨʁɟɦ ɤɨɥɚɱɚ. Ʉɨɥɢɤɨ ɤɨɥɚɱɚ ʄɟɛɢɬɢ ɭʁɟɞɧɨʁɤɭɬɢʁɢ" Ʉɚɤɨʁɟ 15 : 3 = 5, ɬɨʁɟ ɢ 150 : 3 = 50

ĺ

3 3

= =

5Ⱦ 50

L

: :

TA

15Ⱦ 150

1. ɇɚɫɬɚɜɢɞɚ ɪɚɱɭɧɚɲɤɚɤɨʁɟ ɡɚɩɨɱɟɬɨ:

t 120 : 4 = 30; t 210 : 3 = 70; t 360 : 6 =__; t 42 : 7 = __; t 450 : 5 = __; t 640 : 8 = __;

R

t 630 : 9 = __; t 180 : 2 = __; t 300 : 6 = __; t 240 : 3 = __; t 280 : 4 = __.

2. Ɉɞɪɟɞɢ ɛɪɨʁɤɨʁɢʁɟ:

ɜ) 4ɩɭɬɚ ɦɚʃɢɨɞ 360; ___________

ɛ) 7 ɩɭɬɚ ɦɚʃɢɨɞ 210; ___________

ɝ) 8ɩɭɬɚ ɦɚʃɢɨɞ 560; ___________

-P

ɚ) 5ɩɭɬɚ ɦɚʃɢɨɞ 150; ___________

Ɋɚɱɭɧɡɚ ɩɟɬ ɫɥɚɞɨɥɟɞɚ ɩɨ ɢɫɬɨʁɰɟɧɢɢɡɧɨɫɢ 200 ɞɢɧɚɪɚ. Ʉɨɥɢɤɚʁɟ ɰɟɧɚ ʁɟɞɧɨɝɫɥɚɞɨɥɟɞɚ?

U KA

3.

O

t 490 : 7 =__;

_________________________________

Ɉɞɝɨɜɨɪ: __________________________________________________ 4. Ɋɚɱɭɧɡɚ ɬɪɢ ɫɨɤɚɩɨ ɢɫɬɨʁɰɟɧɢɢɡɧɨɫɢ150 ɞɢɧɚɪɚ. Ʉɨɥɢɤɚ ʁɟɰɟɧɚ ʁɟɞɧɨɝɫɨɤɚ? _________________________________

ED

Ɉɞɝɨɜɨɪ: __________________________________________________ 5. Ɇɢʄɚ, Ⱦɭɲɚɧɢ ȳɨɰɚ ɫɭɩɪɨɱɢɬɚɥɢ ɞɨɦɚʄɭɥɟɤɬɢɪɭ ɤɨʁɚ ɢɦɚ 240 ɫɬɪɚɧɚ.Ɇɢʄɚ ʁɟ ɬɭ ɤʃɢɝɭɩɪɨɱɢɬɚɨ ɡɚ 8ɞɚɧɚ, Ⱦɭɲɚɧɡɚ 4 ɞɚɧɚ, ɚ ȳɨɰɚ ɡɚ 3ɞɚɧɚ. ɋɜɚɤɨɝɞɚɧɚɩɪɨɱɢɬɚɥɢ ɫɭʁɟɞɧɚɤɛɪɨʁɫɬɪɚɧɚ. Ʉɨɥɢɤɢɛɪɨʁɫɬɪɚɧɚ ʁɟ ɞɧɟɜɧɨ ɱɢɬɚɨ ɫɜɚɤɢ ɞɟɱɚɤ" Ɇɢʄɚ: __________________ Ⱦɭɲɚɧ _________________ ȳɨɰɚ: __________________ Ɉɞɝɨɜɨɪ: __________________________________________________________________ 6. ɂɡɪɚɱɭɧɚʁɫɥɟɞɟʄɟ ɤɨɥɢɱɧɢɤɟɧɚ ɧɚɱɢɧɤɨʁɢɬɢɧɚʁɜɢɲɟ ɨɞɝɨɜɚɪɚ. Ɣ 120 : 4;

Ɣ 270 : 3;

Ɣ 350 : 5;

Ɣ 420 : 6;

Ɣ 160 : 2;

Ɣ 490 : 7;

Ɣ 480 : 8;

Ɣ 300 : 5;

Ɣ 810 : 9;

Ɣ 140 : 2;

Ɣ 450 : 5;

Ɣ 630 : 9.

22


ȾȿȴȿȵȿȾȿɋȿɌɂɐȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ Ʉʂɭɱɧɟɪɟɱɢ: ɞɟʂɟʃɟ ɞɨ0, ɞɟʂɟʃɟ ɞɟɫɟɬɢɰɚʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

2. ɉɨɩɭɧɢɬɚɛɟɥɟ. 3

120 240 150 270

: 420

6

: 280

300 240 540 480

3. Ɉɞɪɟɞɢ ɩɨɥɨɜɢɧɭɞɚɬɢɯɛɪɨʁɟɜɚ:

350 560 630 210

7

: 400

8

TA

160 200 120 180

: 300

R

2

O

: 140

L

1. Ɉɞɪɟɞɢ ɞɚɬɟ ɤɨɥɢɱɧɢɤɟ.

560 320 160 640

: 540

9

720 360 810 270

4. ɋɜɚɤɢɞɚɬɢɛɪɨʁɭɦɚʃɢ 4ɩɭɬɚ:.

120 __________;

400 __________;

140 __________; 200 __________;

360 __________;

600 __________;

240 __________;

280 __________;

800 __________.

400 __________;

320 __________.

U KA

-P

120 __________;

5. Ɋɚɱɭɧɡɚ 3ɫɜɟɫɤɟ ɢɡɧɨɫɢ 180 ɞɢɧɚɪɚ. Ʉɨɥɢɤɢ ʄɟɛɢɬɢ ɪɚɱɭɧɡɚ 5 ɬɚɤɜɢɯ ɫɜɟɡɚɤɚ? ______________________________

6. 5 kg ʁɚɛɭɤɚ ɤɨɲɬɚ 200 ɞɢɧɚɪɚ. Ʉɨɥɢɤɢɛɢɛɢɨɪɚɱɭɧɡɚ 7 kg ʁɚɛɭɤɚ ɩɨ ɢɫɬɨʁɰɟɧɢ? Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ

__________________________________

Ɉɞɝɨɜɨɪ: _________________________ _________________________________

ED

ɚ) 180ɞɢɧ ɛ) 280 ɞɢɧ ɜ) 300ɞɢɧ ɝ) 320ɞɢɧ

7. ɍ ɦɚɝɚɰɢɧɭʁɟɞɧɟ ɮɚɛɪɢɤɟ ɢɦɚ 540ɩɥɚɫɬɢɱɧɢɯ ɢɝɪɚɱɚɤɚ ɢ 9ɩɭɬɚ ɦɚʃɟ ɞɪɜɟɧɢɯɢɝɪɚɱɚɤɚ. Ʉɨɥɢɤɨ ɭɤɭɩɧɨ ɨɜɢɯ ɢɝɪɚɱɚɤɚ ɢɦɚ ɭ ɦɚɝɚɰɢɧɭ?

ɉɨɞɚɬɤɟ ɢɡ ɬɟɤɫɬɚ ɭɧɟɫɢ ɭɲɟɦɭ ɡɚɞɚɬɤɚ.

_______________________________________ Ɉɞɝɨɜɨɪ: ________________________________ 8. ɌɟɬɤɚɆɢɪɚɩɪɚɜɢɧɚʁɛɨʂɟ ɫɟɧɞɜɢɱɟ ɭ ɝɪɚɞɭ. ɋɜɚɤɢʃɟɧ ɫɟɧɞɜɢɱɢɦɚɩɨ 2 ɤɪɢɲɤɟ ɯɥɟɛɚ. Ɉɧɚ ɤɭɩɭʁɟ ɢɫɟɱɟɧɯɥɟɛ. ȳɟɞɧɨ ɩɚɤɨɜɚʃɟ ɯɥɟɛɚ ɢɦɚ 20 ɤɪɢɲɤɢ. Ʉɨɥɢɤɨʁɟ ɦɨɝɥɚɞɚ ɧɚɩɪɚɜɢ ɫɟɧɞɜɢɱɚ, ɚɤɨ ʁɟ ɭɩɨɬɪɟɛɢɥɚ ɩɟɬ ɢ ɩɨɩɚɤɨɜɚʃɚ ɯɥɟɛɚ" __________________________________________________ Ɉɞɝɨɜɨɪ: __________________________________________

23


Ⱦȿȴȿȵȿ ɁȻɂɊȺ ɂ ɊȺɁɅɂɄȿ ȻɊɈȳȿɆ Ʉʂɭɱɧɟɪɟɱɢ ɫɜɨʁɫɬɜɚ ɞɟʂɟʃɚ, ɞɟʂɟʃɟ ɡɛɢɪɚɛɪɨʁɟɦ, ɞɟʂɟʃɟ ɪɚɡɥɢɤɟɛɪɨʁɟɦ

Ž ɍ ɤɭɬɢʁɢɫɟɧɚɥɚɡɢ 80ɰɪɜɟɧɢɯɥɢɡɚɥɢɰɚ ɢ40 ɲɚɪɟɧɢɯ. Ɍɪɝɨɜɚɰɬɪɟɛɚɞɚ ɢɯ ɪɚɫɩɨɞɟɥɢɭ 4 ɦɚʃɟ ɤɭɬɢʁɟ ɬɚɤɨɞɚ ɫɟ ɭɫɜɚɤɨʁ ɧɚɥɚɡɢ ʁɟɞɧɚɤ ɛɪɨʁ Ʉɨɥɢɤɨ ʄɟɥɢɡɚɥɢɰɚ ɛɢɬɢ ɭʁɟɞɧɨʁ ɦɚʃɨʁɤɭɬɢʁɢ? ɉɨɞɟɥɚɫɟɦɨɠɟ ɢɡɜɪɲɢɬɢ ɧɚ ɞɜɚɧɚɱɢɧɚ 1. ɧɚɱɢɧ (80 + 40  4 = 120  4 = 30 ɉɪɜɨ ɢɡɪɚɱɭɧɚɦɨ ɡɛɢɪɛɪɨʁɟɜɚ, ɚ ɡɚɬɢɦ ɞɨɛɢʁɟɧɢ ɡɛɢɪ ɩɨɞɟɥɢɦɨɞɚɬɢɦ ɛɪɨʁɟɦ.

L

2. ɧɚɱɢɧ (80 + 40  4 = (80  4) + (40  4) = 20 + 10 = 30 ɋɜɚɤɢɫɚɛɢɪɚɤ ɩɨɞɟɥɢɦɨɞɚɬɢɦɛɪɨʁɟɦ,ɩɚɞɨɛɢʁɟɧɟ ɤɨɥɢɱɧɢɤɟɫɚɛɟɪɟɦɨ.

TA

y Ɋɚɱɭɧɚʁɭʄɢ ɧɚ ɨɛɚɧɚɱɢɧɚ, ɞɨɛɢɥɢɫɦɨ ɢɫɬɟ ɪɟɡɭɥɬɚɬɟ. ɍʁɟɞɧɨʁɦɚʃɨʁɤɭɬɢʁɢʄɟɛɢɬɢ 30 ɥɢɡɚɥɢɰɚ Ɂɚɬɨ ɦɨɠɟɦɨ ɡɚɩɢɫɚɬɢɞɚʁɟ (80 + 40 4 = (80  4) + (40  4) = 30

O

R

y Ɂɛɢɪɛɪɨʁɟɜɚ ɦɨɠɟɞɚ ɫɟɞɟɥɢ ɧɟɤɢɦ ɛɪɨʁɟɦ ɬɚɤɨɲɬɨ ɫɟɫɜɚɤɢ ɋɚɛɢɪɰɢɦɨɪɚʁɭ ɛɢɬɢ ɫɚɛɢɪɚɤɩɨɞɟɥɢ ɬɢɦ ɛɪɨʁɟɦ, ɩɚɫɟɞɨɛɢʁɟɧɢ ɤɨɥɢɱɧɢɰɢ ɫɚɛɟɪɭ. ɞɟʂɢɜɢ ɬɢɦɛɪɨʁɟɦ. y Ɉɜɨɜɚɠɧɨ ɫɜɨʁɫɬɜɨ ɫɟɧɚɡɢɜɚɞɟʂɟʃɟ ɡɛɢɪɚɛɪɨʁɟɦ. ɉɪɢɦɟʃɭʁɟɦɨ ɝɚ ɤɚɞɚɞɟɥɢɦɨɞɜɨɰɢɮɪɟɧɟ ɢ ɬɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɟ ʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ

ɚ) 360  3;

ɛ) 480  4;

-P

1. ɂɡɪɚɱɭɧɚʁɤɨɥɢɱɧɢɤɟɧɚ ɩɪɢɤɚɡɚɧɧɚɱɢɧ 448  7 = (420 + 28)  7 = (420  7) + (28  7) = 60 + 4 = 64 ɜ 385  7;

ɝ) 720  6;

ɞ) 600  4;

ɻ) 420  4.

U KA

Ž Ɇɢɥɚɧʁɟ ɢɦɚɨ 400ɞɢɧɚɪɚ. Ʉɭɩɢɨʁɟɩɢɰɭ ɡɚ 180ɞɢɧɚɪɚ, ɚ ɡɚɩɨɥɨɜɢɧɭɩɪɟɨɫɬɚɥɨɝɧɨɜɰɚ ɤɭɩɢɨʁɟɫɨɤ. ɂɡɪɚɱɭɧɚʁɰɟɧɭɫɨɤɚ ɤɨʁɢʁɟ Ɇɢɥɚɧɤɭɩɢɨ. ɐɟɧɭɫɨɤɚ ɦɨɠɟɦɨɞɚ ɢɡɪɚɱɭɧɚɦɨ ɧɚ ɞɜɚ ɧɚɱɢɧɚ (400 – 180  2 = 220  2 = 110 ɂɡɪɚɱɭɧɚɦɨ ɪɚɡɥɢɤɭɛɪɨʁɟɜɚ, ɚ ɡɚɬɢɦ ʁɟɩɨɞɟɥɢɦɨ ɞɚɬɢɦ ɛɪɨʁɟɦ.

2. ɧɚɱɢɧ

(400  2) – (180  2) = 200 – 90 = 110ɞɢɧɚɪɚ. ɍɦɚʃɟɧɢɤɢ ɭɦɚʃɢɥɚɰɩɨɞɟɥɢɦɨ ɞɚɬɢɦ ɛɪɨʁɟɦ, ɩɚ ɞɨɛɢʁɟɧɟ ɤɨɥɢɱɧɢɤɟ ɨɞɭɡɦɟɦɨ.

ED

1. ɧɚɱɢɧ

ɍɨɱɚɜɚɦɨɞɚɫɦɨ ɪɚɱɭɧɚʃɟɦ ɧɚ ɩɪɜɢ ɢ ɞɪɭɝɢ ɧɚɱɢɧɞɨɛɢɥɢɢɫɬɟ ɪɟɡɭɥɬɚɬɟ. ɐɟɧɚ ɫɨɤɚʁɟ 110ɞɢɧɚɪɚ. Ɂɚɬɨ ɦɨɠɟɦɨ ɡɚɩɢɫɚɬɢɞɚʁɟ (400 – 180 2 = (400  2) – (180  2) = 110. y Ɋɚɡɥɢɤɚɛɪɨʁɟɜɚ ɦɨɠɟɞɚ ɫɟɞɟɥɢ ɧɟɤɢɦɛɪɨʁɟɦ ɬɚɤɨɲɬɨ ɫɟ ɭɦɚʃɟɧɢɤ ɢ ɭɦɚʃɢɥɚɰɩɨɞɟɥɟ ɬɢɦ ɛɪɨʁɟɦ, ɩɚɫɟ ɞɨɛɢʁɟɧɢ ɍɦɚʃɟɧɢɤ ɢ ɭɦɚʃɢɥɚɰ ɦɨɪɚʁɭ ɛɢɬɢ ɞɟʂɢɜɢ ɬɢɦ ɛɪɨʁɟɦ. ɤɨɥɢɱɧɢɰɢ ɨɞɭɡɦɭ. y Ɉɜɨ ɜɚɠɧɨ ɫɜɨʁɫɬɜɨ ɫɟɧɚɡɢɜɚɞɟʂɟʃɟ ɪɚɡɥɢɤɟɛɪɨʁɟɦ. ɉɪɢɦɟʃɭʁɟɦɨ ɝɚ ɤɚɞɚɞɟɥɢɦɨɞɜɨɰɢɮɪɟɧɟ ɢ ɬɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɟʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ. 2. ɂɡɪɚɱɭɧɚʁɤɨɥɢɱɧɢɤɟɧɚɩɪɢɤɚɡɚɧɧɚɱɢɧ 570  3 = (600 – 30 3 = (600  3) – (30  3) = 200 – 10 = 190 ɚ) 760  4;

ɛ) 380  2;

ɜ) 470  5;

ɝ) 376  4;

24

ɞ) 720  6;

ɻ) 760  8.


Ⱦȿȴȿȵȿ ɁȻɂɊȺ ɂ ɊȺɁɅɂɄȿ ȻɊɈȳȿɆ Ʉʂɭɱɧɟɪɟɱɢ: ɫɜɨʁɫɬɜɚ ɞɟʂɟʃɚ, ɞɟʂɟʃɟ ɡɛɢɪɚɛɪɨʁɟɦ, ɞɟʂɟʃɟ ɪɚɡɥɢɤɟɛɪɨʁɟɦ

1. Ɉɞɟɪɟɞɢ ɤɨɥɢɱɧɢɤɟ ɤɨʁɢɫɟɤɪɢʁɭ ɢɡɚɞɟɥɨɜɚ ɫɥɚɝɚɥɢɰɟ. ɉɪɢɦɟɧɢɫɜɨʁɫɬɜɨ ɞɟʂɟʃɚ ɡɛɢɪɚɛɪɨʁɟɦ ɚ

ɚ:2

ɚ:4

ɚ:5

220 : 5 = 44 200 + 20

TA

L

140

220

O

R

380

ED

U KA

-P

460

2. ɉɪɢɦɟɧɢɫɜɨʁɫɬɜɨ ɞɟʂɟʃɚ ɪɚɡɥɢɤɟɛɪɨʁɟɦ ɢ ɢɡɪɚɱɭɧɚʁɤɨɥɢɱɧɢɤɟ. 190 : 2 = (200 – 10) : 2 = (___ : 2) – (__ : 2) = ___ – __ = ___ 380 : 5 = (400 – 20) : 5 = (___ : 5) – (__ : 5) = ___ – __ = ___ 343 : 7 = (350 – 7) : 7 = ___________________________________________ 112 : 2 = (120 – __) : 2 = __________________________________________ 171 : 3 = (180 – __) : 3 = ___________________________________________ 195 : 5 = (___ – __) : 5 = _________________________________________ 475 : 5 = (___ – __) : 5 = _________________________________________ 196 : 4 = (___ – __) : 4 = __________________________________________ 392 : 8 = (___ – __) : 8 = __________________________________________

25


ɆɈɀȿȵȿ ȾȼɈɐɂɎɊȿɇɈȽȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɜɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

ƒ Ⱦɚɥɢɡɧɚɲ" Ⱦɢɜʂɢ ɤɭɧɢʄɢ ɝɪɚɞɟʁɚɡɛɢɧɟ ɭ ɨɛɥɢɤɭɥɚɜɢɪɢɧɬɚ, ʁɟɪ ɠɢɜɟ ɭɜɟɨɦɚ ɜɟɥɢɤɢɦ ɡɚʁɟɞɧɢɰɚɦɚ. ȳɟɞɚɧɩɚɪ ɤɭɧɢʄɚ ɦɨɠɟɞɚ ɢɦɚɞɨ ɨɫɚɦ ɦɥɚɞɢɯ. Ⱥɤɨ ɭɫɜɚɤɨʁʁɚɡɛɢɧɢ ɠɢɜɢ 29 ɤɭɧɢʄɚ, ɤɨɥɢɤɨ ɤɭɧɢʄɚ ɢɦɚ ɭ 8 ɬɚɤɜɢɯʁɚɡɛɢɧɚ"

29 w 8 = (20 + 9) w 8 = (20 w 8) + (9 w 8) = ___ + __ = ___

29 w 8 = (30 – 1) w 8 = (30 w 8) – (1 w 8) = ___ – __ = ___

R

ɍ 8ʁɚɡɛɢɧɚ ɧɚɥɚɡɢɫɟ ___ ɤɭɧɢʄɚ.

TA

 Ɇɨɠɟɲɞɚ ɪɚɱɭɧɚɲɩɪɢɦɟɧɨɦɫɜɨʁɫɬɜɚ ɦɧɨɠɟʃɚ ɪɚɡɥɢɤɟ ɛɪɨʁɟɦ:

L

 Ɇɨɠɟɲɞɚ ɪɚɱɭɧɚɲɩɪɢɦɟɧɨɦ ɫɜɨʁɫɬɜɚ ɦɧɨɠɟʃɚ ɡɛɢɪɚɛɪɨʁɟɦ:

O

1. ɂɡɪɚɱɭɧɚʁɞɚɬɟɩɪɨɢɡɜɨɞɟ ɧɚ ɧɚɱɢɧɤɨʁɢɬɢ ɧɚʁɜɢɲɟ ɨɞɝɨɜɚɪɚ. ɚ) 64 w 3 = _________________________________________________________

-P

ɛ) 84 w 5 = _________________________________________________________ ɜ) 65 w 9 = _________________________________________________________ ɝ) 72 w 6 = _________________________________________________________

26 w 6 = ____

U KA

ɞ) 93 w 8 = _________________________________________________________

45 w 3 = ____

85 w 3 = ____

34 w 4 = ____

54 w 8 = ____

54 w 2 = ____

55 w 4 = ____

75 w 5 = ____

45 w 6 = ____

76 w 6 = ____

ɻ) 58 w 7 = _________________________________________________________ 3. ɂɡɪɚɱɭɧɚʁɭɫɦɟɧɨ ɢ ɭɩɢɲɢ ɞɨɛɢʁɟɧɟ ɩɪɨɢɡɜɨɞɟ.

ED

17 w 3 = ____

65 w 2 = ____

35 w 2 = ____

98 w 2 = ____

79 w 3 = ____

4. ȳɚɧɤɨ ɢɦɚ 64 ɡɟɰɚ.Ʉɨɥɢɤɨ ʁɟ ɭɤɭɩɧɨʃɢɯɨɜɢɯɧɨɝɭ" ______________________________________ Ɉɞɝɨɜɨɪ: ________________________________________________ 5. Ⱥɧɚʁɟ ɭ ɚɥɛɭɦ ɡɚɥɟɩɢɥɚ ʁɟɞɚɧ ɛɪɨʁɫɥɢɱɢɰɚ. Ⱦɚʁɟ ɡɚɥɟɩɢɥɚ 3 ɩɭɬɚɜɢɲɟ ɫɥɢɱɢɰɚ ɧɟɝɨɲɬɨ ʁɟɫɬɟ, ɢɦɚɥɚ ɛɢ ɡɚɥɟɩʂɟɧɨ 100 ɫɥɢɱɢɰɚ ɜɢɲɟ. Ʉɨɥɢɤɨʁɟ Ⱥɧɚɡɚɥɟɩɢɥɚ ɫɥɢɱɢɰɚ" Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ.

___________________________________________ ɚ) 20

ɛ) 30

ɜ) 40

ɝ) 50

26


ɆɈɀȿȵȿ ȾȼɈɐɂɎɊȿɇɈȽȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɜɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

1. Ɉɞɪɟɞɢɩɪɨɢɡɜɨɞɟ ɤɨʁɢɫɟ ɤɪɢʁɭ ɢɡɚɞɟɥɨɜɚ ɫɥɚɝɚɥɢɰɟ. ɚ

ɚ·3

ɚ·5

ɚ·7

ɚ·4

ɚ·9

75

L

83

TA

49

ɨɞɝɨɜɚɪɚʁɭʄɢ ɡɧɚɤ ( >, < ɢɥɢ=), ɬɚɤɨɞɚɞɨɛɢʁɟɧɢɡɚɩɢɫɢɛɭɞɭ ɬɚɱɧɢ

U KA

2. ɍɩɢɲɢ ɭ

-P

O

R

67

ɚ) 38 w 5

24 w 8;

ɛ) 26 w 9

39 w 6;

ɜ 98 w 4

59 w 7;

ɝ) 42 w 8

56 w 6.

3. ȼɟɫɧɢʁɟɞɨɡɜɨʂɟɧɨɞɚɞɧɟɜɧɨ ɝɥɟɞɚɰɪɬɚɧɟ ɮɢɥɦɨɜɟ 45 ɦɢɧɭɬɚ. Ⱥɤɨɫɜɚɤɢ ɞɚɧɝɥɟɞɚɰɪɬɚʄɟ ɨɧɨɥɢɤɨ ɤɨɥɢɤɨʁɨʁʁɟɞɨɡɜɨʂɟɧɨ, ɤɨɥɢɤɨʁɟ ɬɨ ɦɢɧɭɬɚ ɭ ɬɨɤɭʁɟɞɧɟ ɫɟɞɦɢɰɟ?

ED

_______________________________________________ Ɉɞɝɨɜɨɪ: _____________________________________________________ 4. ɉɪɚɬɢɫɬɪɟɥɢɰɟ ɢɭɩɪɚɡɧɚɩɨʂɚ ɧɚɩɢɲɢɞɨɛɢʁɟɧɟ ɩɪɨɢɡɜɨɞɟ. w2

w3

w4

w5

ɚ) 13

w7

ɛ) 17

5. ɂɡɦɟɻɭɞɜɟ ɩɭɡɥɟ ɬɪɟɛɚɞɚ ɫɬɚɜɢɲɬɪɟʄɭ, ɬɚɤɨɞɚʁɟɞɧɚɤɨɫɬɢɛɭɞɭ ɬɚɱɧɟ. Ʉɨʁɚ ɩɭɡɥɚ ɩɪɟɞɫɬɚɜʂɚ ɬɚɱɧɨ ɪɟɲɟʃɟ? Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɨɞ ɬɚɱɧɨɝ ɪɟɲɟʃɚ

28 w 5 =

35 w 4

135 =

120 =

140 =

145 =

ɚ)

ɛ)

ɜ 

ɝ)

27


ɆɈɀȿȵȿ ɌɊɈɐɂɎɊȿɇɈȽȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ Ʉʂɭɱɧɟɪɟɱɢ ɦɧɨɠɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

ƒ Ⱦɚɧɢɥɨ ȳɨɜɚɧ ɢ Ȼɨɪɚ ɠɟɥɟ ɡɚʁɟɞɧɨ ɞɚ ɤɭɩɟ ɞɪɭɝɚɪɢɰɢɩɨɤɥɨɧɡɚ ɪɨɻɟɧɞɚɧ Ⱥɤɨɫɜɚɤɢ ɨɞ ʃɢɯɞɚɩɨ 158ɞɢɧɚɪɚ ɦɨʄɢ ʄɟɞɚ ʁɨʁɤɭɩɟ ɩɥɢɲɚɧɨɝɥɚɜɚ. Ʉɨɥɢɤɚʁɟɰɟɧɚ ɬɟ ɢɝɪɚɱɤɟ" Ɋɚɱɭɧɚɲɨɜɚɤɨ 158 w 3 = (100 + 50 + 8) w 3 = (100 w 3) + (50 w 3) + (8 w 3) = 300 + 150 + 24 = 474

L

ɐɟɧɚ ɢɝɪɚɱɤɟ ʁɟ 474ɞɢɧɚɪɚ.

TA

ȳɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦɩɪɜɨ ɩɨɦɧɨɠɢɲɫɬɨɬɢɧɟɩɚɞɟɫɟɬɢɰɟ ɢɧɚ ɤɪɚʁɭʁɟɞɢɧɢɰɟ. Ⱦɨɛɢʁɟɧɟ ɩɪɨɢɡɜɨɞɟɫɚɛɟɪɟɲ

R

1. ɂɡɪɚɱɭɧɚʁɩɪɨɢɡɜɨɞɟɧɚ ɝɨɪɟɩɪɢɤɚɡɚɧɧɚɱɢɧ

t 243 w 2 = (200 + 40 + 3) w 2 = (___ w __) + (___ w __) + (__ w __) = ___ + ___ + ___ = ___

O

t 145 w 6 = (___ + ___ + __) w __ = (___ w __) + (___ w __) + (__ w __) = ___ + ___ + ___ = ___ t 138 w 7 = (___ + ___ + __) w __ = (___ w __) + (___ w __) + (__ w __) = ___ + ___ + ___ = ___

-P

t 185 w 4 = _________________________________________________________________ t 274 w 3 = _________________________________________________________________ 2. ɂɡɪɚɱɭɧɚʁɧɚ ɤɪɚʄɢɧɚɱɢɧ

U KA

Ɇɨɠɟɲɞɚɪɚɱɭɧɚɲɢ ɧɚ ɤɪɚʄɢ ɧɚɱɢɧ ɨɜɚɤɨ

135 w 3 = 300 + 90 + 15 = 405 100 + 30 + 5

100 · 3

30 · 3

5·3

t 137 w 6

t 245 w 2

t

t 142 w 7

t 187 w 5

314 w 3

4. ɍʁɟɞɧɭɰɜɟʄɚɪɭʁɟɞɨɧɟɬɨ 238ɥɚɥɚ ɢ ɬɪɢ ɩɭɬɚɜɢɲɟ ɤɚɪɚɧɮɢɥɚ Ʉɨɥɢɤɨʁɟɞɨɧɟɬɨ ɤɚɪɚɧɮɢɥɚ"

ED

3. ɋɚɲɚ ɢɆɢɥɚɧɱɢɬɚʁɭ ɢɫɬɟ ɤʃɢɝɟ. ɋɚɲɚʁɟɩɪɨɱɢɬɚɨ 185ɫɬɪɚɧɚ ɚ Ɇɢɥɚɧ ɞɜɚ ɩɭɬɚɜɢɲɟ ɨɞʃɟɝɚ. Ʉɨɥɢɤɨ ɫɬɪɚɧɚ ʁɟ ɩɪɨɱɢɬɚɨɆɢɥɚɧ"

t 149 w 4

_______________________

_______________________

Ɉɞɝɨɜɨɪ _____________________________

Ɉɞɝɨɜɨɪ ____________________________

_____________________________________

__________________________________

5. Ɉɞɪɟɞɢ ɛɪɨʁ ɤɨʁɢʁɟ ɚ) 5ɩɭɬɚɜɟʄɢɨɞ 109;

ɛ) 7ɩɭɬɚɜɟʄɢɨɞ 129;

ɜ) 8ɩɭɬɚɜɟʄɢ ɨɞ 118.

__________________

__________________

__________________

Ɍɨʁɟɛɪɨʁ ___.

Ɍɨʁɟ ɛɪɨʁ___.

Ɍɨʁɟɛɪɨʁ___.

28


ɆɈɀȿȵȿ ɌɊɈɐɂɎɊȿɇɈȽȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

1. Ⱥɤɨ ɬɚɱɧɨ ɪɟɲɢɲ ɭɤɪɲɬɟɧɢɰɭ, ɛɪɨʁɟɜɢ ɧɚɩɢɫɚɧɢ ɜɨɞɨɪɚɜɧɨ ɢ ɭɫɩɪɚɜɧɨ ʄɟ ɫɟɩɨɤɥɨɩɢɬɢ

ɍɫɩɪɚɜɧɨ Ļ X 125 w 5

^

Y

_

Z

[

\

]

`

a

^ 143 w 6 _ 233 w 2 Y 248 w 4 ` 71 w 7

L

X

ȼɨɞɨɪɚɜɧɨ ĺ Y 473 w 2

Z 128 w 2

[ 124 w 8

\ 293 w 2

] 34 w 8

R

X 228 w 3

TA

a 311 w 2

O

2. ɍʁɟɞɧɨɦ ɪɟɫɬɨɪɚɧɭ ɢɦɚ 218ɫɬɨɥɨɜɚ.Ʉɨɥɢɤɨ ɢɦɚɫɬɨɥɢɰɚ, ɚɤɨɫɟ ɡɚɫɜɚɤɢɦ ɫɬɨɥɨɦ ɧɚɥɚɡɟɩɨ 4ɫɬɨɥɢɰɟ" _______________________

-P

Ɉɞɝɨɜɨɪ: ____________________________________________________________

U KA

3. ɐɟɧɚ ɛɥɨɤɚ ɡɚɰɪɬɚʃɟʁɟ 146ɞɢɧɚɪɚ, ɚ ɨɧʁɟ 4ɩɭɬɚʁɟɮɬɢɧɢʁɢɨɞ ɬɟɦɩɟɪɚ. ɂɡɪɚɱɭɧɚʁɰɟɧɭ ɬɟɦɩɟɪɚ. ______________

Ɉɞɝɨɜɨɪ: _______________________________________

4. Ⱦɜɚ ɦɚɱɟɬɚ ɢɦɚʁɭʁɟɞɧɚɤɟ ɦɚɫɟ. ȵɢɯɨɜɚ ɦɚɫɚʁɟɞɧɚɤɚ ʁɟ ɦɚɫɢʁɟɞɧɨɝ ɦɥɚɞɭɧɰɚɥɚɜɚ Ⱥɤɨʁɟ ɦɚɫɚ ʁɟɞɧɨɝ ɦɚɱɟɬɚ 458 g, ɤɨɥɢɤɚʁɟ ɦɚɫɚ ɦɥɚɞɭɧɰɚ ɥɚɜɚ" _______________________________

ED

Ɉɞɝɨɜɨɪ: _________________________________________ 5. ɋɬɟɮɚɧɆɚɪɤɨ ɢ ɂɝɨɪɫɚɤɭɩʂɚʁɭ ɢɝɪɚɱɤɟ ɢɡ Ʉɢɧɞɟɪ ʁɚʁɚ.ɋɬɟɮɚɧʁɟɞɨɫɚɞɚ ɫɚɤɭɩɢɨ 163 ɢɝɪɚɱɤɟ, Ɇɚɪɤɨ 2ɩɭɬɚɜɢɲɟ ɨɞʃɟɝɚ, ɚ ɂɝɨɪ ɡɚ 165 ɦɚʃɟ ɨɞ Ɇɚɪɤɚ. Ʉɨɥɢɤɨ ɢɝɪɚɱɚɤɚʁɟɫɚɤɭɩɢɨɆɚɪɤɨ, ɚ ɤɨɥɢɤɨ ɂɝɨɪ" ___________________________________________ ___________________________________________ Ɉɞɝɨɜɨɪ: __________________________________________________________________ 6. ɇɟ ɦɟʃɚʁɭʄɢɪɟɞɨɫɥɟɞɞɚɬɢɯɰɢɮɚɪɚɫɬɚɜɢɢɡɦɟɻɭɧɟɤɢɯ ɨɞʃɢɯ ɡɧɚɤ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ ɦɧɨɠɟʃɚ, ɬɚɤɨɞɚɫɟ ɞɨɛɢʁɟ ɬɚɱɧɚʁɟɞɧɚɤɨɫɬ ɚ) 1 2 3 4 2 = 984 __________________

ɛ) 1 2 5 3 2 = 750 ___________________

29

ɜ) 3 1 4 1 3 = 942 ____________________


ȾȿȴȿȵȿɌɊɈɐɂɎɊȿɇɈȽȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ Ʉʂɭɱɧɟɪɟɱɢ: ɞɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

Ɣ Ɋɚɱɭɧɡɚ ɬɪɢɪɢɛɢɰɟ ɩɨ ɢɫɬɨʁɰɟɧɢɢɡɧɨɫɢ 435ɞɢɧɚɪɚ. Ʉɨɥɢɤɚʁɟ ɰɟɧɚ ʁɟɞɧɟ ɪɢɛɢɰɟ? Ɋɚɱɭɧɚɲɨɜɚɤɨ: 435 : 3 = (300 + 120 + 15) : 3 = 300 : 3 + 120 : 3 + 15 : 3 = 100 + 40 + 5 = 145 ɐɟɧɚ ʁɟɞɧɟ ɪɢɛɢɰɟ ʁɟ 145ɞɢɧɚɪɚ.

L

ɉɪɜɨ ɫɦɨɞɟʂɟɧɢɤɡɚɩɢɫɚɥɢ ɭ ɨɛɥɢɤɭ ɬɪɢ ɫɚɛɢɪɤɚ ɤɨʁɚɫɭɞɟʂɢɜɚɛɪɨʁɟɦ 3. Ɂɚɬɢɦɫɦɨ ɩɪɢɦɟɧɢɥɢ ɫɜɨʁɫɬɜɨɞɟʂɟʃɚ ɡɛɢɪɚɛɪɨʁɟɦ.

TA

1. ɇɚ ɢɫɬɢɧɚɱɢɧɢɡɪɚɱɭɧɚʁɫɥɟɞɟʄɟ ɤɨɥɢɱɧɢɤɟ:

t 381 : 3 = (300 + 60 + 21) : 3 = 300 : 3 + __ : 3 + 21 : 3 = ___ + ___ + __ = ____

R

t 458 : 2 = (400 + 40 + 8) : 2 = ___ : 2 + ___ : 2 + __ : 2 = ___ + ___ + __ = ____

O

t 835 : 5 = (500 + 300 + 35) : 5 = ___ : __ + ___ : __ + ___ : __ = ___ + ___ + __ = ____ t 738 : 3 = (600 + 120 + __) : 3 = ___ : __ + ___ : __ + ___ : __ = ___ + ___ + __ = ____

-P

t 552 : 4 = (___ + ___ + __) : __ = ___ : __ + ___ : __ + ___ : __ = ___ + ___ + __ = ____ t 658 : 7 = (630 + __) : 7 = ___ : __ + ___ : __ + ___ : __ = ___ + ___ + __ = ____

2. ɂɡɪɚɱɭɧɚʁ 371 : 7 184 : 4

U KA

t 792 : 9 = (720 + __) : 9 = ___ : __ + ___ : __ + ___ : __ = ___ + ___ + __ = ____

122 : 2

876 : 6

455 : 7

846 : 2

771 : 3

984 : 8

675 : 5

432 : 9

ED

3. ɉɪɢɦɟɧɢɫɜɨʁɫɬɜɨ ɞɟʂɟʃɚ ɪɚɡɥɢɤɟɛɪɨʁɟɦ ɢ ɢɡɪɚɱɭɧɚʁɤɨɥɢɱɧɢɤɟ: t 796 : 2 = (800 – 4) : 2 = 800 : 2 – 4 : 2 = 400 – 2 = 398 t 693 : 7 = (___– __) : 7 = ___ : __ – ___ : __ = ___ – __ = ___ t 490 : 5 = (___– __) : __ = ___ : __ – ___ : __ = ___ – __ = ___ t 485 : 5 = (500  15) : __ = ___ : __ – ___ : __ = ___ – __ = ___ t 780 : 4 = (___– __) : __ = ___ : __ – ___ : __ = ___ – __ = ___ t 760 : 8 = (___– __) : __ = ___ : __ – ___ : __ = ___ – __ = ___ 4. Ʉɨʁɢʁɟɛɪɨʁ ɚ) 5ɩɭɬɚ ɦɚʃɢ ɨɞ 765?

ɛ) 6ɩɭɬɚ ɦɚʃɢɨɞ 846?

30

ɜ) 7ɩɭɬɚ ɦɚʃɢɨɞ 847?


Ⱦȿȴȿȵȿ ɌɊɈɐɂɎɊȿɇɈȽȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ Ʉʂɭɱɧɟɪɟɱɢ: ɞɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

1. Ɉɞɪɟɞɢ ɤɨɥɢɱɧɢɤɟ ɩɪɢɦɟɧɨɦɞɟʂɟʃɚ ɡɛɢɪɚɛɪɨʁɟɦ. 528 : 2 = (400 + 120 + 8) : 2 = (___ : 2) + (___ : 2) + (__ : 2) = ___ + ___ + __ = ____ 584 : 4 = ______________________________________________________________ 785 : 5 = ______________________________________________________________ 584 : 8 = ______________________________________________________________

TA

2. Ɉɞɪɟɞɢ ɤɨɥɢɱɧɢɤɟɩɪɢɦɟɧɨɦɞɟʂɟʃɚ ɪɚɡɥɢɤɟɛɪɨʁɟɦ.

L

854 : 7 = ______________________________________________________________

594 : 3 = (___– __) : 3 = ___ : 3 – __ : 3 = ___ – __ = ____

980 : 5 = ______________________________________________________________

R

780 : 4 = ______________________________________________________________ 760 : 8 = _______________________________________________________________

O

693 : 7 = ______________________________________________________________

240 156 362 120 (2)

:6

:2

:7

:9

163

144

180

178

288

270

393

300

581

486

390

474

246

226

657

561

672

164

539

739

ED

609

:5

U KA

:3

-P

3. ɂɡɜɪɲɢɞɟʂɟʃɚ ɢ ɩɨɩɭɧɢɬɚɛɟɥɟ. Ⱥɤɨʁɟɞɟʂɟʃɟ ɫɚ ɨɫɬɚɬɤɨɦ, ɡɚɩɢɲɢ ɤɚɨɲɬɨʁɟ ɩɨɤɚɡɚɧɨɧɚɩɪɢɦɟɪɭ.

4. ɋɬɨɥɚɪʁɟɞɚɫɤɭ ɞɭɠɢɧɟ 6 m 15 cm ɢɫɟɤɚɨɧɚ 5ʁɟɞɧɚɤɢɯɞɟɥɨɜɚ. ɂɡɪɚɱɭɧɚʁɞɭɠɢɧɭ ʁɟɞɧɨɝ ɬɚɤɜɨɝɞɟɥɚ.

5. Ɇɚʁɚ ɢ ʃɟɧɟ ɬɪɢ ɞɪɭɝɚɪɢɰɟ ɠɟɥɟ ɞɚ ɩɨɞɟɥɟ 560ɞɢɧɚɪɚ.Ʉɨɥɢɤɨ ɞɢɧɚɪɚ ʄɟɞɨɛɢɬɢ ɫɜɚɤɚ ɨɞʃɢɯ?

__________________________

_________________

ȳɟɞɚɧɬɚɤɚɜɞɟɨ ɢɦɚ ɞɭɠɢɧɭ _____ cm.

ɋɜɚɤɚɞɟɜɨʁɱɢɰɚ ʄɟɞɨɛɢɬɢ ___ ɞɢɧɚɪɚ.

6. ɋɪɻɚɧɢ Ɂɨɪɚɧɫɟ ɬɚɤɦɢɱɟ ɭ ɬɪɱɚʃɭ. Ʉɚɞɚʁɟ ɋɪɻɚɧ ɩɪɟɬɪɱɚɨ 196 m, Ɂɨɪɚɧʁɟɛɢɨɧɚ 2 ɩɭɬɚ ɤɪɚʄɟɦ ɪɚɫɬɨʁɚʃɭ. Ʉɨɥɢɤɨ ɦɟɬɚɪɚʁɟ ɭ ɬɨɦ ɬɪɟɧɭɬɤɭɩɪɟɬɪɱɚɨ Ɂɨɪɚɧ? ____________________ Ɉɞɝɨɜɨɪ: ________________________________________________ 7. ɑɟɬɢɪɢ ɤɭɬɢʁɟ ɤɟɤɫɚ ɩɨ ɢɫɬɨʁɰɟɧɢ ɤɨɲɬɚʁɭ 592 ɞɢɧɚɪɚ. Ʉɨɥɢɤɨ ɤɨɲɬɚʁɭ 3 ɬɚɤɜɟ ɤɭɬɢʁɟ ɤɟɤɫɚ? Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨɢɫɩɪɟɞ ɬɚɱɧɨɝ ɪɟɲɟʃɚ

ɚ) 333 ɛ) 444 ɜ 424 ɝ) 344

31


ȞȿȴȿȾȿ É&#x152;É&#x160;É&#x2C6;É?É&#x201A;É&#x17D;É&#x160;ČżÉ&#x2021;É&#x2C6;ȽȝÉ&#x160;É&#x2C6;ȳȺ ȳȿȞÉ&#x2021;É&#x2C6;É?É&#x201A;É&#x17D;É&#x160;ČżÉ&#x2021;É&#x201A;É&#x2020; ČťÉ&#x160;É&#x2C6;ȳȿÉ&#x2020; É&#x201E;Ę&#x201A;ɭɹɧÉ&#x;ÉŞÉ&#x;ɹɢ É&#x17E;É&#x;Ę&#x201A;É&#x;Ę&#x192;É&#x; ɏɪɨɰɢɎɪÉ&#x;ɧɨÉ? É&#x203A;ÉŞÉ¨Ę É&#x161; Ę É&#x;É&#x17E;ɧɨɰɢɎɪÉ&#x;ɧɢɌ É&#x203A;ÉŞÉ¨Ę É&#x;ÉŚ

1. É&#x201A;ÉĄÉŞÉ&#x161;ɹɭɧÉ&#x161;Ę  528  2 = ____ + ___ + ___ = ____

492  3 = ____ + ___ + ___ = ____

584  4 = ____ + ___ + ___ = ____

732  6 = ____ + ___ + ___ = ____

785  5 = ____ + ___ + ___ = ____

976  8 = ____ + ___ + ___ = ____

854  7 = ____ + ___ + ___ = ____

708  4 = ____ + ___ + ___ = ____

____________________ É&#x2C6;É&#x17E;É?ɨÉ&#x153;ɨɪ _______________________________________

_________________

R

-P

É&#x2C6;É&#x17E;É?ɨÉ&#x153;ɨɪ _________________________

4. É?É&#x;ɧÉ&#x161;ɼɨɊɏÉ&#x; Ę É&#x; 977 É&#x17E;ɢɧÉ&#x161;ÉŞÉ&#x161;. É&#x201E;ɭɊɢĘ&#x201E;É&#x; Ę É&#x; 3É&#x17E;ÉŞÉ­É?É&#x161;, ÉŹÉ&#x161;ɤɨɲɏɨ Ę&#x201E;É&#x;ÉŤÉ&#x153;É&#x161;ɤɢ É&#x17E;É&#x161;ɏɢĘ É&#x;É&#x17E;ɧÉ&#x161;ɤ ɢɥɧɨɍÉ&#x17E;ɢɧÉ&#x161;ÉŞÉ&#x161;. Ć&#x201D; É&#x201E;ɨɼɢɤɨ Ę&#x201E;É&#x; É&#x17E;ɢɧÉ&#x161;ÉŞÉ&#x161; É&#x17E;É&#x161;ɏɢÉŤÉ&#x153;É&#x161;ɤɢ É&#x17E;É&#x;ÉąÉ&#x161;ɤ? _________________________ É&#x2C6;É&#x17E;É?ɨÉ&#x153;ɨɪ ___________________________________ Ć&#x201D; É&#x201E;ɨɼɢɤɨÉ&#x17E;ɢɧÉ&#x161;ÉŞÉ&#x161; Ę&#x201E;É&#x;Ę É¨É˛ɧÉ&#x;É&#x17E;ɨɍɏÉ&#x161;Ę É&#x161;ɏɢ" É&#x2C6;É&#x17E;É?ɨÉ&#x153;ɨɪ ___________________________________

O

3. É É&#x161;ÉŠÉ&#x;ÉŹ ɢɍɏɢɯ ɏɨɪɏɢɊɨɍɼÉ&#x161;ɍɏɢɹÉ&#x161;ÉŞ Ɋɨɏɪɨɲɢ 965 g ɨɪÉ&#x161;ÉŻÉ&#x161;. É&#x201E;ɨɼɢɤɨ ɨɪÉ&#x161;ÉŻÉ&#x161; Ɋɨɏɪɨɲɢ ÉĄÉ&#x161;Ę É&#x;É&#x17E;ɧɭ ÉŹÉ&#x161;ɤÉ&#x153;É­ ɏɨɪɏɭ?

TA

L

2. ČťÉ¨É É˘É&#x17E;É&#x161;ÉŞ É­ ɏɨɤɭĘ É&#x;É&#x17E;ɧÉ&#x; ÉŤÉ&#x;É&#x17E;ɌɢɰÉ&#x;ɊɪɨÉ&#x153;É&#x;É&#x17E;É&#x; 875 ɌɢɧɭɏÉ&#x161;ɹɢɏÉ&#x161;Ę É­Ę&#x201E;ɢ ɤĘ&#x192;ɢÉ?É&#x;. Ⱥɤɨ Ę É&#x;ÉŤÉ&#x153;É&#x161;ɤɢ É&#x17E;É&#x161;ɧɊɪɨÉ&#x153;É&#x;ɨ Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨÉ&#x153;ÉŞÉ&#x;ÉŚÉ&#x; É&#x17E;ɨɤ Ę É&#x; ɹɢɏÉ&#x161;ɨ, ɤɨɼɢɤɨĘ É&#x; ɏɨ ɌɢɧɭɏÉ&#x161; É­ ɏɨɤɭĘ É&#x;É&#x17E;ɧɨÉ?É&#x17E;É&#x161;ɧÉ&#x161;?

_________________________________

U KA

5. É&#x2021;É&#x161; ɥɢÉ&#x17E;É&#x161;Ę&#x192;É­Ę É&#x;É&#x17E;ɧÉ&#x; ɤɭĘ&#x201E;É&#x; ÉŞÉ&#x161;É&#x17E;ɢɼɨ Ę É&#x; 6 ÉŞÉ&#x161;É&#x17E;ɧɢɤÉ&#x161;. É?ɤɭɊɧɨÉŤÉ­ ÉŞÉ&#x161;É&#x17E;ɢɼɢ 912ÉąÉ&#x161;ɍɨÉ&#x153;É&#x161;. É&#x201E;ɨɼɢɤɨ ÉąÉ&#x161;ɍɨÉ&#x153;É&#x161;Ę É&#x; ÉŞÉ&#x161;É&#x17E;ɢɨÉŤÉ&#x153;É&#x161;ɤɢ ÉŞÉ&#x161;É&#x17E;ɧɢɤ É&#x161;ɤɨÉŤÉ­ÉŤÉ&#x153;ɢ ɢɌÉ&#x161;ɼɢ Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨ ÉŞÉ&#x161;É&#x17E;ɧɨ É&#x153;ÉŞÉ&#x;ÉŚÉ&#x;? ______________________

É&#x2C6;É&#x17E;É?ɨÉ&#x153;ɨɪ ___________________________________________________

ED

6. É? ÉŻÉĽÉ&#x161;É&#x17E;Ę&#x192;É&#x161;ɹɢĘ É&#x;É&#x17E;ɧɨÉ? ɤÉ&#x161;ɌɢɨɧÉ&#x161;ɧÉ&#x161;ÉĽÉ&#x161;ɥɢÉŤÉ&#x; 8 É¤É­ÉŹÉ˘Ę É&#x161; ɍɌɪɥɧɭɏÉ&#x; ɪɢÉ&#x203A;É&#x; É&#x2039;É&#x153;É&#x; É¤É­ÉŹÉ˘Ę É&#x; ɢɌÉ&#x161;Ę É­Ę É&#x;É&#x17E;ɧÉ&#x161;ɤÉ&#x; ÉŚÉ&#x161;ÉŤÉ&#x;. É?ɤɭɊɧÉ&#x161; ÉŚÉ&#x161;ÉŤÉ&#x161; É¤É­ÉŹÉ˘Ę É&#x161;Ę É&#x;960 kg. É&#x201E;ɨɼɢɤÉ&#x161;Ę É&#x; ÉŚÉ&#x161;ÉŤÉ&#x161;Ę É&#x;É&#x17E;ɧÉ&#x; É¤É­ÉŹÉ˘Ę É&#x; ÉŤÉ&#x161; ɪɢÉ&#x203A;ɨɌ" ______________________

É&#x2C6;É&#x17E;É?ɨÉ&#x153;ɨɪ __________________________________________ 8. É? ɤĘ&#x192;É˘É É&#x161;ɪɢ ÉŤÉ&#x;ɧÉ&#x161;ÉĽÉ&#x161;ɥɢ ɭɤɭɊɧɨ 375 ÉŤÉ&#x153;É&#x;ÉĄÉ&#x161;ɤÉ&#x161; ɧÉ&#x161; ɤÉ&#x153;É&#x161;É&#x17E;ÉŞÉ&#x161;ɏɢĘ&#x201E;É&#x; ɢ ÉĽÉ˘É§É˘Ę É&#x;. É&#x2039;É&#x153;É&#x161;ɤÉ&#x161;ÉŠÉ&#x;ÉŹÉ&#x161;ÉŤÉ&#x153;É&#x;ɍɤÉ&#x161; Ę É&#x; ɧÉ&#x161; ÉĽÉ˘É§É˘Ę É&#x;.É&#x201E;ɨɼɢɤɨ ɢɌÉ&#x161;ÉŤÉ&#x153;É&#x;ÉĄÉ&#x161;ɤÉ&#x161;ɧÉ&#x161; ɤÉ&#x153;É&#x161;É&#x17E;ÉŞÉ&#x161;ɏɢĘ&#x201E;É&#x;, É&#x161; ɤɨɼɢɤɨ ɧÉ&#x161; ÉĽÉ˘É§É˘Ę É&#x;? _______________________________

7. É&#x2039;ɨĘ&#x192;É&#x161;Ę É&#x;ÉŤÉ&#x161;ÉŤÉ&#x153;É¨Ę É¨ÉŚ É&#x203A;É&#x161;ɤɨɌ ɨɎÉ&#x161;ÉŞÉ&#x203A;É&#x161;ÉĽÉ&#x161; 128 Ę É&#x161;Ę É&#x161;. É&#x2018;É&#x;ÉŹÉ&#x153;ɪɏɢɧÉ&#x161; ɢɯĘ É&#x; É É­ÉŹÉ&#x;É&#x203A;É¨Ę É&#x; É&#x201E;ɨɼɢɤɨĘ É&#x;É&#x203A;ɢɼɨ ɠɭɏɢɯĘ É&#x161;Ę É&#x161;" ________________________

É&#x2C6;É&#x17E;É?ɨÉ&#x153;ɨɪ ______________________________ ______________________________________

É&#x2C6;É&#x17E;É?ɨÉ&#x153;ɨɪ _________________ _________________________________

É&#x201A;ɧɏÉ&#x;ɪɧÉ&#x;ÉŹ É&#x161;É&#x17E;ÉŞÉ&#x;ÉŤÉ&#x161;ɧÉ&#x161; É¤É¨Ę É¨Ę ÉŚÉ¨É É&#x;ɲ É&#x17E;É&#x161; ɊɪɨɧÉ&#x161;ÉťÉ&#x;ɲ ɍɼɢɹɧÉ&#x; ÉĄÉ&#x161;É&#x17E;É&#x161;ɏɤÉ&#x; https// dms.rs/kengur/zadaci/

32


 ɋȺȾȺɁɇȺɆɆɇɈȽɈȼɂɒȿ 



Ʉʂɭɱɧɟɪɟɱɢ:ɦɧɨɠɟʃɟɢɞɟʂɟʃɟɞɨ

   ƔɁɧɚɦɤɚɤɨɫɟɛɪɨʁɟɜɢɦɧɨɠɟɢɞɟɥɟɫɚ10ɢɫɚ100  

Ȼɪɨʁɫɟɦɧɨɠɢɫɚ10ɬɚɤɨɲɬɨɦɭɫɟɫɚ ɞɟɫɧɟɫɬɪɚɧɟɞɨɩɢɲɟʁɟɞɧɚɧɭɥɚ

Ȼɪɨʁɫɟɦɧɨɠɢɫɚ100ɬɚɤɨɲɬɨɦɭɫɟ ɫɚɞɟɫɧɟɫɬɪɚɧɟɞɨɩɢɲɭɞɜɟɧɭɥɟ:

3710 370

100 900

Ȼɪɨʁɫɟɞɟɥɢɫɚ10ɬɚɤɨɲɬɨɦɭɫɟɫɚ ɞɟɫɧɟɢɡɨɫɬɚɜɢʁɟɞɧɚɧɭɥɚ

Ȼɪɨʁɫɟɞɟɥɢɫɚ100ɬɚɤɨɲɬɨɦɭɫɟɫɚ ɞɟɫɧɟɫɬɪɚɧɟɢɡɨɫɬɚɜɟɞɜɟɧɭɥɟ:

540:10 54600:10 60

600:100 

  

L



TA





  

O



ɋɜɨʁɫɬɜɚɨɩɟɪɚɰɢʁɚɦɧɨɠɟʃɚɢɞɟʂɟʃɚɤɨɪɢɫɬɢɦɤɚɨɨɥɚɤɲɢɰɟɩɪɢɪɚɱɭɧɚʃɭ  ɑɢɧɢɨɰɢɦɚɡɚɦɟʃɭʁɟɦɨɦɟɫɬɚ

40w3 3w40 120  3w50w2  w50)w2 3w 50w2) 300

-P



R

Ɣɍɦɟɦɞɚɤɨɪɢɫɬɢɦɩɪɚɜɢɥɚɡɚɦɧɨɠɟʃɟɢɞɟʂɟʃɟ



44:7  420+28)7  420:7)+ 28:7) 60+4 64

 

57:3  60–30):3  600:3)– 303) 200–10 190

Ɇɧɨɠɢɦɪɚɡɥɢɤɭɛɪɨʁɟɦ Ⱦɟɥɢɦɡɛɢɪɛɪɨʁɟɦ ɫɚɛɢɪɰɢɦɨɪɚʁɭɛɢɬɢɞɟʂɢɜɢɬɢɦɛɪɨʁɟɦ) Ⱦɟɥɢɦɪɚɡɥɢɤɭɛɪɨʁɟɦ ɭɦɚʃɟɧɢɤɢɭɦɚʃɢɥɚɰɦɨɪɚʁɭɛɢɬɢ ɞɟʂɢɜɢɬɢɦɛɪɨʁɟɦ)

ED



U KA



150w3  100+50)w3  100w3)+ 50w3) 300+150 450  75w8  80í5)w8  80w8)í 5w8) 640í40 600



Ʉɚɞɚɢɦɚɦɬɪɢɱɢɧɢɨɰɚɡɞɪɭɠɭʁɟɦɞɜɚ ɱɢɧɢɨɰɚɢʃɢɯɨɜɩɪɨɢɡɜɨɞɦɧɨɠɢɦ ɬɪɟʄɢɦɱɢɧɢɨɰɟɦ Ɇɧɨɠɢɦɡɛɢɪɛɪɨʁɟɦ

 ƔɆɧɨɠɢɦɞɟɫɟɬɢɰɟʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ9w40 3605w90 4509w80 720 ƔȾɟɥɢɦɞɟɫɟɬɢɰɟʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ:120:4 0210:3 70360:6 60 ƔɆɧɨɠɢɦɞɜɨɰɢɮɪɟɧɢɛɪɨʁʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ: 29w8  20+9 w8  20w8)+ 9w8) 16072 232 ƔɆɧɨɠɢɦɬɪɨɰɢɮɪɟɧɢɛɪɨʁʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ: 158w3  100508 w3  100w3 + 50w3 + 8w3  30015024 474 ƔȾɟɥɢɦɫɚɨɫɬɚɬɤɨɦ:364:10 36ɢɨɫɬɚɬɚɤ4.ɉɪɨɜɟɪɚɜɚɦ:36w104 364 ƔȾɟɥɢɦɬɪɨɰɢɮɪɟɧɢɛɪɨʁʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ:

435:3  30012015 :3  300:)+ 120:)+ 15:3) 100405 145  

33


ɉɊɈȼȿɊȺȼȺɆɈ ɇȺɍɑȿɇɈ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɢ ɞɟʂɟʃɟ ɞɨ

1. ɂɡɪɚɱɭɧɚʁɫɥɟɞɟʄɟɩɪɨɢɡɜɨɞɟ: 47 w 3 = ____

164 w 4 = ____

328 w 3 = ____

74 w 5 = ____

63 w 8 = ____

123 w 8 = ____

115 w 7 = ____

63 w 7 = ____

89 w 6 = ____

388 w 2 = ____

108 w 9 = ____

98 w 4 = ____

54 w 7 = ____

142 w 6 = ____

187 w 5 = ____

L

86 w 2 = ____

TA

2. ɂɡɪɚɱɭɧɚʁɫɥɟɞɟʄɟ ɤɨɥɢɱɧɢɤɟ: 351 : 3 = ___

398 : 2 = ___________

426 : 3 = ___________

720 : 2 = ___

968 : 8 = ___

720 : 5 = ___________

448 : 7 = ___________

850 : 5 = ___

960 : 6 = ___

654 : 6 = ___________

336 : 8 = ___________

910 : 7 = ___

700 : 5 = ___

780 : 4 = ___________

558 : 9 = ___________

O

R

600 : 4 = ___

-P

3. ɇɟɜɟɧɢɧɚ ɤɭʄɚʁɟ ɨɞɫɩɨɪɬɫɤɟ ɯɚɥɟ ɭɞɚʂɟɧɚ245 ɦɟɬɚɪɚ.ɇɟɜɟɧɚ ɭ ɬɨʁɯɚɥɢ ɢɦɚ ɬɪɟɧɢɧɝɟ ɞɜɚɩɭɬɚɧɟɞɟʂɧɨ.Ʉɨɥɢɤɨ ɦɟɬɚɪɚɇɟɜɟɧɚ ɩɪɟɩɟɲɚɱɢ ɭ ɬɨɤɭ ʁɟɞɧɟ ɧɟɞɟʂɟ, ɨɞɥɚɡɟʄɢ ɧɚ ɬɪɟɧɢɧɝɟ ɢ ɜɪɚʄɚʁɭʄɢ ɫɟ ɤɭʄɢ? _________________ Ɉɞɝɨɜɨɪ: ___________________________________________

U KA

4. ɇɚ ʁɟɞɧɨɦ ɢɦɚʃɭɫɟ ɝɚʁɟ ɝɨɜɟɞɚ. ɍɤɭɩɧɨ ɢɦɚ 636ʃɢɯɨɜɢɯɧɨɝɭ. ɂɡɪɚɱɭɧɚʁɛɪɨʁ ɝɨɜɟɞɚ ɧɚ ɬɨɦ ɢɦɚʃɭ. __________________ Ɉɞɝɨɜɨɪ: __________________________________________ 5. ɋɚɪɚʁɟɥɭɛɟɧɢɰɭ ɦɚɫɟ 8 kg ɩɥɚɬɢɥɚ 360ɞɢɧɚɪɚ. Ɇɢɥɟɧɚɩɨ ɢɫɬɨʁɰɟɧɢ ɩɨ ɤɢɥɨɝɪɚɦɭ) ɤɭɩɢɥɚɥɭɛɟɧɢɰɭ ɦɚɫɟ 6 kg. Ʉɨɥɢɤɨ ʁɟɆɢɥɟɧɚ ɩɥɚɬɢɥɚ ɬɭ ɥɭɛɟɧɢɰɭ?

ED

__________________ Ɉɞɝɨɜɨɪ: __________________________________________ 6. ɍʁɟɞɧɨɦ ɪɟɫɬɨɪɚɧɭ ɢɦɚ 188ɫɬɨɥɢɰɚ.Ʉɨɥɢɤɨ ɢɦɚ ɫɬɨɥɨɜɚ, ɚɤɨ ɫɟ ɡɚɫɜɚɤɢɦ ɫɬɨɥɨɦ ɧɚɥɚɡɟɩɨ 4ɫɬɨɥɢɰɟ" __________________ Ɉɞɝɨɜɨɪ: __________________________________________ 7. ɑɟɬɢɪɢ ɞɪɭɝɚɪɢɰɟ ɤɭɩɭʁɭɞɪɭɝɭɩɨɤɥɨɧɡɚ ɪɨɻɟɧɞɚɧɋɜɚɤɚ ɨɞʃɢɯ ʄɟɞɚɬɢʁɟɞɧɚɤ ɢɡɧɨɫɞɢɧɚɪɚ. Ⱥɤɨɩɨɤɥɨɧ ɤɨɲɬɚ 900ɞɢɧɚɪɚ, ɞɚɥɢ ʄɟ ɛɢɬɢ ɞɨɜɨʂɧɨɞɚɫɜɚɤɚ ɨɞ ʃɢɯɞɚɩɨ 223ɞɢɧɚɪɚ? __________________ Ɉɞɝɨɜɨɪ: __________________________________________ 8. ȳɟɞɚɧɫɨɤ ɤɨɲɬɚ 124ɞɢɧɚɪɚ. Ⱦɜɟ ɢɫɬɟɛɨɦɛɨʃɟɪɟ ɤɨɲɬɚʁɭ ɤɚɨ 5 ɬɚɤɜɢɯɫɨɤɨɜɚ Ʉɨɥɢɤɢ ʄɟ ɛɢɬɢɪɚɱɭɧɚɤɨ ɤɭɩɢɲʁɟɞɧɭɛɨɦɛɨʃɟɪɭ ɢ ɬɪɢ ɫɨɤɚ? __________________ Ɉɞɝɨɜɨɪ: __________________________________________

34


ГЕОМЕТРИЈСКЕ ФИГУРЕ

L

ōřŜŌőōŎŗ ŖʼnŜŠőŅŎš

TA

ƁŻũƐŮżŬũŷűūŹźŻŮŶŮųűžżŬŴŷūũ

R

ŭũűŵŮŶżƐŮƁŮŴŮŵŮŶŻŮżŬŴũ

O

ŭũſŹŻũƁżŬŴŷūŮųŷŹűźŻŮƓűŬŮŷŵŮŻŹűƐźųűŸŹűŪŷŹ

U KA

-P

ŭũŸŹũūűƁŵŷŭŮŴŮżŬŴŷūũűŷŭƒűžźũźŻũūƑũƁ ŹũŰŴűƀűŻŮŽűŬżŹŮ ŷżŰũƐũŵŶŷŵŸŷŴŷůũƐżŸŹũūűž

ED

ŸŹũūŮųŷƐٟٟŮųżűŸũŹũŴŮŴŶŮŸŹũūŮ  ŭũſŹŻũƁŸũŹũŴŮŴŶŮűŶŷŹŵũŴŶŮŸŹũūŮ ųŷŹűźŻŮƓűŬŮŷŵŮŻŹűƐźųűŸŹűŪŷŹ

őŶŻŮŹŶŮŻũŭŹŮźũŶũųŷƐŷƐŵŷůŮƁŭũſŹŻũƁŬŮŷŵŮŻŹűƐźųŮ ŽűŬżŹŮųŷƐŮƓŮƁŸŹŷżƀũūũŻű. https:// geogebra.org/geometry ŌŮŷŬŮŪŹũ MHŸŹŷŬŹũŵŰũŵũŻŮŵũŻűųż. œŷŹűźŻűźŮŰũŶũźŻũūżűżƀŮƒŮŵũŻŮŵũŻűųŮżƁųŷŴũŵũ ŜŷūŷŵŸŹŷŬŹũŵżŵŷůŮƁŭũųŷŶźŻŹżűƁŮƁŬŮŷŵŮŻŹűƐźųŮŽűŬżŹŮŸŷŵŷƓżŵűƁũűũŴũŻũŰũ ųŷŶźŻŹżųſűƐŮųŷƐűźŮŶũŴũŰŮŶũ ŻŹũſűźũũŴũŻűŵũ.

őŰũŪŮŹűŪűŴŷųŷƐűũŴũŻźũ ŻŹũųŮźũũŴũŻűŵũűŸŹŷƀűŻũƐŸŷŵŷƓŰũũŴũŻ  ŭŮźŶŷŷŭ ŻŹũųŮźũũŴũŻűŵũ 


ɍȽȺɈ Ʉʂɭɱɧɟɪɟɱɢ: ɭɝɚɨ, ɰɪɬɚʃɟ ɭɝɥɚ, ɤɪɚɰɢ, ɬɚɱɤɚ, ɬɟɦɟ ɨɛɥɚɫɬ ɭɝɥɚ

a a Ʉɚɡɚʂɤɟɧɚ ɱɚɫɨɜɧɢɤɭɫɟ ɫɜɚɤɨɝ ɬɪɟɧɭɬɤɚɩɨɦɟɪɚʁɭ ɢ ɬɚɤɨ ɡɚɭɡɢɦɚʁɭ ɪɚɡɥɢɱɢɬɟ ɩɨɥɨɠɚʁɟ.

a

a

ɋɜɚɤɢɧɨɜɢɩɨɥɨɠɚʁ ɬɚɤɜɟɞɜɟ ɩɨɥɭɩɪɚɜɟ ɨɛɪɚɡɭʁɭ ɮɢɝɭɪɭ ɤɨʁɚ ɫɟ ɡɨɜɟ ɭɝɚɨ.

Ⱦɜɟ ɤɚɡɚʂɤɟɧɚ ɱɚɫɨɜɧɢɤɭ ɦɨɠɟɦɨɧɚɰɪɬɚɬɢ ɩɨɦɨʄɭ ɞɜɟ ɩɨɥɭɩɪɚɜɟ ɫɚ ɡɚʁɟɞɧɢɱɤɨɦ ɩɨɱɟɬɧɨɦ ɬɚɱɤɨɦ.

e

d

e

n

L

m

u

a

 c

TA

 Ɣ ɐɪɬɚʃɟ ɭɝɥɚ

Ɣ ȿɥɟɦɟɧɬɢɭɝɥɚɫɭ ɤɪɚɰɢ ɢ ɬɟɦɟ. a

R

ɂɡ ɬɚɱɤɟ Ǽ ɧɚɰɪɬɚɦɨ ɞɜɟ ɩɨɥɭɩɪɚɜɟ (Oa ɢ Ob) a

O

ɨɛɥɚɫɬ ɭɝɥɚ

b

Ʉɪɚɰɢɭɝɥɚ ɫɭɩɨɥɭɩɪɚɜɟ Oa ɢ Ob. Ɍɟɦɟ ɭɝɥɚʁɟ ɡɚʁɟɞɧɢɱɤɚ ɬɚɱɤɚ O.

-P

b

U KA

Ɣ ɍɝɚɨ ɨɛɟɥɟɠɚɜɚɦɨ ɡɧɚɤɨɦ , ɤɨʁɢɡɚɦɟʃɭʁɟ ɪɟɱɭɝɚɨ. Ɉɛɥɚɫɬ ɭɝɥɚ ɨɡɧɚɱɚɜɚɦɨɞɟɥɨɦ ɤɪɭɠɧɢɰɟ. Ɍɟɦɟ ɭɝɥɚ ɡɚɩɢɫɭʁɟɦɨɜɟɥɢɤɢɦɲɬɚɦɩɚɧɢɦɫɥɨɜɨɦ ɢ ɭɜɟɤ ɝɚɩɢɲɟɦɨ ɭɫɪɟɞɢɧɢ ɇɚ ɩɪɢɦɟɪ: mOn ɢɥɢ ȿɈȼ. m

̬

mOn (ɭɝɚɨ mOn)

ED

a

ɍɇɍɌɊȺɒȵȺ ɈȻɅȺɋɌ

c

BɈE ɭɝɚɨ BOE)

nOm (ɭɝɚɨ nOm)

n

ɋɉɈȴȺɒȵȺ ɈȻɅȺɋɌ

ȿɈȼ (ɭɝɚɨ EOB)

O

B

ɍɝɚɨ ʁɟ ɝɟɨɦɟɬɪɢʁɫɤɚ ɮɢɝɭɪɚ ɤɨʁɭɱɢɧɟ ɞɜɟ ɩɨɥɭɩɪɚɜɟ ɫɚ ɡɚʁɟɞɧɢɱɤɨɦɩɨɱɟɬɧɨɦ ɬɚɱɤɨɦ ɢ ɞɟɨ ɩɪɨɫɬɨɪɚ ɢɡɦɟɻɭ ɬɢɯ ɩɨɥɭɩɪɚɜɢɯ. ɉɨɥɭɩɪɚɜɟ, ɤɨʁɟ ɨɛɪɚɡɭʁɭ ɭɝɚɨ, ɞɟɥɟ ɪɚɜɚɧ ɧɚ ɞɜɟ ɨɛɥɚɫɬɢ: ɭɧɭɬɪɚɲʃɭ ɢɫɩɨʂɚɲʃɭ ɨɛɥɚɫɬ.ɇɚɰɪɬɟɠɭʁɟɭɧɭɬɪɚɲʃɚ ɨɛɥɚɫɬ ɨɛɨʁɟɧɚ ɡɟɥɟɧɨɦ ɛɨʁɨɦ ɢ ɨɧɚɩɪɢɩɚɞɚ aǰc.

ɍɨɱɚɜɚɦɨɞɚ ɬɚɱɤɚ ȿ ɩɪɢɩɚɞɚ aǰc, ʁɟɪ ɫɟɧɚɥɚɡɢ ɭʃɟɝɨɜɨʁɭɧɭɬɪɚɲʃɨʁɨɛɥɚɫɬɢ. Ɍɚɱɤɚ D ɬɚɤɨɻɟɩɪɢɩɚɞɚ aǰc, ʁɟɪɫɟɧɚɥɚɡɢɧɚʃɟɝɨɜɨɦ ɤɪɚɤɭ ǰa . Ɇɟɻɭɬɢɦ ɬɚɱɤɚ S ɧɟɩɪɢɩɚɞɚ aǰc, ʁɟɪɫɟɧɚɥɚɡɢ ɭʃɟɝɨɜɨʁɫɩɨʂɚɲʃɨʁ ɨɛɥɚɫɬɢ. 1. ɇɚɰɪɬɚʁɬɪɢɭɝɥɚ ɢ ɨɛɟɥɟɠɢ ɢɯɩɨ ɬɜɨʁɨʁɠɟʂɢ 2. ɇɚɰɪɬɚʁ bOc. Ɂɚɬɢɦ ɧɚɰɪɬɚʁɬɚɱɤɭ Ɇ ɤɨʁɚ ɫɟɧɚɥɚɡɢɧɚ ɤɪɚɤɭ Oc, ɢɬɚɱɤɭ G ɤɨʁɚ ɫɟ ɧɚɥɚɡɢ ɭ ɭɧɭɬɪɚɲʃɨʁɨɛɥɚɫɬɢ bOc.

36


ɍȽȺɈ Ʉʂɭɱɧɟɪɟɱɢ: ɭɝɚɨ, ɰɪɬɚʃɟ ɭɝɥɚ, ɤɪɚɰɢ, ɬɚɱɤɚ, ɬɟɦɟ ɨɛɥɚɫɬ ɭɝɥɚ

1.

ɍɨɱɢɧɚ ɰɪɬɟɠɭɫɜɟ ɭɝɥɨɜɟ ɢ ɧɚɩɢɲɢʃɢɯɨɜɟ ɧɚɡɢɜɟ. ɚ)

ɛ) t

a

b

c

a d

L

m

2.

aOd, ______, ______,______, ______,______.

TA

aOm, _______, _______. ɇɚɰɪɬɚʁ dOt, ɬɚɤɨ ɞɚ:

ɛ) ɬɚɱɤɚ Ɇ ɛɭɞɟ ɧɚ ɤɪɚɤɭ Ǽt, ɚ ɬɚɱɤɚ ȿ ɧɚ ɤɪɚɤɭ Ǽd.

R

ɚ) ɬɚɱɤɚ Ⱥ ɛɭɞɟ ɭʃɟɝɨɜɨʁɫɩɨʂɚɲʃɨʁ ɚ ɬɚɱɤɚ ȼ ɭ ɭɧɭɬɪɚɲʃɨʁɨɛɥɚɫɬɢ.

Ɇ

-P

U KA

ȼ

O

Ⱥ

E

4. ɇɚɰɪɬɚɧɟ ɫɭ ɬɚɱɤɟ Ɉ, ȿ, F, D ɢ C. ɇɚɰɪɬɚʁɬɚɤɚɜɭɝɚɨ ɤɨɦɟ ʁɟ ɬɟɦɟ ɬɚɱɤɚ Ɉ, ɚ ɞɚɫɟ ɬɚɱɤɟ ȿ ɢ ɋ ɧɚɥɚɡɟɧɚʃɟɝɨɜɢɦ ɤɪɚɰɢɦɚ. Ɍɚɱɤɚ F ɞɚ ɩɪɢɩɚɞɚʃɟɝɨɜɨʁ ɭɧɭɬɪɚɲʃɨʁɚ ɬɚɱɤɚ D ɫɩɨʂɚɲʃɨʁɨɛɥɚɫɬɢ.

ED

3. ɉɨɥɭɩɪɚɜɚ Ǽm ɬɪɟɛɚɞɚɛɭɞɟ ɡɚʁɟɞɧɢɱɤɢ ɤɪɚɤɞɜɚ ɭɝɥɚ: tOm ɢ mOn. ɇɚɰɪɬɚʁ ɢ ɨɛɟɥɟɠɢ ɤɪɚɤɟ ɭɝɥɨɜɚ ɤɨʁɢ ɧɟɞɨɫɬɚʁɭ. m

C

E F D

t Ʉɪɢɜɢɦ ɥɢɧɢʁɚɦɚ ɨɛɟɥɟɠɢ ɧɚ ɬɚʁɧɚɱɢɧ ɞɨɛɢʁɟɧɟ ɭɝɥɨɜɟ

O

5. ɇɚɰɪɬɚɧɚ ʁɟʁɟɞɧɚ ɢɡɥɨɦʂɟɧɚ ɥɢɧɢʁɚ. ɍɨɱɢɫɜɟɭɝɥɨɜɟ ɤɨʁɟ ɨɛɪɚɡɭʁɭʃɟɧɟ ɞɭɠɢ. Ɉɡɧɚɱɢ ɢɯ ɞɟɥɨɜɢɦɚ ɤɪɭɠɧɟɥɢɧɢʁɟ ɤɚɨɲɬɨʁɟ ɡɚɩɨɱɟɬɨ.

37


ȼɊɋɌȿ ɍȽɅɈȼȺ Ʉʂɭɱɧɟɪɟɱɢ: ɜɪɫɬɟ ɭɝɥɨɜɚ ɩɪɚɜ ɭɝɚɨ, ɨɲɬɚɪɭɝɚɨ, ɬɭɩ ɭɝɚɨ

ɇɚ ɫɥɢɰɢɦɨɠɟɲɞɚ ɭɨɱɢɲɬɪɢ ɪɚɡɥɢɱɢɬɚ ɩɨɥɨɠɚʁɚ ɥɟɩɟɡɟ. ɋɜɚɤɢ ɫɥɟɞɟʄɢ ɩɨɥɨɠɚʁ ɥɟɩɟɡɟ ɨɛɪɚɡɭʁɟ ɧɨɜɢ ɭɝɚɨ.

I

II

III

Ɣ Ʉɜɚɞɪɚɬ ɢɩɪɚɜɨɭɝɚɨɧɢɤɫɭɮɢɝɭɪɟɱɢʁɟɫɬɪɚɧɢɰɟ ɨɛɪɚɡɭʁɭɱɟɬɢɪɢ ʁɟɞɧɚɤɚ ɭɝɥɚ. Ɂɚ ɬɚɤɜɟ ɭɝɥɨɜɟ ɤɚɠɟɦɨɞɚɫɭ ɩɪɚɜɢɭɝɥɨɜɢ.

L

Ⱥɤɨʁɟ ɧɟɤɢ ɭɝɚɨ ɩɪɚɜ, ɨɧɞɚʄɟ ɫɟ ɫɬɪɚɧɢɰɟ ɬɪɨɭɝɚɨɧɨɝ ɥɟʃɢɪɚ (ɤɨʁɟɨɛɪɚɡɭʁɭ ɩɪɚɜ ɭɝɚɨ) ɩɨɤɥɨɩɢɬɢ ɫɚ ɤɪɚɰɢɦɚ ɬɨɝ ɭɝɥɚ.

c

m

cOd ʁɟ ɦɚʃɢɨɞ ɩɪɚɜɨɝɭɝɥɚ ɢ ɡɨɜɟ ɫɟ ɨɲɬɚɪ ɭɝɚɨ.

O

-P

d

k

O

Ǽ

aOm jɟ ɩɪɚɜɭɝɚɨ. Ʉɪɚɰɢɨɜɨɝɭɝɥɚ ɩɨɤɥɚɩɚʁɭ ɫɟɫɬɪɚɧɢɰɚɦɚ ɬɪɨɭɝɚɨɧɢɤɚ.

R

O

TA

a

kOe jɟɜɟʄɢɨɞ ɩɪɚɜɨɝɭɝɥɚ ɢ ɡɨɜɟ ɫɟ ɬɭɩ ɭɝɚɨ. e

U KA

1. ɐɪɜɟɧɨɦ ɛɨʁɨɦ ɡɚɨɤɪɭɠɢ ɛɪɨʁɤɨʁɢɨɡɧɚɱɚɜɚ (ɝɨɪɟɧɚɰɪɬɚɧɭ) ɥɟɩɟɡɭɱɢʁɢ ɤɪɚʁɟɜɢɨɛɪɚɡɭʁɭ ɩɪɚɜɭɝɚɨ. 3. ɇɚɰɪɬɚʁɧɚ ɱɚɫɨɜɧɢɰɢɦɚ ɤɚɡɚʂɤɟ, ɬɚɤɨ ɞɚ ɨɧɟ ɭɛɪɚɡɭʁɭ:

2. Ʉɨʁɢɭɝɚɨ ɡɚɤɥɚɩɚʁɭ ɤɪɚɰɢ ɦɚɤɚɡɚɧɚɰɪɬɟɠɭ?

ɚ ɩɪɚɜɭɝɚɨ;

Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞ ɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ.

ɛ) ɬɭɩ ɭɝɚɨ;

ɜ) ɨɲɬɚɪ ɭɝɚɨ.

ED

ɚ ɩɪɚɜ ɭɝɚɨ ɛ) ɨɲɬɚɪ ɭɝɚɨ ɜ) ɬɭɩ ɭɝɚɨ

4. Ɉɛɥɚɫɬ ɭɝɥɨɜɚ ɧɚ ɰɪɬɟɠɭ ɨɛɟɥɟɠɢ ɤɪɢɜɨɦ ɥɢɧɢʁɨɦ. t

p

b

S v

m

h n

H

e

O

a

Ǻ

A

c

d

ɉɨɩɭɧɢɬɚɛɟɥɭʃɢɯɨɜɢɦ ɧɚɡɢɜɢɦɚ ɤɚɨɲɬɨ ʁɟ ɡɚɩɨɱɟɬɨ. ɨɲɬɚɪɭɝɚɨ

ɬɭɩ ɭɝɚɨ

ɩɪɚɜ ɭɝɚɨ

pHe,

38

O

k


ȼɊɋɌȿ ɍȽɅɈȼȺ Ʉʂɭɱɧɟɪɟɱɢ: ɜɪɫɬɟ ɭɝɥɨɜɚ ɩɪɚɜ ɭɝɚɨ, ɨɲɬɚɪɭɝɚɨ, ɬɭɩ ɭɝɚɨ

1.

ɇɚɰɪɬɚɧɢ ɫɭ ɭɝɥɨɜɢɪɚɡɥɢɱɢɬɟ ɜɟɥɢɱɢɧɟ b

A

M

r

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a

e c

m

t

n

g

O

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g S

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ɛ) ɨɲɬɪɢ

_______________

_______________

_______________

ɇɚɰɪɬɚɧɟ ɫɭ ɬɪɢ ɮɢɝɭɪɟ. ɇɚ ɫɜɚɤɨʁɨɞʃɢɯ ɦɨɠɟɲɞɚ ɭɨɱɢɲɫɚɦɨʁɟɞɧɭɜɪɫɬɭ ɭɝɥɨɜɚ: ɨɲɬɪɟ, ɩɪɚɜɟ ɢɥɢ ɬɭɩɟ

-P

ɇɚɰɪɬɚʁɫɥɢɱɧɭɮɢɝɭɪɭ ɤɨʁɚ ɢɦɚ:

O

R

2.

ɜ) ɬɭɩɢ

TA

ɚ ɩɪɚɜɢ

L

ɂɡɞɜɨʁɢɧɚɩɢɲɢ ɭɝɥɨɜɟ ɤɨʁɢɫɭ:

ɚ) ɫɚɦɨ ɩɪɚɜɟ ɭɝɥɨɜɟ ɢɨɛɨʁ ʁɟ ɠɭɬɨɦ ɛɨʁɨɦ

U KA

ɛ) ɫɚɦɨ ɨɲɬɪɟ ɭɝɥɨɜɟ ɢɨɛɨʁ ʁɟ ɰɪɜɟɧɨɦ ɛɨʁɨɦ ɜ) ɫɚɦɨ ɬɭɩɟ ɭɝɥɨɜɟ ɢɨɛɨʁ ʁɟ ɡɟɥɟɧɨɦɛɨʁɨɦ. ɇɚɰɪɬɚʁɩɨɞɜɚ: ɚ) ɨɲɬɪɚ ɭɝɥɚ

ɛ ɬɭɩɚ ɭɝɥɚ

ɜ)ɩɪɚɜɚ ɭɝɥɚ.

ED

3.

4. ɇɚɰɪɬɚɧʁɟ ɬɭɩ ɭɝɚɨ aOb. ɉɨɞɟɥɢ ɝɚ ɩɨɥɭɩɪɚɜɨɦɧɚʁɟɞɚɧɩɪɚɜɢ ʁɟɞɚɧ ɨɲɬɚɪ ɭɝɚɨ. Ɂɚɩɢɲɢ ɞɨɛɢʁɟɧɟ ɭɝɥɨɜɟ

5. Ʉɨɥɢɤɨɧɚɰɪɬɟɠɭ ɢɦɚɩɪɚɜɢɯ ɭɝɥɨɜɚ" Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨɢɫɩɪɟɞɬɚɱɧɨɝɨɞɝɨɜɨɪɚ

ɚ) 4 a

ɛ) 8 ɜ) 6 O

ɝ) 16

b

______________________

39


ɐɊɌȺȵȿ ɉɊȺȼɈȽ ɍȽɅȺ Ʉʂɭɱɧɟɪɟɱɢ ɩɪɚɜ ɭɝɚɨ, ɰɪɬɚʃɟ ɩɪɚɜɨɝɭɝɥɚ

Ɣ Ʉɪɚʄɟɫɬɪɚɧɢɰɟ ɬɪɨɭɝɚɨɧɢɤɚ ɨɛɪɚɡɭʁɭɩɪɚɜɭɝɚɨ. Ɂɚɬɨ ɩɪɚɜɭɝɚɨ ɥɚɤɨ ɦɨɠɟɦɨɞɚɧɚɰɪɬɚɦɨ ɧɚ ɫɥɟɞɟʄɢɧɚɱɢɧ

TA

Ǽ

L

b

1. ɇɚɰɪɬɚʁɬɪɢɩɪɚɜɚ ɭɝɥɚɧɚ ɝɨɪɟ ɩɪɢɤɚɡɚɧɧɚɱɢɧ

a

2.

3.

4.

U KA

-P

O

1.

R

Ɣ ɉɪɚɜ ɭɝɚɨ ɦɨɠɟɦɨɞɚɧɚɰɪɬɚɦɨ ɭɱɟɬɢɪɢ ɤɨɪɚɤɚ, ɩɨɦɨʄɭ ɬɪɨɭɝɚɨɧɢɤɚ ɢɥɟʃɢɪɚ, ɨɜɚɤɨ

Ʉɨɥɢɤɨɫɦɨ ɩɪɚɜɢɯɭɝɥɨɜɚ ɞɨɛɢɥɢ ɰɪɬɚʁɭʄɢ ɧɚ ɨɜɚʁɧɚɱɢɧ"

ED

2. ɇɚɰɪɬɚʁɞɜɚ ɩɪɚɜɚ ɭɝɥɚ ɤɚɨ ɲɬɨʁɟɩɪɢɤɚɡɚɧɨ ɭɩɪɟɬɯɨɞɧɨɦɩɪɢɦɟɪɭ.

Ɂɚɛɚɜɢɬɟɫɟɩɪɟɫɚɜɢʁɚʃɟɦ ɯɚɪɬɢʁɟ ɭɛɨʁɢ ɩɪɚɜʂɟɦ ɥɟɩɟɡɚ ɢ ɪɚɡɥɢɱɢɬɢɯɮɢɝɭɪɚ...

M

N

O

1. ɒɢɪɟʃɟɦ ɧɚɩɪɚɜʂɟɧɢɯɥɟɩɟɡɚ ɨɛɪɚɡɭʁɬɟ ʃɟɧɟ ɪɚɡɥɢɱɢɬɟ ɩɨɥɨɠɚʁɟ. Ʉɨʁɟɜɪɫɬɟ ɭɝɥɨɜɚ ɭɨɱɚɜɚɬɟ"

Ɣ Ɉɞɧɚɩɪɚɜʂɟɧɢɯɥɟɩɟɡɚ ɩɪɚɜɢɬɟ ɪɚɡɥɢɱɢɬɟɮɢɝɭɪɟ. Ⱦɚʁɟɦɨ ɜɚɦ ɧɟɤɨɥɢɤɨɩɪɢɦɟɪɚ.

40


ȼɊɋɌȿ ɍȽɅɈȼȺ Ʉʂɭɱɧɟɪɟɱɢ ɜɪɫɬɟ ɭɝɥɨɜɚ ɩɪɚɜ ɭɝɚɨɨɲɬɚɪɭɝɚɨ ɬɭɩ ɭɝɚɨ ɰɪɬɚʃɟ ɭɝɥɨɜɚ

Ɉɛɟɥɟɠɢɧɚɰɪɬɚɧɟ ɭɝɥɨɜɟ ɢ ɩɨɩɭɧɢɬɚɛɟɥɭ.

1.

ɍɝɚɨ

TA

2.

L

ȼɪɫɬɚ ɭɝɥɚ

ɇɚɰɪɬɚʁ ɛ) ɨɲɬɚɪ ɭɝɚɨ;

ɜ ɬɭɩɭɝɚɨ.

5.

U KA

Ⱦɚɬɨ ʁɟ ɬɟɦɟ Ǽ ɩɪɚɜɨɝɭɝɥɚ ȟǼȓ. ɇɚɰɪɬɚʁɤɪɚɤɟ ɬɨɝ ɭɝɥɚɩɨɦɨʄɭ ɬɪɨɭɝɚɨɧɢɤa.

4. ɉɨɥɭɩɪɚɜɚ Om ʁɟ ɤɪɚɤ ɩɪɚɜɨɝ ɭɝɥɚ nOm ɇɚɰɪɬɚʁɬɚʁɭɝɚɨ.

m

ED

3.

-P

O

R

ɚ ɩɪɚɜ ɭɝɚɨ;

ɉɚɠʂɢɜɨ ɩɨɫɦɚɬɪɚʁɧɚɰɪɬɚɧɟ ɭɝɥɨɜɟ. ɉɨɪɟɻɚʁɢɯɩɨ ɜɟɥɢɱɢɧɢ ɨɞɧɚʁɦɚʃɟɝ ɞɨɧɚʁɜɟʄɟɝ. O d

m n B

n

t

______B __BBBBB

k T

g

e

_____________

41

D


ȼɊɋɌȿ ɍȽɅɈȼȺ Ʉʂɭɱɧɟɪɟɱɢ: ɜɪɫɬɟ ɭɝɥɨɜɚ ɩɪɚɜ ɭɝɚɨ, ɨɲɬɚɪɭɝɚɨ, ɬɭɩ ɭɝɚɨ, ɰɪɬɚʃɟ ɭɝɥɨɜɚ

1. ɇɚɰɪɬɚɧʁɟ mOn.ɍʃɟɝɨɜɨʁ ɭɧɭɬɪɚɲʃɨʁɨɛɥɚɫɬɢ ɧɚɰɪɬɚʁ ɬɚɱɤɭ Ⱥ, ɚ ɭɫɩɨʂɚɲʃɨʁɨɛɥɚɫɬɢ ɧɚɰɪɬɚʁɬɚɱɤɭ ȼ. Ǽ

Ɉɛɟɥɟɠɢ ɧɚɰɪɬɚɧɟ ɭɝɥɨɜɟ, ɚ ɡɚɬɢɦ ɧɚɩɢɲɢ ɤɨʁɨʁɜɪɫɬɢ ɭɝɥɨɜɚ ɩɪɢɩɚɞɚʁɭ.

2.

n

__________

3. ɇɚɰɪɬɚʁ: a) ɩɪɚɜɭɝɚɨ aǰc;

__________

__________

ɜ) ɬɭɩ ɭɝɚɨ eOs.

U KA

-P

O

R

ɛ) ɨɲɬɚɪ ɭɝɚɨ mOn;

_____ʁɟ

L

m

_____ʁɟ

TA

_____ ʁɟ

4. ɉɚɠʂɢɜɨ ɩɨɫɦɚɬɪɚʁɰɪɬɟɠ.

ɇɚɩɢɲɢ ɧɚɡɢɜɟ ɭɝɥɨɜɚ

n

ɚ ɉɪɚɜɭɝɚɨʁɟ _______.

t

ɛ) ɭɝɥɨɜɢ ɫɭ ______________________. ______________________. ɜ) Ɉɲɬɪɢ Ɍɭɩɢɭɝɥɨɜɢɫɭ

ED

a Mp

5. ɇɚɰɪɬɚɧʁɟ ɤɪɚɤɈa . Ɉɧʁɟ ɡɚʁɟɞɧɢɱɤɢ ɤɪɚɤ ɩɪɚɜɨɝɭɝɥɚ aOd ɢɨɲɬɪɨɝ ɭɝɥɚ m Ɉa . ɇɚɰɪɬɚʁɬɟ ɭɝɥɨɜɟ Ǽ

6. ɇɚɰɪɬɚʁʁɟɞɚɧɬɭɩɢ ʁɟɞɚɧɨɲɬɚɪ ɭɝɚɨ ɫɚ ɡɚʁɟɞɧɢɱɤɢɦ ɤɪɚɤɨɦ

a

GeoGebra ɉɨɦɨʄɭ ɚɥɚɬɤɟ

ɰɪɬɚɲɭɝɚɨ.

42


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ȳɨÉ&#x153;É&#x161;ɧĘ É&#x; ɧÉ&#x161;É°ÉŞÉŹÉ&#x161;ɨÉŠÉĽÉ&#x161;ɧÉŤÉ&#x153;ɨÉ?É&#x161; ɤɪÉ&#x161;Ę É&#x161;. É?ÉŠÉĽÉ&#x161;ɧĘ É&#x; ɭɧÉ&#x;ɨɧÉ&#x161;ɥɢÉ&#x153;É&#x;ɧÉ&#x;ɤɨɼɢɤɨ ɭɼɢɰÉ&#x161;. É É&#x161;Ɍɢɍɼɢ É&#x17E;É&#x161;ÉŤÉ­ ɧÉ&#x161;É°ÉŞÉŹÉ&#x161;ɧÉ&#x; ɭɼɢɰÉ&#x; ÉŠÉŞÉ&#x161;É&#x153;É&#x;. É&#x2030;ɨɌɨĘ&#x201E;É­É&#x17E;É&#x153;É&#x; ÉŠÉŞÉ&#x161;É&#x153;É&#x; ɧÉ&#x161;É°ÉŞÉŹÉ&#x161;Ę&#x201E;É&#x;Ɍɨ É?É&#x153;É˘Ę É˘Ę&#x201E;É&#x;É&#x153;É­ ɢÉ&#x201E;ɢɍÉ&#x161;ɹɤɭ ɭɼɢɰɭ. É&#x2C6;É&#x203A;É&#x;ÉĽÉ&#x;É É˘Ę&#x201E;É&#x;Ɍɨ ɢɯ ɍɼɨÉ&#x153;ɢɌÉ&#x161; a ɢ b. É?ɨɹÉ&#x161;É&#x153;É&#x161;ɌɨÉ&#x17E;É&#x161; ÉŤÉ&#x;ÉŠÉŞÉ&#x161;É&#x153;É&#x; a ɢ b ÉŤÉ&#x; ÉŤÉ&#x;ÉŤÉ&#x;ɤɭ É­Ę É&#x;É&#x17E;É§É¨Ę ÉŹÉ&#x161;ɹɤɢ.É&#x152;É&#x161;ɹɤɭĘ&#x192;ɢɯɨÉ&#x153;ɨÉ?ÉŠÉŞÉ&#x;ÉŤÉ&#x;ɤÉ&#x161; ɨÉ&#x203A;É&#x;ÉĽÉ&#x;ɠɢɼɢɍɌɨɍɼɨÉ&#x153;ɨɌÇź.

a

É&#x2C6;

ED

b

ČžÉ&#x153;É&#x;ÉŠÉŞÉ&#x161;É&#x153;É&#x; ÉŤÉ&#x;ÉŤÉ&#x;ɤɭ É&#x161;ɤɨ ɢɌÉ&#x161;Ę É­ ÉŤÉ&#x161;Ɍɨ Ę É&#x;É&#x17E;ɧɭ ÉĄÉ&#x161;Ę É&#x;É&#x17E;ɧɢɹɤɭ ÉŹÉ&#x161;ɹɤɭ.

Ć&#x201D; É&#x201E;É¨Ę É&#x; ÉŤÉ&#x; ɭɼɢɰÉ&#x; ÉŤÉ&#x;ɤɭ ɊɨÉ&#x17E;ÉŠÉŞÉ&#x161;É&#x153;ɢɌ É­É?ɼɨɌ? É&#x2030;ɪɨÉ&#x153;É&#x;ɪɢ ɊɨɌɨĘ&#x201E;É­ ÉŠÉŞÉ&#x161;É&#x153;ɨÉ?É­É?ÉĽÉ&#x161;ɧÉ&#x161; ɏɪɨɭÉ?É&#x161;ɨɧɢɤɭ. É É&#x161; ÉŠÉŞÉ&#x161;É&#x153;É&#x; m ɢ n É¤É¨Ę É&#x; ÉŤÉ&#x;ÉŤÉ&#x;ɤɭɊɨÉ&#x17E;ÉŠÉŞÉ&#x161;É&#x153;ɢɌ É­É?ɼɨɌ ɤÉ&#x161;É É&#x;ɌɨÉ&#x17E;É&#x161;ÉŤÉ­ ɧɨɪɌÉ&#x161;ɼɧÉ&#x;. É&#x152;É&#x161;ɹɤɭĘ&#x192;ɢɯɨÉ&#x153;ɨÉ?ÉŠÉŞÉ&#x;ÉŤÉ&#x;ɤÉ&#x161; ɨÉ&#x203A;É&#x;ÉĽÉ&#x;ɠɢɼɢ ɍɌɨɍɼɨÉ&#x153;ɨɌ Čż. m

n

É&#x2021;ɨɪɌÉ&#x161;ɼɧÉ&#x; ÉŠÉŞÉ&#x161;É&#x153;É&#x; ɨÉ&#x203A;É&#x;ÉĽÉ&#x;É É&#x161;É&#x153;É&#x161;Ɍɨ ɥɧÉ&#x161;ɤɨɌĹ? . É É&#x161;Ɋɢɍm Ĺ? n ɹɢɏÉ&#x161;Ɍɨ: ÉŠÉŞÉ&#x161;É&#x153;É&#x; m ɢ n ÉŤÉ­ É­ÉĄÉ&#x161;Ę É&#x161;Ɍɧɨ ɧɨɪɌÉ&#x161;ɼɧÉ&#x;.

É&#x201A;ɧɏÉ&#x;ɪɧÉ&#x;ÉŹ É&#x161;É&#x17E;ÉŞÉ&#x;ÉŤÉ&#x161; ɧÉ&#x161; É¤É¨Ę É¨Ę ÉŚÉ¨É É&#x;ɲ É&#x17E;É&#x161; ɤɨɪɢɍɏɢɲ ÉŚÉ&#x161;ÉŠÉ&#x;ɧÉ&#x161;ÉŤÉ&#x;Ę&#x201A;É&#x161;: https://www.google.rs mape É&#x2021;É&#x161;É­É&#x153;É&#x;ɼɢɹÉ&#x161;ɧɢɌ ÉŚÉ&#x161;ÉŠÉ&#x161;ÉŚÉ&#x161; ɌɨɠÉ&#x;ɲ É&#x17E;É&#x161; ɭɨɹɢɲÉ­ ɤÉ&#x161;ɤÉ&#x153;ɨɌ ÉŤÉ­ ÉŚÉ&#x;ɝɭɍɨÉ&#x203A;ɧɨɌ ɊɨɼɨɠÉ&#x161;Ę É­ ɭɼɢɰÉ&#x;É­ ɧÉ&#x161;ÉŤÉ&#x;Ę&#x201A;É­.

43


ɐɊɌȺȵȿ ɉȺɊȺɅȿɅɇɂɏ ɉɊȺȼɂɏ Ʉʂɭɱɧɟɪɟɱɢ: ɭɡɚʁɚɦɧɢ ɩɨɥɨɠɚʁ ɞɜɟ ɩɪɚɜɟ, ɰɪɬɚʃɟ ɩɚɪɚɥɟɥɧɢɯ ɩɪɚɜɢɯ

2. ɍɫɜɟɫɰɢ ɛɟɡ ɥɢɧɢʁɚ ɤɨɪɢɫɬɢɲɩɚɪɚɥɟɥɧɟ ɢɜɢɰɟɧɚ ɬɪɨɭɝɚɨɧɢɤɭ ɢɥɢ ɥɟʃɢɪɭ. ɇɚɰɪɬɚʁɬɚɤɨ: r II n, s II v.

R

TA

L

1. ɍ ɫɜɟɫɰɢ ɧɚ ɤɜɚɞɪɚɬɢʄɟ ɰɪɬɚɲɩɚɪɚɥɟɥɧɟ ɩɪɚɜɟ, ɬɚɤɨ ɲɬɨ ɤɨɪɢɫɬɢɲɜɟʄ ɨɞɲɬɚɦɩɚɧɟ ɩɚɪɚɥɟɥɧɟ ɥɢɧɢʁɟ. ɇɚɰɪɬɚʁɬɚɤɨ: c II e, n II u.

ɉɚɪɚɥɟɥɧɟ ɩɪɚɜɟ ɦɨɠɟɲɥɚɤɨ ɢɩɪɟɰɢɡɧɨ ɞɚ ɧɚɰɪɬɚɲ ɩɨɦɨʄɭ:

Ɣ ɬɪɨɭɝɚɨɧɢɤɚ ɢɥɟʃɢɪɚ. a b

U KA

n

-P

m

O

Ɣ ɞɜɚ ɬɪɨɭɝɚɨɧɢɤɚ;

a II b

m II n

ED

3. ɇɚɰɪɬɚʁ ɧɚ ɝɨɪɟɩɪɢɤɚɡɚɧɧɚɱɢɧ) ɞɜɟ ɩɚɪɚɥɟɥɧɟ ɩɪɚɜɟ a ɢ b.

4. ɇɚɰɪɬɚɧɟ ɫɭɩɪɚɜɚ m ɢ ɬɚɱɤɚ ȿ. ɇɚɰɪɬɚʁɩɪɚɜɭ n ɤɨʁɨʁɩɪɢɩɚɞɚ ɬɚɱɤɚ ȿ, ɚɥɢ ɬɚɤɨɞɚ ʁɟ n II m. m

ȿ 5. ɇɚɰɪɬɚʁ ɩɚɪɚɥɟɥɧɟ ɩɪɚɜɟa ɢ b, ɬɚɤɨɞɚɫɟɧɚɥɚɡɟ ɧɚ ɪɚɫɬɨʁɚʃɭ 1 cm. 6. ɇɚɰɪɬɚʁ ɩɨɦɨʄɭ ɬɪɨɝɚɨɧɢɤɚ ɢ ɥɟʃɢɪɚ ɫɥɟɞɟʄɟɩɪɚɜɟ: ɚ) a II b;

44

ɛ) c II d;

ɜ) m II s.


ɐɊɌȺȵȿ ɉȺɊȺɅȿɅɇɂɏ ɉɊȺȼɂɏ Ʉʂɭɱɧɟɪɟɱɢ: ɭɡɚʁɚɦɧɢ ɩɨɥɨɠɚʁ ɞɜɟ ɩɪɚɜɟ, ɰɪɬɚʃɟ ɩɚɪɚɥɟɥɧɢɯ ɩɪɚɜɢɯ

1. ɇɚɰɪɬɚʁɬɪɢ ɦɟɻɭɫɨɛɧɨ ɩɚɪɚɥɟɥɧɟ ɩɪɚɜɟ

2. ɇɚɰɪɬɚɧɚ ʁɟɩɪɚɜɚ n ɢ ɬɚɱɤɟ Ⱥ ɢ ȼ. ɇɚɰɪɬɚʁɩɪɚɜɭ a ɤɨʁɨʁɩɪɢɩɚɞɚ ɬɚɱɤɚ Ⱥ ɢɩɪɚɜɭ b ɤɨʁɨʁɩɪɢɩɚɞɚ ɬɚɱɤɚ ȼ, ɬɚɤɨ ɞɚɫɭɩɪɚɜɟn, a ɢ b ɦɟɻɭɫɨɛɧɨ ɩɚɪɚɥɟɥɧɟ

TA

L

n

3. ɇɚɰɪɬɚʁɬɪɢ ɩɚɪɚɥɟɥɧɟ ɩɪɚɜɟ s, e ɢ p, ɬɚɤɨɞɚ ɫɜɚɤɚɩɪɚɜɚ ɫɚɞɪɠɢ ʁɟɞɧɭ ɨɞɧɚɰɪɬɚɧɢɯ ɬɚɱɚɤɚ.

4. ɉɪɚɜɚɦɚ n ɢ m ɧɚɰɪɬɚʁɩɚɪɚɥɟɥɧɟ

R

ɩɪɚɜɟ t ɢ o, ɬɚɤɨɞɚʁɟ n II t

m II o

U KA

-P

O

n

6. ɇɚɰɪɬɚʁɞɜɟ ɩɚɪɚɥɟɥɧɟ ɩɪɚɜɟȓ ɢ g, ɬɚɤɨɞɚɩɪɚɜɚȓ ɫɚɞɪɠɢ ɬɚɱɤɭ Ɉ, ɚ ɩɪɜɚg ɞɚɫɚɞɪɠɢ ɬɚɱɤɭ D.

ED

5. ɇɚɰɪɬɚʁ ɩɪɚɜɭ a ɤɨʁɚ ʄɟɛɢɬɢ ɩɚɪɚɥɟɥɧɚ ɫɚɩɪɚɜɨɦp.

p

m

Ɂɚɛɚɜɢɬɟɫɟ ɫɚɜɢʁɚʃɟɦɥɢɫɬɚ ɯɚɪɬɢʁɟ, ɬɚɤɨɞɚɫɟʃɟɝɨɜɟ ɢɜɢɰɟɩɪɟɤɥɚɩɚʁɭ... ɉɪɟɤɨ ɫɚɜɢʁɟɧɢɯ ɬɪɚɝɨɜɚ ɧɚ ɩɚɩɢɪɭ ɩɨɜɭɰɢɬɟ ɥɢɧɢʁɟ ɍ ɤɚɤɜɨɦ ɫɭ ɭɡɚʁɚɦɧɨɦ ɩɨɥɨɠɚʁɭ ɬɟ ɥɢɧɢʁɟ? Ɣ Ɉɞ ɫɚɜɢʁɟɧɟ ɯɚɪɬɢʁɟ ɧɚɩɪɚɜɢɬɟ ɪɚɡɥɢɱɢɬɟ ɮɢɝɭɪɟ. Ⱦɚʁɟɦɨ ɜɚɦʁɟɞɚɧ ɩɪɢɦɟɪ. Ɣ

45


ɐɊɌȺȵȿ ɇɈɊɆȺɅɇɂɏ ɉɊȺȼɂɏ Ʉʂɭɱɧɟɪɟɱɢ: ɭɡɚʁɚɦɧɢ ɩɨɥɨɠɚʁ ɞɜɟ ɩɪɚɜɟ, ɰɪɬɚʃɟ ɧɨɪɦɚɥɧɢɯ ɩɪɚɜɢɯ

 ɍɫɜɟɫɰɢ ɧɚ ɤɜɚɞɪɚɬɢʄɟ ɦɨɠɟɲɞɚ

2 ɇɚɰɪɬɚɧɚ ʁɟɩɪɚɜɚ t ɢɧɚʃɨʁɨɡɧɚɱɟɧɟ ɬɚɱɤɟ A, B ɢ ɋ Ʉɪɨɡ ɫɜɚɤɭ ɬɚɱɤɭ ɩɨɜɭɰɢ ɩɨ ʁɟɞɧɭɩɪɚɜɭ, ɬɚɤɨɞɚɫɜɚɤɚ ɨɞ ʃɢɯ ɛɭɞɟɧɨɪɦɚɥɧɚ ɧɚɩɪɚɜɭ t

ɧɚɰɪɬɚɲɧɨɪɦɚɥɧɟ ɩɪɚɜɟ ɤɨɪɢɫɬɟʄɢ ɜɟʄ ɨɞɲɬɚɦɩɚɧɟ ɥɢɧɢʁɟ ɇɚɰɪɬɚʁɬɚɤɨ: c ŏ e, n ŏ u. n

t ȼ

m

TA

m n

ɋ

L

Ⱥ

M

a

O

a

N

ɉɪɢɫɥɨɧɢɲ ɥɟʃɢɪ ɭɡ ɧɚʁɞɭɠɭ ɫɬɪɚɧɢɰɭ ɬɪɨɭɝɚɨɧɢɤɚ

U KA

ɍɡ ɫɬɪɚɧɢɰɭ ɬɪɨɭɝɚɨɧɢɤɚ ɩɨɜɥɚɱɢɲ ɩɪɚɜɭ a

-P

a

R

Ɣ ɇɨɪɦɚɥɧɟ ɩɪɚɜɟ ɦɨɠɟɲɩɪɟɰɢɡɧɨ ɞɚɧɚɰɪɬɚɲɩɨɦɨʄɭɞɜɚ ɬɪɨɭɝɚɨɧɢɤɚ ɢɥɢ ɬɪɨɭɝɚɨɧɢɤɚ ɢ ɥɟʃɢɪɚ Ɉɜɚɤɨ:

O

Ʌɟʃɢɪ ɞɪɠɢɲ ɱɜɪɫɬɨ, ɚɬɪɨɭɝɚɨɧɢɤ ɩɨɦɟɪɚɲ ɞɭɠ ɥɟʃɢɪɚ ɫɜɟ ɞɨɤ ɫɬɪɚɧɢɰɚɬɪɭɝɚɨɧɢɤɚ ɧɟ ɩɪɟɻɟ ɧɚɰɪɬɚɧɭ ɩɪɚɜɭ a

b

n

a

P ɍɡ ɫɬɪɚɧɢɰɭ ɬɪɨɭɝɚɨɧɢɤɚ ɩɨɜɥɚɱɢɲ ɩɪɜɨ ɩɪɜɭ b ɚɡɚɬɢɦ ɩɪɚɜɭ n b ŏa n ŏa

ED

3 ɇɚɰɪɬɚʁɩɪɚɜɟm ŏ n, ɧɚ ɝɨɪɟɩɪɢɤɚɡɚɧɧɚɱɢɧ

Ɂɚɛɚɜɢɬɟɫɟ ɫɚɜɢʁɚʃɟɦɥɢɫɬɚ ɯɚɪɬɢʁɟ, ɬɚɤɨɞɚɫɟʃɟɝɨɜɟ ɢɜɢɰɟ ɩɪɟɤɥɚɩɚʁɭ Ɣ ɉɪɟɤɨɫɚɜɢʁɟɧɢɯ

 ɩɪɟɫɚɜɢʁɚʃɟ ɧɚɩɨɥɨɜɢɧɭ

ɬɪɚɝɨɜɚ ɧɚ ɯɚɪɬɢʁɢ ɩɨɜɭɰɢɬɟ ɥɢɧɢʁɟ Ʉɨɥɢɤɨɢɦɚɥɢɧɢʁɚ" Ɣ ɍ ɤɚɤɜɨɦ ɫɭ ɭɡɚʁɚɦɧɨɦ ɩɨɥɨɠɚʁɭ ɥɢɧɢʁɟ" Ɣ Ʉɚɤɜɟ ɭɝɥɨɜɟ ɬɟ ɥɢɧɢʁɟɨɛɪɚɡɭʁɭ" ɉɪɨɜɟɪɢ ɩɨɦɨʄɭ ɩɪɚɜɨɝ ɭɝɥɚ ɧɚ ɬɪɨɭɝɚɨɧɢɤɭ

 ɩɪɟɫɚɜɢʁɚʃɟ ɧɚɩɨɥɨɜɢɧɭ

46


ɐɊɌȺȵȿ ɇɈɊɆȺɅɇɂɏ ɉɊȺȼɂɏ Ʉʂɭɱɧɟɪɟɱɢ: ɭɡɚʁɚɦɧɢ ɩɨɥɨɠɚʁ ɞɜɟ ɩɪɚɜɟ, ɰɪɬɚʃɟ ɧɨɪɦɚɥɧɢɯ ɩɪɚɜɢɯ

1. ɇɚ ɫɜɚɤɨɦɰɪɬɟɠɭ ɭɨɱɢɫɜɟɩɚɪɨɜɟ ɧɨɪɦɚɥɧɢɯɩɪɚɜɢɯ Ɂɚɩɢɲɢ ɢɯ. ɚ)

ɛ) c

d

n

e

d

L

a

m

TA

b

a  c,

a

O

e

a

c

t

a

U KA

a

O

N

-P

M

R

Ɣ ɇɨɪɦɚɥɧɟ ɩɪɚɜɟ ɦɨɠɟɲɞɚɧɚɰɪɬɚɲ ɢ ɧɚ ɨɜɚʁɧɚɱɢɧ, ɨɜɚɤɨ:

ED

2. ɇɚɰɪɬɚʁɧɟɤɨɥɢɤɨɧɨɪɦɚɥɧɢɯɩɪɚɜɢɯ, ɧɚ ɝɨɪɟɩɪɢɤɚɡɚɧɧɚɱɢɧ

3. ɇɚɰɪɬɚʁɩɪɚɜɭ a ɤɨʁɚ ɫɚɞɪɠɢ ɬɚɱɤɭ Ɉ ɢ ɧɨɪɦɚɥɧɚ ʁɟɧɚ ɩɪɚɜɭ e

4. ɇɚɰɪɬɚʁɩɪɚɜɟm ɢ n, ɬɚɤɨɞɚɫɭɧɨɪɦɚɥɧɟ ɧɚ ɩɪɚɜɟc ɢ t c

e Ɉ

47

t


ɍɁȺȳȺɆɇɂ ɉɈɅɈɀȺȳ Ⱦȼȿ ɉɊȺȼȿ Ʉʂɭɱɧɟɪɟɱɢ: ɭɡɚʁɚɦɧɢ ɩɨɥɨɠɚʁ ɞɜɟ ɩɪɚɜɟ, ɰɪɬɚʃɟ ɩɚɪɚɥɟɥɧɢɯ ɢ ɧɨɪɦɚɥɧɢɯ ɩɪɚɜɢɯ

1. ɇɚɩɢɲɢɨɞɝɨɜɚɪɚʁɭʄɢɡɧɚɤ(II ɢɥɢ ) ɢ ɬɚɤɨ ɨɞɪɟɞɢ ɦɟɻɭɫɨɛɧɢɨɞɧɨɫɧɚɰɪɬɚɧɢɯɩɪɚɜɢɯ. ɚ)

ɛ) a

ɜ)

m

e

n

s n n __ m

e __ s

2. ɇɚɰɪɬɚʁɩɪɚɜɟs ɢ p: ɛ) ɬɚɤɨɞɚɫɭɩɚɪɚɥɟɥɧɟ;

s __ n

ɜ) ɬɚɤɨɞɚ ɫɟɧɚɥɚɡɟ ɭ ɦɟɻɭɫɨɛɧɨ ɧɨɪɦɚɥɧɨɦ ɩɨɥɨɠɚʁɭ.

U KA

-P

O

R

ɚ) ɬɚɤɨɞɚɫɟ ɫɟɤɭ, ɚɧɢɫɭ ɭ ɦɟɻɭɫɨɛɧɨ ɧɨɪɦɚɥɧɨɦ ɩɨɥɨɠɚʁɭ;

e __n

TA

a __ b

L

b

.

5.

4. ɇɚɰɪɬɚʁɩɚɪɚɥɟɥɧɟ ɩɪɚɜɟa ɢ b ɤɨʁɟ ɤɨʁɟ ɫɭɧɨɪɦɚɥɧɟ ɫɚɩɪɚɜɨɦp, ɬɚɤɨ ɞɚɩɪɚɜɚ a ɫɚɞɪɠɢ ɬɚɱɤɢɈ, ɚɩɪɚɜɚb ɫɚɞɪɠɢ ɬɚɱɤɭ R. p

ED

3. ɇɚɰɪɬɚʁɬɚɱɤɭ Ⱥ ɢ ɬɪɢɩɪɚɜɟ ɤɨʁɟɫɟ ɫɟɤɭ ɭ ɬɚɱɤɢȺ.

Ɉ

R

ɇɚɰɪɬɚʁɩɪɚɜɭ p ɤɨʁɚ ɩɪɨɥɚɡɢ ɤɪɨɡ ɬɚɱɤɭ Ɉ ɢ ɫɚ ɩɪɚɜɨɦ m ʁɟ ɚ) ɩɚɪɚɥɟɥɧɚ;

ɛ) ɧɨɪɦɚɥɧɚ. m Ɉ

m

Ɉ GeoGebra ɉɨɦɨʄɭ ɨɜɟ ɞɜɟ ɚɥɚɬɤɟ

ɰɪɬɚɲ ɩɚɪɚɥɟɥɧɟ ɢ ɧɨɪɦɚɥɧɟ ɩɪɚɜɟ.

48


ɋȺȾȺ ɁɇȺɆ ɆɇɈȽɈ ȼɂɒȿ ɋȺȾȺ ɁɇȺɆ ɆɇɈȽɈ ȼɂɒȿ Ʉʂɭɱɧɟɪɟɱɢ: ɭɝɚɨ, ɜɪɫɬɟ ɭɝɥɨɜɚ, ɭɡɚʁɚɦɧɢ ɩɨɥɨɠɚʁ ɞɜɟ ɩɪɚɜɟ

Ɣ ɍɝɚɨ ʁɟ ɝɟɨɦɟɬɪɢʁɫɤɚɮɢɝɭɪɚ ɤɨʁɭɱɢɧɟ ɞɜɟɩɨɥɭɩɪɚɜɟ ɫɚɡɚʁɟɞɧɢɱɤɨɦɩɨɱɟɬɧɨɦ ɬɚɱɤɨɦ ɢɞɟɨ ɩɪɨɫɬɨɪɚ ɢɡɦɟɻɭ ɬɢɯɩɨɥɭɩɪɚɜɢɯ. Ɣ ɐɪɬɚʃɟ ɭɝɥɚ

Ɣ ȿɥɟɦɟɧɬɢɭɝɥɚɫɭ ɤɪɚɰɢ ɢ ɬɟɦɟ.

ɂɡ ɬɚɱɤɟ Ɉ ɧɚɰɪɬɚɦɨɞɜɟ ɩɨɥɭɩɪɚɜɟ (Oa ɢ Ob) a

a

TA

b

Ʉɪɚɰɢɭɝɥɚ ɫɭɩɨɥɭɩɪɚɜɟ Oa ɢ Ob. Ɍɟɦɟ ɭɝɥɚʁɟ ɡɚʁɟɞɧɢɱɤɚ ɬɚɱɤɚ O .

b

R

aǼb

c

-P

O

n

e

L

ɨɛɥɚɫɬ ɭɝɥɚ

E

B

m

nǼm ʁɟ ɨɲɬɚɪ ɭɝɚɨ

EOB ʁɟ ɬɭɩ ɭɝɚɨ

U KA

cǼe ʁɟɩɪɚɜɭɝɚɨ

ED

a b

ɉɚɪɚɥɟɥɧɟ ɩɪɚɜɟ ɫɭ ɭɜɟɤɧɚ ɢɫɬɨɦ ɪɚɫɬɨʁɚʃɭ. ȹ Ɂɚɩɢɫa II b ɱɢɬɚɦɨ: ɩɪɚɜɟ a ɢ b ɫɭ ɭɡɚʁɚɦɧɨ ɩɚɪɚɥɟɥɧɟ.

m

Ɉ

Ⱦɜɟ ɩɪɚɜɟɫɟ ɫɟɤɭ ɚɤɨ ɢɦɚʁɭʁɟɞɧɭ ɡɚʁɟɞɧɢɱɤɭ ɬɚɱɤɭ.

n c d Ⱥ

ɇɨɪɦɚɥɧɟ ɩɪɚɜɟɫɟ ɫɟɤɭɩɨɞɩɪɚɜɢɦ ɭɝɥɨɦ. Ɉɛɟɥɟɠɚɜɚɦɨ ɢɯ ɡɧɚɤɨɦ ŏ . ȹ Ɂɚɩɢɫc ŏ d ɱɢɬɚɦɨ: ɩɪɚɜɟ c ɢ d ɫɭ ɭɡɚʁɚɦɧɨ ɧɨɪɦɚɥɧɟ.

49


ɉɊɈȼȿɊȺȼȺɆɈ ɇȺɍɑȿɇɈ Ʉʂɭɱɧɟɪɟɱɢ: ɭɝɚɨ, ɜɪɫɬɟ ɭɝɥɨɜɚ, ɭɡɚʁɚɦɧɢ ɩɨɥɨɠɚʁ ɞɜɟ ɩɪɚɜɟ

1. ɇɚɰɪɬɚʁ: ɛ) ɨɲɬɚɪ ɭɝɚɨ tOs;

ɜ) ɬɭɩɭɝɚɨ mOn.

TA

L

a) ɩɪɚɜɭɝɚɨ aǼb;

2. ɉɨɫɦɚɬɪɚʁɰɪɬɟɠ. Ʉɨɥɢɤɨɧɚʃɟɦɭ ɭɨɱɚɜɚɲɭɝɥɨɜɚ" m

n

ɚ ɉɪɚɜɢɯ ɭɝɥɨɜɚ ɢɦɚ __. Ɍɨɫɭ ɭɝɥɨɜɢ _________________

R

e

ɛ Ɉɲɬɪɢɯɭɝɥɨɜɚ ɢɦɚ __. Ɍɨɫɭ ɭɝɥɨɜɢ _________________ Ǽ

d

t

-P

3. Ɂɚɩɢɲɢ ɩɚɪɨɜɟ ɩɪɚɜɢɯ ɤɨʁɟ ɫɭ ɦɟɻɭɫɨɛɧɨ:

b m

U KA

a

Ɍɨɫɭ ɭɝɥɨɜɢ _________________

O

ɜ) Ɍɭɩɢɯ ɭɝɥɨɜɚ ɢɦɚ __.

ɚ ɩɚɪɚɥɟɥɧɟ ɛ) ɧɨɪɦɚɥɧɟ.

n

5. ɇɚɰɪɬɚʁɩɪɚɜɭ ȓ ɤɨʁɚ ɩɪɨɥɚɡɢ ɤɪɨɡ ɬɚɱɤɭ Ⱥ, ɬɚɤɨɞɚʁɟɧɨɪɦɚɥɧɚ ɫɚɩɪɚɜɨɦ Ȟ.

ED

4. ɇɚɰɪɬɚʁɩɪɚɜɭ a ɤɨʁɚ ɩɪɨɥɚɡɢ ɤɪɨɡ ɬɚɱɤɭ Ɉ, ɬɚɤɨɞɚʁɟ ɩɚɪɚɥɟɥɧɚ ɫɚ ɩɪɚɜɨɦȞ.

A

Ȟ

O

Ȟ

6. ɇɚɰɪɬɚʁɩɪɚɜɟa ɢ b ɤɨʁɟ ɩɪɨɥɚɡɟ ɤɪɨɡ ɬɚɱɤɭ ȿ, ɬɚɤɨ ɞɚʁɟ a II m, b ŏ m ȿ m

ɂɧɬɟɪɧɟɬ ɚɞɪɟɫɚ ɧɚ ɤɨʁɨʁ ɦɨɠɟɲ ɞɚ ɩɪɨɧɚɻɟɲ ɫɥɢɱɧɟ ɡɚɞɚɬɤɟ:https:// dms.rs/kengur/zadaci/

50


САБИРАЊЕ И ОДУЗИМАЊЕ ДО 1000

TA

L

ōřŜŌőōŎŗ

O

R

ŖʼnŜŠőŅŎš

-P

ųũųŷŭũźũŪűŹũƁŻŹŷſűŽŹŮŶŮŪŹŷƐŮūŮŸűźŵŮŶűŵŸŷźŻżŸųŷŵ

U KA

ųũųŷŭũŷŭżŰűŵũƁŻŹŷſűŽŹŮŶŮŪŹŷƐŮūŮŸűźŵŮŶűŵŸŷźŻżŸųŷŵ ųũųŷŭũźũŪŮŹŮƁūűƁŮŭūŷſűŽŹŮŶűžűŻŹŷſűŽŹŮŶűžŪŹŷƐŮūũ

ED

ŭũŹŮƁũūũƁŰũŭũŻųŮźũŭūŮŷŸŮŹũſűƐŮ


ɉɂɋɆȿɇɈ ɋȺȻɂɊȺȵȿɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ: 437 + 352 Ʉʂɭɱɧɟɪɟɱɢ: ɫɚɛɢɪɚʃɟɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000

ɉɨɞɫɟɬɢʄɟɦɨɫɟ ɤɚɤɨɫɦɨ ɭɫɦɟɧɢɦ ɩɨɫɬɭɩɤɨɦɫɚɛɢɪɚɥɢ ɬɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɟ. 437 + 352 = 437 + (300 + 50 + 2) = (437 + 300) + 50 + 2 = (737 + 50) + 2 = 787 + 2 = 789 ɂɥɢɨɜɚɤɨ: 437 + 352 = (400 + 30 + 7) + (300 + 50 + 2) = (400 + 300) + (30 + 50) + (7 + 2) = 789 Ɍɪɨɰɢɮɪɟɧɟɛɪɨʁɟɜɟ ɦɨɠɟɦɨ ɫɚɛɪɚɬɢ ɢɧɚɞɪɭɝɢ ɧɚɱɢɧ.

ɋȾȳ

Ɉɜɚʁɩɨɫɬɭɩɚɤ ɫɟ ɡɨɜɟ ɩɢɫɦɟɧɨɫɚɛɢɪɚʃɟ.

400 + 30 + 7 + 300 + 50 + 2 700 + 80 + 9

R

437 +352 789

TA

Ɣ ɉɪɜɨɫɟɫɚɛɟɪɭ ʁɟɞɢɧɢɰɟ, ɡɚɬɢɦ ɞɟɫɟɬɢɰɟ ɢ ɧɚ ɤɪɚʁɭɫɬɨɬɢɧɟ

L

Ɣ ɋɚɛɢɪɤɟ ɡɚɩɢɫɭʁɟɦɨʁɟɞɚɧɢɫɩɨɞɞɪɭɝɨɝ, ɚɥɢ ɬɚɤɨɞɚɫɭʁɟɞɢɧɢɰɟ ɡɚɩɢɫɚɧɟ ɢɫɩɨɞʁɟɞɢɧɢɰɚ, ɞɟɫɟɬɢɰɟ ɢɫɩɨɞɞɟɫɟɬɢɰɚ, ɚɫɬɨɬɢɧɟ ɢɫɩɨɞɫɬɨɬɢɧɚ

ȳ 7

3

5

2

7

8

9

1. ɂɡɪɚɱɭɧɚʁ

ɋɚɛɢɪɚɦɨɞɟɫɟɬɢɰɟ 3+5=8

Ȼɟɡ ɬɚɛɥɢɰɟ ɢɡɝɥɚɞɚ ɨɜɚɤɨ:

437 +352 789

ɋɚɛɢɪɚɦɨɫɬɨɬɢɧɟ: 4+3=7

5 1 6 + 2 7 2

ED

3 4 8 + 2 3 1

ɋɚɛɢɪɚɦɨ ʁɟɞɢɧɢɰɟ 7+2=9

-P

Ⱦ 3

U KA

+

ɋ 4

O

Ɣ Ɇɨɠɟɦɨ ɤɨɪɢɫɬɢɬɢ ɬɚɛɥɢɰɭɫɚ ɨɡɧɚɱɟɧɢɦ ɫɬɨɬɢɧɚɦɚ (ɋ ɞɟɫɟɬɢɰɚɦɚ Ⱦ ɢ ʁɟɞɢɧɢɰɚɦɚ ȳ).

4 5 3 + 4 3 6

7 6 4 + 2 3 4

6 3 5 + 3 6 3

8 0 6 + 1 9 2

Ɂɛɢɪ ɦɨɠɟɦɨ ɞɚ ɨɞɪɟɞɢɦɨ ɢ ɤɚɞɚ ɫɚɛɢɪɤɟ ɡɚɩɢɲɟɦɨ ɭ ɢɫɬɨɦ ɪɟɞɭ. ɂɨɜɨ ʁɟɩɢɫɦɟɧɨ ɫɚɛɢɪɚʃɟ. 437 + 352=

ɋɚɛɢɪɚɦɨʁɟɞɢɧɢɰɟ: 7 + 2 = 9, ɰɢɮɪɭ 9 ɩɢɲɟɦɨ ɦɚɥɨ ɞɚʂɟ ɨɞ ɡɧɚɤɚ ʁɟɞɧɚɤɨɫɬɢ.

9

437 + 352= ɋɚɛɢɪɚɦɨɞɟɫɟɬɢɰɟ: 3 + 5 = 8, ɰɢɮɪɭ 8 ɩɢɲɟɦɨ ɢɫɩɪɟɞ ɰɢɮɪɟ ʁɟɞɢɧɢɰɚ.

89

437 + 352= 789 ɋɚɛɢɪɚɦɨ ɫɬɨɬɢɧɟ: 4 + 3 = 7, ɰɢɮɪɭ 7 ɩɢɲɟɦɨ ɢɫɩɪɟɞ ɰɢɮɪɟ ɞɟɫɟɬɢɰɚ

2. ɂɡɪɚɱɭɧɚʁɡɛɢɪ ɧɚ ɝɨɪɟɩɪɢɤɚɡɚɧ ɧɚɱɢɧ. ɚ) 246 + 153 = ____;

ɛ) 425 + 231 = ____;

ɜ) 184 + 515 = ____;

ɝ) 631 + 367 = ____;

ɞ) 802 + 197 = ____;

ɻ) 773 + 215 = ____;

ɟ) 546 + 233 =____;

ɠ 404 + 385 = ____.

52


ɉɂɋɆȿɇɈ ɈȾɍɁɂɆȺȵȿ ɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ: 698 – 352 Ʉʂɭɱɧɟɪɟɱɢ: ɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000

ɉɨɞɫɟɬɢʄɟɦɨɫɟ ɤɚɤɨɫɦɨ ɭɫɦɟɧɢɦɩɨɫɬɭɩɤɨɦɨɞɭɡɢɦɚɥɢ ɬɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɢ. 698 – 345 = 698 – (300 + 40 + 5) = (698 – 300) – 40 – 5 = (398 – 40) – 5 = 358 – 5 = 353 Ɉɞɭɦɚʃɟɧɢɤɚɩɪɜɨ ɨɞɭɡɢɦɚɦɨɫɬɨɬɢɧɟ, ɡɚɬɢɦɞɟɫɟɬɢɰɟ,ɩɚ ɬɟɤ ɨɧɞɚʁɟɞɢɧɢɰɟ ɭɦɚʃɢɨɰɚ.

L

Ɍɪɨɰɢɮɪɟɧɟɛɪɨʁɟɜɟ ɦɨɠɟɦɨ ɨɞɭɡɢɦɚɬɢ ɢɧɚɞɪɭɝɢ ɧɚɱɢɧ.

TA

Ɣ ɍɦɚʃɢɥɚɰɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞɭɦɚʃɟɧɢɤɚ, ɨɜɚɤɨ: ʁɟɞɢɧɢɰɟ ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞʁɟɞɢɧɢɰɚ, ɞɟɫɟɬɢɰɟ ɢɫɩɨɞɞɟɫɟɬɢɰɚ, ɚɫɬɨɬɢɧɟ ɢɫɩɨɞɫɬɨɬɢɧɚ. Ɣ ɉɪɜɨ ɫɟ ɨɞɭɡɢɦɚʁɭʁɟɞɢɧɢɰɟ, ɡɚɬɢɦ ɞɟɫɟɬɢɰɟ ɢ ɧɚ ɤɪɚʁɭɫɬɨɬɢɧɟ. Ɉɜɚʁɩɨɫɬɭɩɚɤɫɟ ɡɨɜɟ ɩɢɫɦɟɧɨ ɨɞɭɡɢɦɚʃɟ.

ɋȾȳ

600 + 90 + 8 – 300  40 – 5 300 + 50 + 3

O

R

698 –345 353

Ɣ Ɇɨɠɟɦɨ ɤɨɪɢɫɬɢɬɢ ɬɚɛɥɢɰɭɫɚ ɨɡɧɚɱɟɧɢɦ ɫɬɨɬɢɧɚɦɚ (ɋ ɞɟɫɟɬɢɰɚɦɚ Ⱦ ɢ ʁɟɞɢɧɢɰɚɦɚ ȳ).

6

9

8

3

4

5

3

5

3

Ɉɞɭɡɢɦɚɦɨʁɟɞɢɧɢɰɟ: 8– 5=3

-P

ȳ

Ɉɞɭɡɢɦɚɦɨɞɟɫɟɬɢɰɟ 9– 4=5

U KA

ɋ Ⱦ

Ȼɟɡ ɬɚɛɥɢɰɟ ɢɡɝɥɚɞɚ ɨɜɚɤɨ:

Ɉɞɭɡɢɦɚɦɨʁɟɞɢɧɢɰɟ: 6– 3=3

698 –345 353

1. Ɉɞɪɟɞɢ ɫɥɟɞɟʄɟ ɪɚɡɥɢɤɟ: 2 9 6 – 1 8 4

ED

3 1 7 – 1 0 5

8 2 5 – 5 1 3

9 6 6 – 7 4 5

7 8 9 – 5 7 6

8 7 8 – 7 5 6

Ɋɚɡɥɢɤɭ ɦɨɠɟɦɨɞɚ ɨɞɪɟɞɢɦɨ ɢ ɤɚɞɚ ɭɦɚʃɟɧɢɤɢ ɭɦɚʃɢɥɚɰɡɚɩɢɲɟɦɨ ɭ ɢɫɬɨɦ ɪɟɞɭ. ɂ ɨɜɨ ʁɟ ɩɢɫɦɟɧɨ ɨɞɭɡɢɦɚʃɟ. 549 – 312=

7

Ɉɞɭɡɢɦɚɦɨʁɟɞɢɧɢɰɟ: 9 – 2 = 7, ɰɢɮɪɭ 7 ɩɢɲɟɦɨ ɦɚɥɨɞɚʂɟ ɨɞ ɡɧɚɤɚ ʁɟɞɧɚɤɨɫɬɢ.

549 – 312=

37

549 – 312= 237

Ɉɞɭɡɢɦɚɦɨɞɟɫɟɬɢɰɟ: 4 – 1 = 3, ɰɢɮɪɭ 3 ɩɢɲɟɦɨ ɢɫɩɪɟɞ ɰɢɮɪɟʁɟɞɢɧɢɰɚ.

Ɉɞɭɡɢɦɚɦɨ ɫɬɨɬɢɧɟ: 5 – 3 = 2, ɰɢɮɪɭ 2 ɩɢɲɟɦɨ ɢɫɩɪɟɞ ɰɢɮɪɟɞɟɫɟɬɢɰɚ.

2. Ɂɚɩɢɲɢ ɭɦɚʃɟɧɢɤɢ ɭɦɚʃɢɥɚɰ ɭ ɢɫɬɨɦ ɪɟɞɭ ɢ ɨɞɪɟɞɢɪɚɡɥɢɤɟ: ɚ) 746 – 513 = ____;

ɛ) 974 – 653 = ____;

ɜ) 848 – 317 = ____;

ɜ) 966 – 754 = ____;

ɝ) 418 – 115 = ____;

ɞ) 547 – 326 = ____;

ɻ) 759 – 543 = ____;

ɟ) 888 – 642 = ____.

53


ɉɂɋɆȿɇɈ ɋȺȻɂɊȺȵȿ ɂ ɈȾɍɁɂɆȺȵȿ ɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ 437 + 352; 698 – 345 Ʉʂɭɱɧɟɪɟɱɢ: ɫɚɛɢɪɚʃɟɢɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 100

1. Ⱦɚɬɟ ɡɛɢɪɨɜɟ ɢɡɪɚɱɭɧɚʁɧɚɩɪɢɤɚɡɚɧɟ ɧɚɱɢɧɟ: 6 2 8 + 1 7 1

4 6 3 + 3 2 1

2 5 7 + 7 3 2

3 5 4 + 2 4 4 = 5 2 8 + 2 5 1 =

8 6 5 + 1 2 3

3 14 + 6 8 4

7 2 4 + 2 7 3

1 6 4 + 7 3 5 =

L

8 7 1 + 1 2 7 = 3. ɐɟɧɚ ɫɜɟɫɤɟ ʁɟ 145ɞɢɧɚɪɚ. ɒɟɫɬɚɪ ʁɟ ɡɚ 253ɞɢɧɚɪɚɫɤɭɩʂɢ ɨɞɫɜɟɫɤɟ. ɂɡɪɚɱɭɧɚʁɰɟɧɭɲɟɫɬɚɪɚ.

TA

2. ɋɚɲɚ ʁɟ ɤɭɩɢɨ ɤɚɩɭ ɢɧɚɨɱɚɪɟ ɡɚɩɥɢɜɚʃɟ. Ʉɨɥɢɤɢ ʁɟ ɛɢɨ ɪɚɱɭɧɡɚ ɤɭɩʂɟɧɟ ɫɬɜɚɪɢ?

523 ɞɢɧ.

Ɉɞɝɨɜɨɪ: _________________________

-P

Ɉɞɝɨɜɨɪ: ________________________

O

R

365 ɞɢɧ

________________________________

_________________________________

8 3 4 – 3 0 3

3 9 5 – 1 7 4

4 9 5 – 2 7 4

6 4 7 – 5 2 4

5 4 7– 3 1 6 = 8 2 5– 6 0 3 =

9 4 6 – 3 3 7

ED

7 8 9 – 6 5 1

U KA

4. Ⱦɚɬɟ ɪɚɡɥɢɤɟ ɢɡɪɚɱɭɧɚʁɧɚɩɪɢɤɚɡɚɧɟɧɚɱɢɧɟ

5. ɍɪɨɲʁɟɢɦɚɨ 789ɞɢɧɚɪɚ. Ʉɭɩɢɨʁɟ ɢɝɪɚɱɤɭ ɡɚ 625ɞɢɧɚɪɚ. Ʉɨɥɢɤɨ ɞɢɧɚɪɚ ɦɭʁɟ ɨɫɬɚɥɨ?

4 6 9– 2 5 8 = 9 8 7– 73 5 = 6. ɍɩɢɲɢ ɨɞɝɨɜɚɪɚʁɭʄɟɰɢɮɪɟ ɭ ɨɛɨʁɟɧɢɦɩɨʂɢɦɚ.

Ɉɞɝɨɜɨɪ: _________________________ _________________________

7.

ɍɫɜɚɤɨɦ ɫɚɛɢɪɚʃɭɧɚɻɢ ɜɪɟɞɧɨɫɬ ɡɚ , ɢ .

– 7 4 6 1 3 2

6 3 + 4 1 7 8

– 5 2 4 3 6 4

1 6 + 3 3 8 1

= __ = __ = __

+ 7 9 8

54

+ 5 7 6

= __ = __ = __

5 9 4 6 – 0 2 9 –

7 5

6

1


ɉɂɋɆȿɇɈ ɋȺȻɂɊȺȵȿ ɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ: 538 + 245 Ʉʂɭɱɧɟɪɟɱɢ: ɫɚɛɢɪɚʃɟɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000

ɉɨɞɫɟɬɢʄɟɦɨ ɫɟ ɤɚɤɨɫɦɨɫɚɛɢɪɚɥɢ ɬɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɟ ɱɢʁɢʁɟ ɡɛɢɪʁɟɞɢɧɢɰɚ ɜɟʄɢɨɞ 9. 538 + 245 = 538 + (200 + 40 + 5) = (538 + 200) + 40 + 5 = (738 + 40) + 5 = 778 + 5 = 783 ɂɥɢɨɜɚɤɨ: 538 + 245 = (500 + 30 + 8) + (200 + 40 + 5) = (500 + 200) + (30 + 40) + (8 + 5) = 700 + 70 + 13 = 783 ɋȾȳ

ɂɥɢɤɪɚʄɟ, ɩɨɦɨʄɭ ɬɚɛɥɢɰɟ:

ɋɚɛɢɪɚɦɨʁɟɞɢɧɢɰɟ: 8 + 5 = 13, 13ȳ = 1Ⱦ 3ȳ ɐɢɮɪɭ 3 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ʁɟɞɢɧɢɰɚ, ɚʁɟɞɧɭ ɞɟɫɟɬɢɰɭ ɞɨɞɚʁɟɦɨ ɞɟɫɟɬɢɰɚɦɚ.

ȳ

R

ɋ Ⱦ 1

3 4

8 5

7

8

3

ɋɚɛɢɪɚɦɨɞɟɫɟɬɢɰɟ: 1 + 3 + 4 = 8. ɐɢɮɪɭ 8 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɞɟɫɟɬɢɰɚ.

O

+

5 2

10

500 + 30 + 8 + 200 + 40 + 5 700 + 80 + 3

TA

ɞɟɱɚɤ

538 +245 783

8 + 5 = 13

L

ɋɚɞɚ ʄɟɦɨɩɢɫɦɟɧɢɦ ɩɨɫɬɭɩɤɨɦ ɨɞɪɟɞɢɬɢ ɡɛɢɪɛɪɨʁɟɜɚ 53ɢ5.

13 = 10 + 3

Ȼɟɡ ɬɚɛɥɢɰɟ 1

538 + 245 783

-P

ɋɚɛɢɪɚɦɨɫɬɨɬɢɧɟ: 5 + 2 = 7. ɐɢɮɪɭ 7 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɫɬɨɬɢɧɚ

U KA

1. Ɂɚɩɢɲɢ ɫɚɛɢɪɤɟ ʁɟɞɚɧɢɫɩɨɞɞɪɭɝɨɝ ɢ ɨɞɪɟɞɢ ʃɢɯɨɜɡɛɢɪ. t 249 ɢ 246; t 417 ɢ 378; t 526 ɢ 456; t 608 ɢ 288;

t 819 ɢ 175.

ED

‡ ɋɚɛɢɪɤɟ ɡɚɩɢɫɭʁɟɦɨ ɭ ɢɫɬɨɦ ɪɟɞɭ. 538 + 245=

3

ɋɚɛɢɪɚɦɨ ʁɟɞɢɧɢɰɟ:

8 + 5 = 13 13ȳ 1Ⱦ 3ȳ, ɰɢɮɪɭ 3 ɩɢɲɟɦɨ ɦɚɥɨ ɞɚʂɟɨɞ ɡɧɚɤɚʁɟɞɧɚɤɨɫɬɢ ȳɟɞɧɭ ɞɟɫɟɬɢɰɭ ɞɨɞɚʁɟɦɨɞɟɫɟɬɢɰɚɦɚ

538 + 245=

83

ɋɚɛɢɪɚɦɨɞɟɫɟɬɢɰɟ: 3 + 4 + 1 = 8, ɰɢɮɪɭ 8 ɩɢɲɟɦɨ ɢɫɩɪɟɞ ɰɢɮɪɟ ʁɟɞɢɧɢɰɚ.

538 + 245= 783 ɋɚɛɢɪɚɦɨ ɫɬɨɬɢɧɟ: 5 + 2 = 7 ɰɢɮɪɭ 7 ɩɢɲɟɦɨ ɢɫɩɪɟɞ ɰɢɮɪɟ ɞɟɫɟɬɢɰɚ

2. Ɉɞɪɟɞɢ ɞɚɬɟ ɡɛɢɪɨɜɟ, ɪɚɱɭɧɚʁɭʄɢ ɭ ɢɫɬɨɦ ɪɟɞɭ. t 246 + 156 = ____; t 425 + 237 = ____ ; t 184 + 519 = ____; t 638 + 358 = ____; t 802 + 198 = ____; t 773 + 219 = ____; t 237 + 655 = ____; t 715 + 169 = ____. 3. Ɇɚʁɚ ɢɦɚ 269 ɞɢɧɚɪɚ. ɀɟɥɢɞɚɤɭɩɢɚɥɛɭɦ ɡɚɮɨɬɨɝɪɚɮɢʁɟ, ɚɥɢ ʁɨʁɧɟɞɨɫɬɚʁɟ ʁɨɲ 117ɞɢɧɚɪɚ. Ʉɨɥɢɤɚʁɟ ɰɟɧɚ ɬɨɝ ɚɥɛɭɦɚ?

55


ɉɂɋɆȿɇɈ ɋȺȻɂɊȺȵȿɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ: 538 + 245 Ʉʂɭɱɧɟɪɟɱɢ: ɫɚɛɢɪɚʃɟɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000

1. Ɉɞɪɟɞɢ ɡɛɢɪɧɚɩɪɢɤɚɡɚɧɧɚɱɢɧ 3 2 8 + 2 4 7

5 3 6 + 4 4 5

4 6 9 + 3 2 7

845 + 145 = ____

7 8 4 + 2 1 6

3 6 7 + 5 0 4

2 5 8 + 6 2 8

517 + 367 = ____

623 + 249 = ____

TA

L

768 + 209 = ____

ɍɩɪɜɨʁɤɨɲɧɢɰɢɫɟɧɚɥɚɡɢ 134ɩɱɟɥɟ, ɚ ɭɞɪɭɝɨʁɡɚ 127ɩɱɟɥɚɜɢɲɟ. ɍ ɬɪɟʄɨʁ ɤɨɲɧɢɰɢɫɟ ɧɚɥɚɡɢ 129ɩɱɟɥɚ. Ʉɨɥɢɤɨ ɢɦɚ ɩɱɟɥɚ ɭɫɜɟ ɬɪɢ ɤɨɲɧɢɰɟ"

O

R

3.

2. ɋɚɛɢɪɚʁɭ ɢɫɬɨɦ ɪɟɞɭ:

Ⱦɚɬɢɫɭɩɨɞɚɰɢɨ ɭɞɚʂɟɧɨɫɬɢ ɢɡɦɟɻɭɧɟɤɢɯ ɝɪɚɞɨɜɚ ɭɋɪɛɢʁɢ Ʉɨɥɢɤɨɤɢɥɨɦɟɬɚɪɚ ɩɪɟɻɟɜɨɡɚɱɚɭɬɨɦɨɛɢɥɚ ɚɤɨ ɜɨɡɢ ɨɞʁɟɞɧɨɝɞɨɞɪɭɝɨɝ ɝɪɚɞɚ ɭ ɨɛɚɩɪɚɜɰɚ"

U KA

4.

-P

Ɉɞɝɨɜɨɪ: ____________________________________

ED

Ʉɪɚʂɟɜɨ – ɋɭɛɨɬɢɰɚ 348 km

_____________________

ɑɚɱɚɤ– ɇɨɜɢ ɋɚɞ 229 km

ȳɚɝɨɞɢɧɚ – Ʌɟɫɤɨɜɚɰ 144 km

_____________________

_____________________

7. Ʉɨʁɚɢɫɬɚ ɰɢɮɪɚ ɦɨɪɚɛɢɬɢ ɭɩɢɫɚɧɚ ɭ ɨɛɚɩɪɚɡɧɚɩɨʂɚ, ɞɚɛɢɫɚɛɢɪɚʃɟ ɛɢɥɨ ɬɚɱɧɨ"

6. ɋɚɦɨʁɟɞɚɧɩɭɬ ɨɞ ɡɟɰɚɞɨɲɚɪɝɚɪɟɩɟ, ɩɪɨɥɚɡɢ ɩɪɟɤɨɛɪɨʁɟɜɚ ɱɢʁɢʁɟ ɡɛɢɪ 584. ɉɪɨɧɚɻɢ ɬɚʁɩɭɬ ɢɨɛɨʁɢɝɚɰɪɜɟɧɨɦɛɨʁɨɦ.

ɚ)

1 2 + 3 4 4 7 6

ɜ)

56

4 4 + 2 3 6 8 2

ɝ) 5 1 2 3 7 5 8

___ + ___ = 584

ɛ)

7 4 + 2 2 9 7 4


ɉɂɋɆȿɇɈ ɈȾɍɁɂɆȺȵȿ ɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ: 674 – 238 Ʉʂɭɱɧɟɪɟɱɢ: ɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 000

ɉɨɞɫɟɬɢʄɟɦɨ ɫɟ ɤɚɤɨ ɫɦɨ ɨɞɭɡɢɦɚɥɢ ɬɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɟɱɢʁɢʁɟɛɪɨʁ ʁɟɞɢɧɢɰɚ ɭɦɚʃɟɧɢɤɚ ɦɚʃɢɨɞ ɛɪɨʁɚ ʁɟɞɢɧɢɰɚ ɭɦɚʃɢɨɰɚ. 674 – 238 = 674 – (200 + 30 + 8) = (674 – 200) – 30 – 8 = 474 – 30 – 8 = 444 – 8 = 436 Ɋɚɡɥɢɤɭɛɪɨʁɟɜɚ 674 ɢ 238 ɨɞɪɟɞɢʄɟɦɨɩɢɫɦɟɧɢɦɩɨɫɬɭɩɤɨɦ, ɨɜɚɤɨ: 0

70 – 0 = 60 0 + 4 = 4  – 8 = 6

ɂɥɢɤɪɚʄɟ,ɩɨɦɨʄɭ ɬɚɛɥɢɰɟ:

14

7 3

4 8

4

3

6

R

6

6 2

ȳɟɞɧɭ ɞɟɫɟɬɢɰɭ ɫɦɨɩɨɡɚʁɦɢɥɢ, ɩɚ ɧɚɦʁɟ ɨɫɬɚɥɨ6 ɞɟɫɟɬɢɰɚ 6 – 3 = 3, ɰɢɮɪɭ 3 ɩɢɲɟɦɢɫɩɨɞ ɞɟɫɟɬɢɰɚ. 6 – 2 = 4, ɰɢɮɪɭ 4 ɩɢɲɟɦɢɫɩɨɞ ɫɬɨɬɢɧɚ

-P

Ɉɞ 4ʁɟɞɢɧɢɰɟ ɧɟ ɦɨɠɟɦɨɨɞɭɡɟɬɢ 8 ʁɟɞɢɧɢɰɚ,ʁɟɪʁɟ ɦɚʃɟ ɨɞ 8. Ɂɚɬɨ ɩɨɡɚʁɦʂɭʁɟɦɨ ɞɟɫɟɬɢɰɭ ɢ ɩɪɟɬɜɚɪɚɦɨʁɟ ɭ 0 ʁɟɞɢɧɢɰɚ: 0ȳ + ȳ = ȳ  – 8 = 6, ɰɢɮɪɭ 6 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ʁɟɞɢɧɢɰɚ.

ȳ

O

ɋ Ⱦ

L

60

600 + 70 + 4 – 200 – 30 – 8 400 + 30 + 6

TA

ɋȾȳ

674 –238 436

. ɉɨɬɩɢɲɢɭɦɚʃɢɥɚɰɢɫɩɨɞ ɭɦɚʃɟɧɢɤɚ ɢ ɨɞɪɟɞɢ ɫɥɟɞɟʄɟ ɪɚɡɥɢɤɟ:

U KA

Ø 837 – 9; Ø 374 – 48; Ø 983 – 565; Ø 782 – 346; Ø 87 – 735; Ø 966 – 527. Ɋɚɡɥɢɤɭ ɞɜɚ ɛɪɨʁɚ ɦɨɠɟɦɨ ɨɞɪɟɞɢɬɢ ɢ ɤɪɚʄɢɦ ɩɭɬɟɦ, ɨɜɚɤɨ:

ȳ

6 2

7 3

4 8

4

3

6

ɍɨɱɚɜɚɦɨ ɞɚʁɟ ɦɚʃɟ ɨɞ 8. Ɂɚɬɨɩɨɫɦɚɬɪɚɦɨ ɨɜɚɤɨ: 4 – 8 = 6, 6 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ʁɟɞɢɧɢɰɚ. ɂɡɧɚɞ 7Ⱦ ɫɬɚɜʂɚɦɨ ɬɚɱɤɭ. Ɍɚɱɤɨɦ ɢɡɧɚɞ ɛɪɨʁɚɨɡɧɚɱɚɜɚɦɨ ɞɚʁɟ ɬɚʁ ɛɪɨʁ ɡɚ  ɦɚʃɢ!

ED

ɋ Ⱦ

674 – 238 436

6 – 3 = 3, 3 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɞɟɫɟɬɢɰɚ 6 – 2 = 4, 4 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɫɬɨɬɢɧɚ

ɍɦɚʃɟɧɢɤ ɢ ɭɦɚʃɢɥɚɰɡɚɩɢɫɭʁɟɦɨ ɭ ɢɫɬɨɦ ɪɟɞɭ ɢ ɪɚɱɭɧɚɦɨ ɧɚ ɢɫɬɢ ɧɚɱɢɧ 674 – 238 = _ _ 6

674 – 238 = _ 36

674 – 238 = 436

2. ɉɨɬɩɢɲɢɭɦɚʃɢɥɚɰɢɫɩɨɞ ɭɦɚʃɟɧɢɤɚ ɢ ɨɞɪɟɞɢ ɪɚɡɥɢɤɭɛɪɨʁɟɜɚ ɧɚ ɤɪɚʄɢ ɧɚɱɢɧ Ø 564 ɢ 237; Ø 763 ɢ 524; Ø 948 ɢ 409;

Ø 872 ɢ 557; Ø 39 ɢ 56;

Ø 753 ɢ 67.

3. Ɋɚɱɭɧɚʁɭ ɢɫɬɨɦ ɪɟɞɭ ɢ ɨɞɪɟɞɢ ɪɚɡɥɢɤɟ: Ø 485 – 57 = ___;

Ø 588 – 469 = ___; Ø 3 – 54 = ___; Ø 830 – 8 = ___;

Ø 762 – 634 = ___;

Ø 945 – 39 = ___; Ø 954 – 738 = ___; Ø 862 – 439 = ___.

57


ɉɂɋɆȿɇɈ ɈȾɍɁɂɆȺȵȿɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ: 674 – 238 Ʉʂɭɱɧɟɪɟɱɢ: ɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000

1. ɉɨɩɭɧɢɬɚɛɥɢɰɭ ɨɞɝɨɜɚɪɚʁɭʄɢɦ ɪɚɡɥɢɤɚɦɚ. ɚ 742 b 536 a–b

561 438

467 248

874 727

658 429

751 237

427 209

551 324

933 715

546 319

TA

L

2. ɍ ɢɡɥɨɝɭɫɭ ɞɜɟ ɦɚɪɚɦɟ. ȳɟɞɧɚ ɤɨɲɬɚ 748ɞɢɧɚɪɚ, ɚ ɞɪɭɝɚ 629ɞɢɧɚɪɚ. Ʉɨɥɢɤɚʁɟ ɪɚɡɥɢɤɚ ɭʃɢɯɨɜɢɦ ɰɟɧɚɦɚ?

Ɉɞɝɨɜɨɪ: _________________________________________

Ʉɨʁɢʁɟ ɛɪɨʁɡɚ 324 ɦɚʃɢ ɨɞ ɛɪɨʁɚ 861?

Ʌ

O

t

R

Ɋɟɲɢɬɚɱɧɨ ɫɥɟɞɟʄɟ ɡɚɞɚɬɤɟ. ɉɪɨɧɚɻɢ ɪɟɡɭɥɬɚɬɟ ɭ ɤʂɭɱɭɡɚɞɚɬɤɚ ɢ ɭɩɢɲɢ ɨɞɝɨɜɚɪɚʁɭʄɚɫɥɨɜɚ.Ɉɬɤɪɢʄɟɲ ɪɟɲɟʃɟ ɡɚɝɨɧɟɬɤɟ.

3.

Ɇɚʁɚ ɢ ɋɚɲɚ ɫɭ ɤɭɩɢɥɢ ɩɟɪɧɢɰɟ. Ɇɚʁɢɧɚɩɟɪɧɢɰɚ ʁɟ ɤɨɲɬɚɥɚ 755ɞɢɧɚɪɚ, ɚɋɚɲɢɧɚ 549ɞɢɧɚɪɚ. Ɂɚ ɤɨɥɢɤɨ ɞɢɧɚɪɚ ʁɟ ɋɚɲɢɧɚ ɩɟɪɧɢɰɚʁɟɮɬɢɧɢʁɚ?

U KA

t

-P

Oɞɝɨɜɨɪ: __________________________________________

Ɉ

Oɞɝɨɜɨɪ: __________________________________________ t

ȼɢɫɢɧɚ ɯɪɚɫɬɚʁɟ 216 cm, ɚɜɢɫɢɧɚʁɟɥɟʁɟ 435 cm. Ɂɚ ɤɨɥɢɤɨɰɟɧɬɢɦɟɬɚɪɚʁɟ ʁɟɥɚɜɢɲɚ ɨɞ ɯɪɚɫɬɚ?

Ƚ

Oɞɝɨɜɨɪ: __________________________________________ ɍɪɨɲɱɢɬɚ ɤʃɢɝɭ ɤɨʁɚ ɢɦɚ 345ɫɬɪɚɧɚ. ɉɪɨɱɢɬɚɨʁɟ 127ɫɬɪɚɧɚ.Ʉɨɥɢɤɨ ɫɬɪɚɧɚ ɬɪɟɛɚɞɚɩɪɨɱɢɬɚɞɨ ɤɪɚʁɚ ɤʃɢɝɟ?

ED

t

ɂ

Oɞɝɨɜɨɪ: __________________________________________

218 219 537 206 4.

Ɂɚɜɪɲɟɧɨ ʁɟ ɲɤɨɥɫɤɨ ɬɚɤɦɢɱɟʃɟ ɭ ɤɜɢɡɭ ɡɧɚʃɚ. Ʌɟɧɚ,Ɇɢɥɨɲɢ Ɉɝʃɟɧɫɭ ɨɫɜɨʁɢɥɢ ɩɪɜɚ ɬɪɢ ɦɟɫɬɚ. Ʌɟɧɚʁɟ ɨɫɜɨʁɢɥɚ 455ɛɨɞɨɜɚ.Ɇɢɥɨɲʁɟ ɨɫɜɨʁɢɨ 128ɛɨɞɨɜɚ ɦɚʃɟ ɨɞ Ʌɟɧɟ, ɚ Ɉɝʃɟɧ219ɛɨɞɨɜɚɜɢɲɟ ɨɞɆɢɥɨɲɚ.Ʉɨʁɟ ɩɨɛɟɞɧɢɤɨɜɨɝɤɜɢɡɚ"

Ɉɞɝɨɜɨɪ: ________________________________________

58


ɉɂɋɆȿɇɈɋȺȻɂɊȺȵȿ ɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ: 185 + 163 Ʉʂɭɱɧɟɪɟɱɢ: ɫɚɛɢɪɚʃɟɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000

ɉɨɞɫɟɬɢʄɟɦɨ ɫɟɤɚɤɨɫɦɨ ɫɚɛɢɪɚɥɢ ɬɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɟ ɱɢʁɢʁɟ ɡɛɢɪ ɞɟɫɟɬɢɰɚ ɜɟʄɢ ɨɞ 9. 274 + 155 = 274 + (100 + 50 + 5) = (274 + 100) + 50 + 5 = (374 + 50) + 5 = 424 + 5 = 429 ɂɥɢ ɨɜɚɤɨ: 274 + 155 = (200 + 70 + 4) + (100 + 50 + 5) = (200 + 100) + (70 + 50) + (4 + 5) = 300 + 120 + 9 = 429

Ɣ Ɇɢʂɚɧɚʁɟ ɩɪɨɱɢɬɚɥɚ ɤʃɢɝɭ ɡɚɞɜɟ ɧɟɞɟʂɟ. ɍɩɪɜɨʁɧɟɞɟʂɢʁɟɩɪɨɱɢɬɚɥɚ 185ɫɬɪɚɧɚ, ɚ ɭ ɞɪɭɝɨʁ163ɫɬɪɚɧɟ. Ʉɨɥɢɤɨ ɫɬɪɚɧɚ ɢɦɚ ɤʃɢɝɚ ɤɨʁɭʁɟ Ɇɢʂɚɧɚ ɩɪɨɱɢɬɚɥɚ?

100

ɋȾȳ

100 + 80 + 5 + 100 + 60 + 3 300 + 40 + 8

185 +163 348

80 + 60 = 140 140 = 100 + 40

TA

L

Ɂɛɢɪ ɛɪɨʁɟɜɚ 185 ɢ 163 ɨɞɪɟɞɢʄɟɦɨ ɩɢɫɦɟɧɢɦ ɩɨɫɬɭɩɤɨɦɧɚ ɫɥɟɞɟʄɢ ɧɚɱɢɧ

R

Ʉʃɢɝɚ ɤɨʁɭɆɢʂɚɧɚɱɢɬɚ ɢɦɚ ___ɫɬɪɚɧɚ. ɂɥɢɤɪɚʄɟ, ɩɨɦɨʄɭ ɬɚɛɥɢɰɟ: ȳ

5 + 3 = 8, ɰɢɮɪɭ ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞʁɟɞɢɧɢɰɚ.

O

ɋ Ⱦ 1

5 3

8 + 6 = 14, 1Ⱦ = 1ɋ 4Ⱦ. ɐɢɮɪɭ 4 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɞɟɫɟɬɢɰɚ ɚ 1 ɫɬɨɬɢɧɭ ɞɨɞɚʁɟɦɨ ɫɬɨɬɢɧɚɦɚ.

3

4

8

1 + 1 + 1 = 3, ɰɢɮɪɭ 3 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɫɬɨɬɢɧɚ.

Ȼɟɡ ɬɚɛɥɢɰɟ ɢɡɝɥɟɞɚ ɨɜɚɤɨ: 1

185 + 163 348

1. Ɂɚɩɢɲɢ ɫɚɛɢɪɤɟ ʁɟɞɚɧɢɫɩɨɞ ɞɪɭɝɨɝ ɢɨɞɪɟɞɢ ʃɢɯɨɜɡɛɢɪ. t 372 ɢ 274; t 584 ɢ 235; t 394 ɢ 524; t 662 ɢ 265;

t 627 ɢ 291; t 785 ɢ 174;

t 475 ɢ 353; t 544 ɢ 264.

ɋɚɛɢɪɤɟ ɡɚɩɢɫɭʁɟɦɨ ɭ ɢɫɬɨɦ ɪɟɞɭ ɢ ɪɚɱɭɧɚɦɨɧɚ ɢɫɬɢɧɚɱɢɧ

ED

t

-P

8 6

U KA

+

1 1

185 + 163 = _ _ 8

Æ

185 + 163 = _ 48

Æ 185 + 163 = 348

ɍ ɫɥɟɞɟʄɢɦɡɚɞɚɰɢɦɚ, ɫɚɛɢɪɤɟ ɡɚɩɢɲɢɭ ɢɫɬɨɦ ɪɟɞɭ ɢ ɨɞɪɟɞɢ ʃɢɯɨɜɡɛɢɪ.

2. ɍɪɨɲʁɟ ɜɢɫɨɤ 75 cm, ɚʃɟɝɨɜɬɚɬɚʁɟ ɡɚ 132 cm ɜɢɲɢɨɞʃɟɝɚ. Ʉɨɥɢɤɨʁɟɜɢɫɨɤ ɍɪɨɲɟɜ ɬɚɬɚ? ________________

Ɉɞɝɨɜɨɪ: __________________________________________________

3. Ⱥɥɟɤɫɚ ɢɦɚ 253ɞɢɧɚɪɚ, ɚ Ɋɚɲɚɡɚ 165 ɞɢɧɚɪɚ ɜɢɲɟ. Ʉɨɥɢɤɨ ɞɢɧɚɪɚ ɢɦɚ Ɋɚɲɚ? ________________

Ɉɞɝɨɜɨɪ: __________________________________________________

4. Ɇɢɥɢɰɚ ʁɟ ɤɭɩɢɥɚɲɟɫɬɚɪ ɢɥɟʃɢɪ. ɐɟɧɚ ɲɟɫɬɚɪɚ ʁɟ 482ɞɢɧɚɪɚ, ɚɰɟɧɚɥɟʃɢɪɚ ʁɟ 135ɞɢɧɚɪɚ. Ʉɨɥɢɤɢ ʁɟ ɛɢɨ ɪɚɱɭɧɡɚ ɬɭ ɤɭɩɨɜɢɧɭ? ________________

Ɉɞɝɨɜɨɪ: __________________________________________________

59


ɉɂɋɆȿɇɈ ɋȺȻɂɊȺȵȿ ɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ 185 + 163 Ʉʂɭɱɧɟɪɟɱɢ ɫɚɛɢɪɚʃɟɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000

1. ɂɡɪɚɱɭɧɚʁ 6 7 2 + 2 6 3

3 4 5 + 3 9 2

2 4 2 + 6 8 7

7 9 5 +1 9 4

5 8 3 + 3 3 5

4 4 5 + 4 7 4

5 6 2 + 2 8 4

3 7 1 + 5 7 8

6 9 3 +1 8 3

7 7 7 + 1 5 2

5 2 6 + 3 8 3

TA

327 + 482 = ____

465 + 462 = ____

524 + 193 =____

O

743 + 175 = ____

U KA

-P

658 + 271 =____

R

2. ɂɡɜɪɲɢɫɚɛɢɪɚʃɚ ɢ ɨɛɨʁɢɰɪɬɟɠ 572 + 386 = ____

L

4 6 3 + 3 7 2

3. Ɉɞɪɟɞɢ ɡɛɢɪ ɪɚɱɭɧɚʁɭʄɢ ɭ ɢɫɬɨɦ ɪɟɞɭ

ɚ) 572 + 386 = ____; ɛ) 658 + 271 =____; ɜ) 465 + 462 = ____; ɝ) 524 + 193 =____. 4. Ɉɞɪɟɞɢ ɛɪɨʁɤɨʁɢʁɟ

_________________

ɌɨʁɟɛɪɨʁB___.

ɛ ɡɚ 555 ɜɟʄɢɨɞɛɪɨʁɚ 364;

_________________

ɌɨʁɟɛɪɨʁB___.

ED

ɚ ɡɚ 246 ɜɟʄɢɨɞɛɪɨʁɚ 572;

5. ɍɱɟɧɢɰɢ ʁɟɞɧɟɲɤɨɥɟ ɫɭ ɫɚɤɭɩɢɥɢ 246 kg ɫɬɚɪɟ ɯɚɪɬɢʁɟ, ɢ ɡɚ 193 kg ɜɢɲɟɩɥɚɫɬɢɱɧɟ ɚɦɛɚɥɚɠɟ. Ʉɨɥɢɤɨʁɟ ɭɤɭɩɧɨ ɤɢɥɨɝɪɚɦɚ ɬɨɝ ɨɬɩɚɞɚɫɚɤɭɩʂɟɧɨ" Ɉɞɝɨɜɨɪ _______________________________________________

6. ɍ ɨɛɨʁɟɧɚ ɩɨʂɚɧɚɩɢɲɢ ɨɞɝɨɜɚɪɚʁɭʄɟɰɢɮɪɟ. ɚ)

6 3 + 3 4 6 5

ɛ)

8 6 + 2 3 7 9

ɜ)

60

4 7 + 4 6 3 8

ɝ)

6 5 + 1 8 2 1


ɉɂɋɆȿɇɈ ɈȾɍɁɂɆȺȵȿ ɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ: 358 – 185 Ʉʂɭɱɧɟɪɟɱɢ: ɨɞɭɡɢɦɚʃɟɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000

ɉɨɞɫɟɬɢʄɟɦɨɫɟ ɤɚɤɨɫɦɨ ɨɞɭɡɢɦɚɥɢ ɬɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɟɱɢʁɢ ʁɟ ɛɪɨʁɞɟɫɟɬɢɰɚɭɦɚʃɟɧɢɤɚ ɦɚʃɢ ɨɞɛɪɨʁɚɞɟɫɟɬɢɰɚ ɭɦɚʃɢɨɰɚ. 539 – 264 = 539 – (200 + 60 + 4) = (539 – 200) – 60 – 4 = (339 – 60) – 4 = 279 – 4 = 275 ‡ ɍʁɟɞɧɨɦ ɜɨʄʃɚɤɭ ɭɛɪɚɧɨ ʁɟ 358 kg ɜɢɲɚʃɚ ɢ 185 kg ɬɪɟɲɚʃɚ. Ʉɨɥɢɤɨ ɤɢɥɨɝɪɚɦɚʁɟɜɢɲɟ ɭɛɪɚɧɨ ɜɢɲɚʃɚ ɨɞ ɬɪɟɲɚʃɚ? Ɋɚɡɥɢɤɭɛɪɨʁɟɜɚ 358 ɢ 185 ɨɞɪɟɞɢʄɟɦɨɩɢɫɦɟɧɢɦɩɨɫɬɭɩɤɨɦ, ɨɜɚɤɨ:

TA

L

ɋȾȳ 300 – 100 = 200 200 100 300 + 50 + 8 358 100 + 50 = 150 – 100 – 80 – 5 –185 150 – 80 = 70 100 + 70 + 3 173 Ɣ ȼɢɲɚʃɚ ʁɟ ɭɛɪɚɧɨ ɡɚ 173 kg ɜɢɲɟɧɟɝɨ ɬɪɟɲɚʃɚ.

ɋ Ⱦ

ȳ

8 – 5 = 3, ɰɢɮɪɭ 3ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ʁɟɞɢɧɢɰɚ.

15

3 1

5 8

8 5

Ɉɞ 5 ɞɟɫɟɬɢɰɚɧɟ ɦɨɠɟɦɨ ɨɞɭɡɟɬɢ 8 ɞɟɫɟɬɢɰɚ, ʁɟɪ ʁɟ ɦɚʃɟ ɨɞ 8. Ɂɚɬɨ ɩɨɡɚʁɦʂɭʁɟɦɨ1 ɫɬɨɬɢɧɭ ɢ ɩɪɟɬɜɚɪɚɦɨ ʁɟ ɭ 10 ɞɟɫɟɬɢɰɚ. 10Ⱦ + 5ȳ = 15Ⱦ. 15 – 8 = 7, ɰɢɮɪɭ ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɞɟɫɟɬɢɰɚ

1

7

3

2 – 1 = 1, ɰɢɮɪɭ 1ɩɢɲɟɦɨ ɢɫɩɨɞ ɫɬɨɬɢɧɚ.

2 15

358 – 185 173

ɂɥɢɨɜɚɤɨ:

-P

Ȼɟɡ ɬɚɛɥɢɰɟ ɢɡɝɥɟɞɚ ɨɜɚɤɨ:

O

2

1. ɉɨɬɩɢɲɢɭɦɚʃɢɥɚɰɢɫɩɨɞ ɭɦɚʃɟɧɢɤɚ ɢ ɨɞɪɟɞɢ ɫɥɟɞɟʄɟ ɪɚɡɥɢɤɟ:

U KA

R

Ɇɨɠɟɦɨ ɞɚ ɪɚɱɭɧɚɦɨ ɢɧɚ ɤɪɚʄɢ ɧɚɱɢɧ, ɩɨɦɨʄɭ ɬɚɛɥɢɰɟ:

358 – 185 173

Ɣ 437 ɢ 256; Ɣ 629 ɢ 498; Ɣ 516 ɢ 234; Ɣ 735 ɢ 552; Ɣ 849 ɢ 677; Ɣ 915 ɢ 893; Ɣ 756 ɢ 585; Ɣ 924 ɢ 762.

‡ ɍɦɚʃɟɧɢɤ ɢ ɭɦɚʃɢɥɚɰɡɚɩɢɫɭʁɟɦɨ ɭ ɢɫɬɨɦ ɪɟɞɭ ɢ ɪɚɱɭɧɚɦɨɧɚ ɜɟʄɩɨɡɧɚɬɢ ɧɚɱɢɧ 358 – 185 = _ 73

ED

358 – 185 = _ _ 3

358 – 185 = 173

2. Ɉɞɪɟɞɢ ɞɚɬɟ ɪɚɡɥɢɤɟ, ɪɚɱɭɧɚʁɭʄɢ ɭ ɢɫɬɨɦ ɪɟɞɭ. ɚ) 537 – 365 = ___; ɛ) 769 – 587 = ___; ɜ 824 – 673 = ___; ɝ) 918 – 455 = ___. 3. ȳɨɜɚɧɢʁɟ ɦɚɦɚ ɤɭɩɢɥɚɥɨɩɬɭ, ɝɭɦɭ ɡɚɩɥɢɜɚʃɟ, ɧɚɨɱɚɪɟ ɢɩɚɩɭɱɟ.ɇɚ ɨɫɧɨɜɭ ɪɚɱɭɧɚ ɡɚɞɜɚ ɤɭɩʂɟɧɚ ɩɪɟɞɦɟɬɚ, ɨɞɪɟɞɢ ɩɨʁɟɞɢɧɚɱɧɟɰɟɧɟ. +

+

+

+

Ɣ ɐɟɧɚ

ʁɟ ____________________; Ɣ ɐɟɧɚ

ʁɟ ____________________;

Ɣ ɐɟɧɚ

ʁɟ ____________________; Ɣ ɐɟɧɚ

ʁɟ ____________________.

61


ɉɂɋɆȿɇɈ ɈȾɍɁɂɆȺȵȿɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ: 358 – 185 Ʉʂɭɱɧɟɪɟɱɢ: ɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000

1. Ɉɞɪɟɞɢ ɫɥɟɞɟʄɟ ɪɚɡɥɢɤɟ:

5 6 6 1 8 5

5 5 9 4 6 3

9 2 4 4 6 2

7 1 6 3 5 2

8 6 5 1 9 1

L

8 5 7 2 7 4

7 1 5 3 2 2

TA

6 7 8 1 9 7

6 4 8 4 7 4

ɍʁɟɞɧɨɦ ɫɬɚɞɭ ɢɦɚ 438ɛɟɥɢɯ ɢ 276ɰɪɧɢɯ ɨɜɚɰɚ. Ɂɚ ɤɨɥɢɤɨ ɢɦɚɜɢɲɟɛɟɥɢɯ ɨɜɚɰɚ?

R

2.

4 3 7 2 4 5

ɋɚɲɚ ɢɦɚ 257ɫɥɢɱɢɰɚ, ɚ Ɇɚɪɤɨ 348. Ʉɨɥɢɤɨ ɫɥɢɱɢɰɚ ɋɚɲɢ ɧɟɞɨɫɬɚʁɟ ɞɚɛɢ ɢɦɚɨ ɢɫɬɢɛɪɨʁɤɚɨɆɚɪɤɨ?

7. ɍɩɢɲɢ ɰɢɮɪɟ ɤɨʁɟ ɧɟɞɨɫɬɚʁɭ ɭɛɟɥɢɦɩɨʂɢɦɚ.

U KA

-P

3.

O

Ɉɞɝɨɜɨɪ: _____________________________________________

Ɉɞɝɨɜɨɪ: _____________________ _____________________________

956 – 793 183

7 6 – 384 4

4. Ɉɞɪɟɞɢ ɛɪɨʁɤɨʁɢʁɟ ɡɚ 546 ɦɚʃɢɨɞ ɡɛɢɪɚɛɪɨʁɟɜɚ 363 ɢ 454.

ED

_____________________________________

Ɍɨʁɟɛɪɨʁ___.

5. Ɍɚɦɚɪɚʁɟ ɬɚɱɧɨɩɨɪɟɻɚɥɚɞɟɥɨɜɟ ɫɥɚɝɚɥɢɰɟ ɧɚ ɫɥɢɰɢ Ʉɨʁɢɞɟɨ ʁɟɫɬɚɜɢɥɚ ɧɚ ɦɟɫɬɨ ɨɡɧɚɱɟɧɢɦ ɭɩɢɬɧɢɤɨɦ? ɚ)

ɛ)

ɜ)

? Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ.

62


ɉɂɋɆȿɇɈ ɋȺȻɂɊȺȵȿ ɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ 359 + 364 Ʉʂɭɱɧɟɪɟɱɢ ɫɚɛɢɪɚʃɟɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000

ɉɨɞɫɟɬɢʄɟɦɨ ɫɟɤɚɤɨɫɦɨ ɫɚɛɢɪɚɥɢ ɬɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɟ ɱɢʁɢʁɟ ɡɛɢɪʁɟɞɢɧɢɰɚ ɢ ɞɟɫɟɬɢɰɚɜɟʄɢ ɨɞ 9. 468 + 267 = 468 + (200 + 60 + 7) = (468 + 200) + 60 + 7 = (668 + 60) + 7 = 728 + 7 = 735 ɂɥɢɨɜɚɤɨ 468 + 267 = (400 + 60 + 8) + (200 + 60 + 7) = (400 + 200) + (60 + 60) + (8 + 7) = 600 + 120 + 15 = 735

100

10

9 + 4 = 13

300 + 50 + 9 + 300 + 60 + 4 700 + 20 + 3

Ʌɟɫɤɨɜɚɰ

13 = 10 + 3 10 + 50 + 60 = 120

364 km ɒɚɛɚɰ

R

ɋȾȳ

359 +364 723

359 km

TA

Ɣ Ɂɛɢɪ ɛɪɨʁɟɜɚ 359 ɢ 364 ɨɞɪɟɞɢʄɟɦɨ ɩɢɫɦɟɧɢɦɩɨɫɬɭɩɤɨɦ

ȼɪɲɚɰ

L

‡ ȼɪɲɚɰʁɟɨɞ Ʌɟɫɤɨɜɰɚ ɭɞɚʂɟɧ 359 km, ɚ ɒɚɛɚɰʁɟ ɨɞ Ʌɟɫɤɨɜɰɚ 364 km. Ʉɨɥɢɤɨ ɤɢɥɨɦɟɬɚɪɚɩɪɟɻɟɜɨɡɚɱɚɭɬɨɛɭɫɚ, ɚɤɨɩɭɬɭʁɟ ɨɞ ȼɪɲɰɚ ɞɨ ɒɚɩɰɚ ɩɪɟɤɨ Ʌɟɫɤɨɜɰɚ.

120 = 100 + 20

O

ȼɨɡɚɱ ɚɭɬɨɛɭɫɚ ʄɟ ɩɪɟʄɢ ___ km. ɂɥɢ ɤɪɚʄɟ, ɩɨɦɨʄɭ ɬɚɛɥɢɰɟ

9 + 4 = 13, 13ȳ = 1Ⱦ 3ȳ. ɐɢɮɪɭ 3 ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞ ʁɟɞɢɧɢɰɚ , ɚ 1 ɞɟɫɟɬɢɰɭ ɞɨɞɚʁɟɦɨ ɞɟɫɟɬɢɰɚɦɚ. 1 + 5 + 6 = 12, 12ȳ = 1Ⱦ 2ȳ. ɐɢɮɪɭ 2ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞ ɞɟɫɟɬɢɰɚ ɚ 1 ɫɬɨɬɢɧɭ ɞɨɞɚʁɟɦɨ ɫɬɨɬɢɧɚɦɚ

1

1

3 3

5 6

9 4

7

2

3

Ȼɟɡ ɬɚɛɥɢɰɟ ɢɡɝɥɟɞɚ ɨɜɚɤɨ 1 1

ED

359 + 364 723

-P

+

ȳ

U KA

ɋ Ⱦ

1 + 3 + 3 = 7, ɰɢɮɪɭ 7ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɫɬɨɬɢɧɚ

1. Ɂɚɩɢɲɢ ɫɚɛɢɪɤɟʁɟɞɚɧɢɫɩɨɞɞɪɭɝɨɝ ɢ ɨɞɪɟɞɢ ʃɢɯɨɜɡɛɢɪ. t 377 ɢ 274; t 588 ɢ 235; t 627 ɢ 296;

t 477 ɢ 357;

t 396 ɢ 524; t 664 ɢ 269; t 785 ɢ 178;

t 542 ɢ 269.

t ɋɚɛɢɪɤɟ ɡɚɩɢɫɭʁɟɦɨ ɭ ɢɫɬɨɦ ɪɟɞɭ ɢ ɪɚɱɭɧɚɦɨɧɚ ɢɫɬɢɧɚɱɢɧ 1

359 + 364 = _ _ 3

11

11

359 + 364 = _ 23

359 + 364 = 723

Ɂɚɩɢɲɢ ɫɚɛɢɪɤɟ ɭ ɢɫɬɨɦ ɪɟɞɭ ɢ ɨɞɪɟɞɢ ʃɢɯɨɜɡɛɢɪ. 2. Ʉɨʁɢʁɟ ɛɪɨʁ ɡɚ 248ɜɟʄɢɨɞɛɪɨʁɚ 368? ___________________ Ɉɞɝɨɜɨɪ _________________________________________ 3. ɐɟɧɚ ɲɟɫɬɚɪɚ ʁɟ 279ɞɢɧɚɪɚ. ɉɟɪɧɢɰɚʁɟ ɡɚ 565ɞɢɧɚɪɚɫɤɭɩʂɚ. Ʉɨɥɢɤɚ ʁɟɰɟɧɚ ɩɟɪɧɢɰɟ? ___________________ Ɉɞɝɨɜɨɪ _________________________________________

63


ɉɂɋɆȿɇɈ ɋȺȻɂɊȺȵȿ ɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ 359 + 364 Ʉʂɭɱɧɟɪɟɱɢ ɫɚɛɢɪɚʃɟɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000

ɂɡɪɚɱɭɧɚʁ

+

9

2

7

6

4

9

9

2

7

5

+

+

1

8

5

5

6

7

7

5

8

1

8

6

+

+

7

4

8

1

6

3

4

8

2

3

9

8

+

+

6

3

4

2

9

7

3

6

5

3

6

6

+

+

5

6

9

3

6

9

4

7

3

2

9

8

Ɉɬɤɪɢʁɩɪɚɜɢɥɨɩɨ ɤɨɦ ɫɭɧɚɩɢɫɚɧɢɛɪɨʁɟɜɢ ɭɩɪɜɚ ɞɜɚ ɬɪɨɭɝɥɚ. ɇɚɩɢɲɢ ɛɪɨʁɟɜɟ ɤɨʁɢɧɟɞɨɫɬɚʁɭ ɭ ɨɫɬɚɥɢɦ ɬɪɨɭɝɥɨɜɢɦɚ.

____________

_____________

____________

Ȼɢɨɫɤɨɩɫɤɭɩɪɟɞɫɬɚɜɭʁɟ ɝɥɟɞɚɥɨ 197ɩɨɫɟɬɢɥɚɰɚ. Ⱥɤɨʁɟ 48 ɫɟɞɢɲɬɚɛɢɥɨɫɥɨɛɨɞɧɨ, ɤɨɥɢɤɨɛɢɨɫɤɨɩɫɤɚ ɫɚɥɚ ɢɦɚ ɫɟɞɢɲɬɚ?

U KA

3.

____________

-P

____________

O

R

2.

5

TA

+

3

L

1.

Ɉɞɝɨɜɨɪ ________________________________ ________________________________________

4. ɇɚ ɞɟɫɧɨʁ ɫɬɪɚɧɢɭɥɢɰɟ ɢɦɚ 175 ɤɭʄɚ, ɚɧɚɥɟɜɨʁ 176. Ʉɨɥɢɤɨ ɭ ɬɨʁɭɥɢɰɢ ɢɦɚ ɤɭʄɚ?

5.

ED

Ɉɞɝɨɜɨɪ _______________________________________________

ɂɡɜɪɲɢɫɚɛɢɪɚʃɚ ɢ ɭɩɢɲɢɨɞɝɨɜɚɪɚʁɭʄɟ ɡɛɢɪɨɜɟ. 147 + 164

+ 296

+ 257

6. ȳɨɰɚʁɟ ɬɚɱɧɨ ɪɟɲɢɨ ɨɜɚʁɡɚɞɚɬɚɤ, ɚɥɢ ʁɟ ɩɪɟɤɪɢɨɞɜɟ ɰɢɮɪɟ ɤɨʁɟɫɭ ɦɟɻɭɫɨɛɧɨ ʁɟɞɧɚɤɟ. Ʉɨʁɚ ɰɢɮɪɚʁɟɩɪɟɤɪɢɜɟɧɚ? Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨɢɫɩɪɟɞɬɚɱɧɨɝɨɞɝɨɜɨɪɚ. 3

7+4

ɚ) 6

6 = 893

64

ɛ) 7

ɜ) 8

ɝ) 9


ɉɂɋɆȿɇɈ ɈȾɍɁɂɆȺȵȿ ɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ: 934 – 796; 500 – 385; 1000 – 738 Ʉʂɭɱɧɟɪɟɱɢ: ɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000 ɉɨɞɫɟɬɢʄɟɦɨ ɫɟɤɚɤɨɫɦɨ ɨɞɭɡɢɦɚɥɢ ɬɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɟ ɱɢʁɢʁɟ ɛɪɨʁ ʁɟɞɢɧɢɰɚɢ ɞɟɫɟɬɢɰɚ ɭɦɚʃɟɧɢɤɚɦɚʃɢ ɨɞ ɛɪɨʁɚ ʁɟɞɢɧɢɰɚ ɢ ɞɟɫɟɬɢɰɚ ɭɦɚʃɢɨɰɚ 765 – 487 = 765 – (400 + 80 + 7) = (765 – 400) – 80 – 7 = 365 – 80 – 7 = 285 – 7 = 278

Ɣ Ɋɚɡɥɢɤɭɛɪɨʁɟɜɚ 934 ɢ 796 ɨɞɪɟɞɢʄɟɦɨɩɢɫɦɟɧɢɦ ɩɨɫɬɭɩɤɨɦ ɧɚ ɫɥɟɞɟʄɢ ɧɚɱɢɧ: 90 100

800

10

900  100 = 800 100 – 10 = 90

900 + 30 + 4  700  90  6 100 + 30 + 8

90 + 30 = 120

10 + 4 = 14 14 – 6 = 8

120 – 90 = 30

TA

934 796 138

L

ɋȾȳ

Ɇɨɠɟɦɨ ɞɚ ɪɚɱɭɧɚɦɨ ɢɧɚ ɤɪɚʄɢ ɧɚɱɢɧ ɩɨɦɨʄɭ ɬɚɛɥɢɰɟ:

8

12

14

9 7

3 9

4 6

1

3

8

Ɉɞ 4 ʁɟɞɢɧɢɰɟɧɟ ɦɨɠɟɦɨɨɞɭɡɟɬɢ 6 ʁɟɞɢɧɢɰɚ ʁɟɪ ʁɟ4 ɦɚʃɟ ɨɞ 6 Ɂɚɬɨ ɩɨɡɚʁɦʂɭʁɟɦɨ 1 ɞɟɫɟɬɢɰɭ ɢ ɩɪɟɬɜɚɪɚɦɨ ʁɟ ɭ 10 ʁɟɞɢɧɢɰɚ 10ȳ + 4ȳ = 14ȳ 14 – 6 = 8 ɰɢɮɪɭ 8 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ʁɟɞɢɧɢɰɚ

R

ȳ

Ɉɞ 2 ɞɟɫɟɬɢɰɟɧɟ ɦɨɠɟɦɨɨɞɭɡɟɬɢ 9 ɞɟɫɟɬɢɰɚ ʁɟɪ ʁɟ 2 ɦɚʃɟɨɞ 9 Ɂɚɬɨ ɩɨɡɚʁɦʂɭʁɟɦɨ 1 ɫɬɨɬɢɧɭ ɢɩɪɟɬɜɚɪɚɦɨʁɟ ɭ 10 ɞɟɫɟɬɢɰɚ 10Ⱦ + 2Ⱦ = 12Ⱦ 12 – 9 = 3 ɰɢɮɪɭ 3 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɞɟɫɟɬɢɰɚ

O

ɋ Ⱦ

Ȼɟɡ ɬɚɛɥɢɰɟ ɢɡɝɥɟɞɚ ɨɜɚɤɨ:

ɂɥɢɨɜɚɤɨ:

8 12 14

 ɉɨɬɩɢɲɢɭɦɚʃɢɥɚɰ ɢɫɩɨɞ ɭɦɚʃɟɧɢɤɚ ɢ ɨɞɪɟɞɢ ɪɚɡɥɢɤɟ

U KA

934 – 796 138

934 – 796 138

-P

8 – 7 = 1ɰɢɮɪɭ 1 ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞ ɫɬɨɬɢɧɚ

t 437 ɢ 256; t 629 ɢ 499; t 557 ɢ 298; t 872 ɢ 294; t 849 ɢ 677; t 915 ɢ 688; t 756 ɢ 585; t 941 ɢ 762

ɋɚɞɚ ʄɟɦɨ ɨɞɪɟɞɢɬɢ ɪɚɡɥɢɤɭɛɪɨʁɟɜɚ 500 ɢ 385  ɇɚɦɟɫɬɭʁɟɞɢɧɢɰɚ ɢ ɞɟɫɟɬɢɰɚ ɧɚɥɚɡɢ ɫɟɧɭɥɚ ɨɞ ɤɨʁɟ ɧɟ ɦɨɠɟɦɨɨɞɭɡɢɦɚɬɢ Ɂɚɬɨ ɩɨɡɚʁɦʂɭʁɟɦɨ ɫɬɨɬɢɧɭ ɢ ɩɪɟɬɜɚɪɚɦɨ ʁɟɭ ɞɟɫɟɬɢɰɟ: 1ɋ = 10Ⱦ

ɋ Ⱦ 4

9 10 10

5 3 1

0 8 1

ɉɨɡɚʁɦʂɭʁɟɦɨ 1 ɞɟɫɟɬɢɰɭ ɢɩɪɟɬɜɚɪɚɦɨ ʁɟ ɭ ʁɟɞɢɧɢɰɟ 1Ⱦ = 10ȳ 10 – 5 = 5 ɰɢɮɪɭ 5 ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞ ʁɟɞɢɧɢɰɚ

ED

ȳ 0 5 5

Ɉɞɩɪɟɨɫɬɚɥɢɯ 9 ɞɟɫɟɬɢɰɚ ɨɞɭɡɢɦɚɦɨ 8 ɞɟɫɟɬɢɰɚ 9 – 8 =  ɰɢɮɪɭ ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɞɟɫɟɬɢɰɚ 4 – 3 =  ɰɢɮɪɭ ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɫɬɨɬɢɧɚ

. 9 10

500 – 385 115

2 ɂɡɪɚɱɭɧɚʁɪɚɡɥɢɤɭɛɪɨʁɟɜɚ: t 800 ɢ 537; t 400 ɢ 217; t 600 ɢ 439; t 900 ɢ 195 Ɣ ɇɚ ɢɫɬɢ ɧɚɱɢɧɨɞɭɡɢɦɚɦɨ ɬɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɟ ɨɞʁɟɞɧɟ ɯɢʂɚɞɟ t ɉɨɡɚʁɦʂɭʁɟɦɨ 1 ɯɢʂɚɞɭ ɢɩɪɟɬɜɚɪɚɦɨʁɟ ɭ ɫɬɨɬɢɧɟ: 1ɏ = 10ɋ ɏ ɋ Ⱦ ȳ 9 9 10 10 10

1 –

0 7 2

0 3 6

0 8 2

t Ɉɞ 10 ɫɬɨɬɢɧɚɩɨɡɚʁɦʂɭʁɟɦɨ 1 ɫɬɨɬɢɧɭ ɢ ɩɪɟɬɜɚɪɚɦɨʁɟ ɭ ɞɟɫɟɬɢɰɟ ɋ= 10 Ⱦ Ɉɫɬɚʁɟɧɚɦ 9 ɫɬɨɬɢɧɚ

t Ɉɞ 10 ɞɟɫɟɬɢɰɚɩɨɡɚʁɦʂɭʁɟɦɨ1 ɞɟɫɟɬɢɰɭ ɢɩɪɟɬɜɚɪɚɦɨʁɟ ɭ ʁɟɞɢɧɢɰɟ 1Ⱦ = 10ȳɈɫɬɚʁɟɧɚɦ 9 ɞɟɫɟɬɢɰɚ

. 9 9 10

1000 – 738 262

t ɋɚɞɚɩɪɢɫɬɭɩɚɦɨɨɞɭɡɢɦɚʃɭ: ʁɟɞɢɧɢɰɟɨɞɭɡɢɦɚɦɨɨɞ ʁɟɞɢɧɢɰɚ ɞɟɫɟɬɢɰɟ ɨɞ ɞɟɫɟɬɢɰɚɢ ɫɬɨɬɢɧɟɨɞ ɫɬɨɬɢɧɚ

3 ɂɡɪɚɱɭɧɚʁɪɚɡɥɢɤɭɛɪɨʁɟɜɚ: t 1000 ɢ 478; t 1000 ɢ 362; t 1000 ɢ 826; t 1000 ɢ 459

65


ɉɂɋɆȿɇɈ ɈȾɍɁɂɆȺȵȿ ɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ 934 – 796; 500 – 385; 1000 – 738 Ʉʂɭɱɧɟɪɟɱɢ: ɨɞɭɡɢɦɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000

1. Ɋɟɲɢɬɚɱɧɨɫɥɟɞɟʄɟ ɡɚɞaɬɤɟ ɢ ɩɨɪɟɻɚʁɫɥɨɜɚ ɢɡ ɤʂɭɱɚ Ɉɬɤɪɢʄɟɲɪɟɲɟʃɚ ɞɚɬɢɯ ɡɚɝɨɧɟɬɤɢ. ɍ ɉɊɈɅȿȶȿ ɈɇȺ ɋɌɂɀȿ, ɄɊɈȼɈȼȿ ɇȺɆ ɇȺɋɌȺɇɂ, ɄɊȺȴɂɐȺ ȳȿ ɋȼɂɏ ɉɌɂɐȺ, ɀȺȻȺɆȺ ɋȿ ɏɊȺɇɂ.

ɄȺȾȺ ɋɂɇȿ ɉɈɋɅȿ Ʉɂɒȿ ɇȺ ɅɂɋɌɍ ɅɈɄȼȺȵȺ, ɉɍɒɌȺ ɇȿɄȿ ɑɍȾɇȿɁȼɍɄȿ, ɈȾ ɊɈȾȿ ɋȿ ɍ ȻȺɊɍ ɋɄɅȺȵȺ.

__ __ __ __

L

__ __ __ __ 7 2 4 – 5 8 7

3 7 2 – 2 8 4

8 7 1 – 6 9 5

5 1 8 – 4 6 9

3 6 6 – 1 8 9

9 4 2 – 7 6 7

5 3 7 – 3 7 9

R

86 Ɋ

176 Ⱥ

49 Ⱦ

O

177 Ⱥ

88 ɀ

158 Ⱥ

-P

137 Ɉ

TA

4 5 1 – 3 6 5

175 Ȼ

2. Ɋɚɱɭɧɚʁɭ ɢɫɬɨɦ ɪɟɞɭɢ ɨɞɪɟɞɢ ɫɥɟɞɟʄɟ ɪɚɡɥɢɤɟ: 400 – 267 = ____

U KA

700 – 369 = ____ 900 – 677 = ____

500 – 345 = ____

800 – 399 = ____

600 – 578 = ____

400 – 224 = ____

900 – 773 = ____

3. ɍʁɟɞɧɨɦ ɪɟɫɬɨɪɚɧɭʁɟ ɭɞɟɰɟɦɛɪɭɩɨɬɪɨɲɟɧɨ 500 kg ɤɪɨɦɩɢɪɚ, ɚ ɭʁɚɧɭɚɪɭɡɚ 138 kg ɦɚʃɟ. Ʉɨɥɢɤɨ ɤɢɥɨɝɪɚɦɚɤɪɨɦɩɢɪɚʁɟɩɨɬɪɨɲɟɧɨ ɭ ʁɚɧɭɚɪɭ ɦɟɫɟɰɭ?

4.

ED

Ɉɞɝɨɜɨɪ: _______________________________________________ Ⱥɥɟɤɫɚ ɢɦɚ 438ɞɢɧɚɪɚ. ɀɟɥɢɞɚ ɤɭɩɢ ɫɥɚɝɚɥɢɰɭ ɧɚ ɫɥɢɰɢ. Ʉɨɥɢɤɨ ɞɢɧɚɪɚ ɦɭɧɟɞɨɫɬɚʁɟ" Ɉɞɝɨɜɨɪ: ________________________________ ________________________________________ 5. ɂɡɪɚɱɭɧɚʁ

700 ɞɢɧ

1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 4 2 9  – 2 5 3  – 8 3 6  – 5 1 9 –

6. ɍ ɬɚɛɟɥɢ ɫɭɧɚɩɢɫɚɧɟ ɬɚɱɧɟ ɪɚɡɥɢɤɟ. Ʉɨʁɢɛɪɨʁɫɟ ɤɪɢʁɟ ɢɡɚ ɡɜɟɡɞɢɰɟ" –

Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ

326 714 266 537 463

ɚ) 844

66

ɛ) 464

ɜ 564

ɝ) 734

ɞ) 264


ɋȺȻɂɊȺȵȿȼɂɒȿ ɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ Ʉʂɭɱɧɟɪɟɱɢ: ɫɚɛɢɪɚʃɟɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000

Ɂɛɢɪ ɬɪɢ ɢɥɢɜɢɲɟ ɫɚɛɢɪɚɤɚ ɨɞɪɟɻɭʁɟ ɫɟɩɨ ɢɫɬɨɦ ɩɨɫɬɭɩɤɭ ɤɚɨ ɡɛɢɪɞɜɚ ɫɚɛɢɪɤɚ. ɉɪɜɨ ɫɟ ɫɚɛɢɪɚʁɭʁɟɞɢɧɢɰɟ, ɡɚɬɢɦ ɞɟɫɟɬɢɰɟ ɢ ɧɚ ɤɪɚʁɭɫɬɨɬɢɧɟ Ɣ ȳɨɜɚɧɚʁɟ ɡɚɫɜɨʁɟ ɩɫɟ ɤɭɩɢɥɚɯɪɚɧɭ, ɱɟɬɤɭ ɢɲɚɦɩɨɧ. Ʉɨɥɢɤɢ ʁɟ ɪɚɱɭɧɡɚ ɬɭ ɤɭɩɨɜɢɧɭ? 1 1

2 2 5 ɞɢɧ

ȳɟɞɢɧɢɰɟ: 5 + 4 + 8 = 17, 1Ⱦ 7ȳ

ɱɟɬɤɚ

3 7 4 ɞɢɧ

Ⱦɟɫɟɬɢɰɟ: 1 + 2 + 7 + 4 = 14, 1ɋ 4Ⱦ

ɪɚɱɭɧ

ɋɬɨɬɢɧɟ:

+ 2 4 8 ɞɢɧ 8 4 7 ɞɢɧ

1+2+3+2=8

Ɋɚɱɭɧɡɚ ɬɭ ɤɭɩɨɜɢɧɭ ɢɡɧɨɫɢ 847ɞɢɧɚɪɚ.

TA

ɲɚɦɩɨɧ

L

ɯɪɚɧɚ

1. Ɂɚɩɢɲɢ ɫɚɛɢɪɤɟ ʁɟɞɚɧɢɫɩɨɞɞɪɭɝɨɝ ɢ ɨɞɪɟɞɢ ʃɢɯɨɜɡɛɢɪ: ɛ) 420, 279 ɢ 181;

-P

456 g

168 g

326 g

U KA

3. ɋɚɛɢɪɚʁɭ ɢɫɬɨɦ ɪɟɞɭ:

ɚ) 248 + 232 + 319 = ___;

ɝ) 148, 135, 326 ɢ 201.

O

2. ɂɡɪɚɱɭɧɚʁɭɤɭɩɧɭ ɦɚɫɭɩɨɜɪʄɚɧɚɫɥɢɰɢ

ɜ) 358, 154 ɢ 97;

R

ɚ) 254, 126 ɢ 347;

ɛ) 320 + 284 + 154 = ___;

Ɇɚɫɚɩɨɜɪʄɚʁɟ ___ g.

ɜ 423 + 165 + 235 = ___.

4. ɇɚ ʁɟɞɧɨɦɩɨʂɨɩɪɢɜɪɟɞɧɨɦ ɢɦɚʃɭ ɢɦɚ 470ɩɢɥɢʄɚ, 316 ɤɨɤɨɲɚɤɚ ɢ 184 ɩɟɬɥɨɜɚ. Ʉɨɥɢɤɨɧɚ ɬɨɦ ɢɦɚʃɭ ɢɦɚ ɭɤɭɩɧɨ ɠɢɜɢɧɟ? ɇɚ ɢɦɚʃɭ ɭɤɭɩɧɨɢɦɚ ___ ɠɢɜɢɧɟ

ED

__________________________________

5. Ⱦɚɛɢɫɬɢɝɥɢ ɞɨɩɟʄɢɧɟ,ɩɥɚɧɢɧɚɪɢ ɦɨɪɚʁɭɞɚɫɟ ɤɪɟʄɭɫɬɚɡɨɦ ɤɨʁɚɩɪɨɥɚɡɢɩɨɪɟɞ ɜɨɞɨɩɚɞɚɢ ɦɚɧɚɫɬɢɪɚ. Ʉɨɪɢɫɬɢɩɨɞɚɬɤɟɫɚɫɥɢɤɟ ɢ ɢɡɪɚɱɭɧɚʁɞɭɠɢɧɭɫɬɚɡɟ ɤɨʁɚ ɜɨɞɢɞɨ ɩɟʄɢɧɟ. ȼɨɞɨɩɚɞ 397 m ĺ

Ɇɚɧɚɫɬɢɪ 268 m ĺ

ɉɟʄɢɧɚ 215 m ĺ

________________________________ Ɉɞɝɨɜɨɪ: ______________________________________________________________

67


ɋȺȻɂɊȺȵȿ ȼɂɒȿ ɌɊɈɐɂɎɊȿɇɂɏ ȻɊɈȳȿȼȺ Ʉʂɭɱɧɟɪɟɱɢ: ɫɚɛɢɪɚʃɟ ɬɪɨɰɢɮɪɟɧɢɯ ɛɪɨʁɟɜɚ ɞɨ 1000

1. Ɉɞɪɟɞɢ ɜɪɟɞɧɨɫɬ ɢɡɪɚɡɚ: ɚ) 358 + 463 + 152 = __________________________________________________ ɛ) 420 + 236 + 180 + 64 = ______________________________________________

L

ɜ) 195 + 247 + 305 + 53 = ______________________________________________ 2. ɉɨɩɭɧɢɬɚɛɟɥɭ.

3. ɍɩɢɲɢɛɪɨʁɤɨʁɢɧɟɞɨɫɬɚʁɟ.

359

172

523

b

337

263

175

c

251

428

135

328 + ____ + 173 = 700

TA

a

O

R

a+b+c

5. ɇɚʁɜɟʄɢ ɧɟɩɚɪɚɧɛɪɨʁɬɪɟʄɟɫɬɨɬɢɧɟ ɭɜɟʄɚʁɡɚ ɡɛɢɪɛɪɨʁɟɜɚ 405 ɢ 211.

ɍʁɟɞɧɨʁ ɲɤɨɥɢ ɢɦɚ 124 ɭɱɟɧɢɤɚɩɪɜɨɝɪɚɡɪɟɞɚ ɢ ɡɚ 96 ɭɱɟɧɢɤɚɜɢɲɟɞɪɭɝɨɝ ɪɚɡɪɟɞɚ. ɍ ɬɪɟʄɟɦ ɢ ɱɟɬɜɪɬɨɦ ɪɚɡɪɟɞɭ ɢɦɚ 326 ɭɱɟɧɢɤɚ. Ʉɨɥɢɤɨ ɭ ɬɨʁ ɲɤɨɥɢ ɢɦɚ ɭɱɟɧɢɤɚ ɧɢɠɢɯ?

ED

6.

U KA

-P

4. Ɂɛɢɪɛɪɨʁɟɜɚ 269 ɢ 358 ɭɜɟʄɚʁ ɡɚ 162.

ɍɤɭɩɚɧɛɪɨʁ ɭɱɟɧɢɤɚ ɭɲɤɨɥɢ ʁɟ ____. 7.

ɍɦɟɫɬɨ ɫɥɨɜɚ Ɇɧɚɩɢɲɢɨɞɝɨɜɚɪɚʁɭʄɭ ɰɢɮɪɭ. Ɇ Ɇ 3 +

6

Ɇ

Ɇ Ɇ Ɇ 9

7

5

3

6

9

7

+

68

5


ɁȺȾȺɐɂ ɋȺ ȾȼȿɈɉȿɊȺɐɂȳȿ– ɋȺȻɂɊȺȵȿɂ ɈȾɍɁɂɆȺȵȿ Ʉʂɭɱɧɟɪɟɱɢ: ɡɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ, ɫɚɛɢɪɚʃɟ ɢ ɨɞɭɡɢɦɚʃɟ ɞɨ 1000

‡ Ⱦɚ ɫɟɩɨɞɫɟɬɢɦɨ: ɍ ɢɡɪɚɡɭɫɚɫɚɛɢɪɚʃɟɦ ɢ ɨɞɭɡɢɦɚʃɟɦ ɛɟɡ ɡɚɝɪɚɞɚ, ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ ɫɟ ɨɛɚɜʂɚʁɭ ɨɧɢɦɪɟɞɨɫɥɟɞɨɦ ɤɚɤɨ ɫɭ ɡɚɩɢɫɚɧɟ

ɇɚ ɩɪɢɦɟɪ: 800 – (483 + 276) = 800 – 759 = 41 1 ɂɡɪɚɱɭɧɚʁ

TA

Ⱥɤɨɫɟ ɭ ɢɡɪɚɡɭɧɚɥɚɡɟ ɡɚɝɪɚɞɟ, ɩɪɜɨɫɟ ɨɛɚɜʂɚʁɭ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ ɤɨʁɚ ɫɟɧɚɥɚɡɟ ɭ ɡɚɝɪɚɞɚɦɚ

L

ɇɚɩɪɢɦɟɪ: 800 – 483 + 276 = 317 + 276 = 593

t 740 – (421 + 159);

t 249 + (831 – 327);

t 724 – (108 + 316);

t 278 + 639 – 500;

t (1000 – 483) +183

O

R

t 995 – 527 + 368;

-P

Ɇɢɥɨɲɢɦɚɧɨɜɱɚɧɢɰɭ ɨɞ 500 ɞɢɧɚɪɚ Ʉɭɩɢɨʁɟ ɞɪɠɚɱɡɚ ɨɥɨɜɤɟ ɱɢʁɚ ʁɟɰɟɧɚ 346ɞɢɧɚɪɚ ɢ ɡɚɪɟɡɚɱɱɢʁɚ ʁɟ ɰɟɧɚ 125ɞɢɧɚɪɚ Ʉɨɥɢɤɨɞɢɧɚɪɚ ɢɡɧɨɫɢɆɢɥɨɲɟɜɤɭɫɭɪ?

U KA

Ź Ɇɢɥɨɲʁɟ ɢɦɚɨ 500ɞɢɧɚɪɚ Ź Ⱦɪɠɚɱɡɚ ɨɥɨɜɤɟ ɢ ɡɚɪɟɡɚɱ ɤɨɲɬɚʁɭ 346 + 125ɞɢɧɚɪɚ Ź Ⱦɚɛɢɫɦɨ ɢɡɪɚɱɭɧɚɥɢɆɢɥɨɲɟɜɤɭɫɭɪ, ɫɚɫɬɚɜɢʄɟɦɨ ɢɡɪɚɡ ɢ ɨɞɪɟɞɢʄɟɦɨʃɟɝɨɜɭɜɪɟɞɧɨɫɬ 500 – (346 + 125) = 500 – 471 = 29 Ź ȼɪɟɞɧɨɫɬ ɢɡɪɚɡɚʁɟ 29

Ɇɢɥɨɲʁɟ ɞɨɛɢɨ ɤɭɫɭɪ 29ɞɢɧɚɪɚ

ED

2 ȳɨɜɚɧɚ ɢɦɚ 1000ɞɢɧɚɪɚ ɀɟɥɢɞɚ ɤɭɩɢ ɥɨɩɬɭ ɢ ɧɚɨɱɚɪɟ ɡɚɩɥɢɜɚʃɟ Ʉɨɥɢɤɢ ʄɟ ɛɢɬɢ ȳɨɜɚɧɢɧɤɭɫɭɪ? ɂɡɪɚɡ: ____________________________________ Ɉɞɝɨɜɨɪ: _____________________________________________ 3 ɋɚɫɬɚɜɢ ɢɡɪɚɡ ɢ ɢɡɪɚɱɭɧɚʁʃɟɝɨɜɭɜɪɟɞɧɨɫɬ ɚ) Ɋɚɡɥɢɤɭɛɪɨʁɟɜɚ 936 ɢ 749 ɭɜɟʄɚʁɡɚ 587 ___________________________________________________ ɛ) Ɂɛɢɪɛɪɨʁɟɜɚ 408 ɢ 493 ɭɦɚʃɢ ɡɚɧɚʁɦɚʃɢ ɛɪɨʁɩɟɬɟɫɬɨɬɢɧɟ ___________________________________________________ ɜ) Ɉɞɪɟɞɢ ɛɪɨʁɤɨʁɢʁɟ ɡɚ 377 ɦɚʃɢɨɞ ɡɛɢɪɚɛɪɨʁɟɜɚ 492 ɢ 288 ___________________________________________________ ɝ Ʉɨʁɢ ʁɟ ɛɪɨʁɡɚ 256ɜɟʄɢɨɞ ɪɚɡɥɢɤɟɛɪɨʁɟɜɚ 1000 ɢ 736? ___________________________________________________

69

348ɞɢɧ 357ɞɢɧ


ɁȺȾȺɐɂ ɋȺ Ⱦȼȿ ɈɉȿɊȺɐɂȳȿ– ɋȺȻɂɊȺȵȿ ɂ ɈȾɍɁɂɆȺȵȿ Ʉʂɭɱɧɟɪɟɱɢ: ɡɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ, ɫɚɛɢɪɚʃɟ ɢ ɨɞɭɡɢɦɚʃɟ ɞɨ 1000

1. ɇɚ ɰɪɬɟɠɢɦɚɫɭɧɟɩɪɚɜɢɥɧɨ ɩɨɪɟɻɚɧɢɞɨɝɚɻɚʁɢ ɢɡ ɛɚʁɤɟ „ɉɢɧɨɤɢɨ”. Ɋɟɲɢ ɡɚɞɚɬɤɟ ɢ ɞɨɛɢʁɟɧɟ ɛɪɨʁɟɜɟɩɪɨɧɚɻɢɧɚ ɰɪɬɟɠɢɦɚ. ɍɩɢɲɢ ɭ ɤɪɭɝɨɜɟɨɞɝɨɜɚɪɚʁɭʄɟɛɪɨʁɟɜɟ ɨɞ 1 ɞɨ 11. Ɍɚɤɨ ʄɟɲɞɨɛɢɬɢ ɬɚɱɚɧɪɟɞɨɫɥɟɞɞɨɝɚɻɚʁɚ ɨɜɟ ɥɟɩɟɛɚʁɤɟ. Ɋɟɲɟʃɟ: ___

5

t Ɂɛɢɪɛɪɨʁɟɜɚ 639 ɢ 294 ɭɦɚʃɢ ɡɚ 728.

Ɋɟɲɟʃɟ: ___

1

t Ɋɚɡɥɢɤɭɛɪɨʁɟɜɚ 1000 ɢ 837 ɭɜɟʄɚʁɡɚ 579.

Ɋɟɲɟʃɟ: ___

9

t Ɂɛɢɪɛɪɨʁɟɜɚ 652 ɢ 268 ɭɦɚʃɢ ɡɚ ʃɢɯɨɜɭ ɪɚɡɥɢɤɭ.

Ɋɟɲɟʃɟ: ___

3

Ɋɟɲɟʃɟ: ___

11

Ɋɟɲɟʃɟ: ___

6

L

t Ɂɚ ɤɨɥɢɤɨ ʁɟɛɪɨʁ900 ɜɟʄɢ ɨɞ ɡɛɢɪɚɛɪɨʁɟɜɚ 337 ɢ 368?

TA

t Ɋɚɡɥɢɤɭɛɪɨʁɟɜɚ 852 ɢ 464 ɭɜɟʄɚʁɡɚɫɥɟɞɛɟɧɢɤɛɪɨʁɚ 565.

t Ɉɞɧɚʁɜɟʄɟɝ ɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚ ɨɞɭɡɦɢɪɚɡɥɢɤɭɛɪɨʁɟɜɚ 514 ɢ 178.

O

R

t ȳɟɞɚɧɯɨɬɟɥ ɢɦɚ 415ɫɥɨɛɨɞɧɢɯ ɤɪɟɜɟɬɚ. ɋɬɢɝɥɟɫɭɞɜɟ ɝɪɭɩɟ ɭɱɟɧɢɤɚ. ɍ ʁɟɞɧɨʁɝɪɭɩɢɢɦɚ 126 ɭɱɟɧɢɤɚ, ɭɞɪɭɝɨʁɡɚ 86 ɭɱɟɧɢɤɚ ɜɢɲɟ.Ʉɨɥɢɤɨʁɟ ɬɚɞɚɫɥɨɛɨɞɧɢɯ ɤɪɟɜɟɬɚ ɨɫɬɚɥɨ ɧɚ ɪɚɫɩɨɥɚɝɚʃɭ? Ɋɟɲɟʃɟ: ___ 2 t Ⱥɰɢɧɚɛɚɤɚ ʁɟ ɫɚɤɭɩɢɥɚ 600ʁɚʁɚ ɡɚɩɪɨɞɚʁɭ. Ʉɨɞ ɤɭʄɟʁɟɩɪɨɞɚɥɚ 238 ʁɚʁɚ ɚɧɚɩɢʁɚɰɢ ɡɚ 59ɜɢɲɟ. Ʉɨɥɢɤɨʁɚʁɚ ʁɟ ɨɫɬɚɥɨɧɟɩɪɨɞɚɬɨ" Ɋɟɲɟʃɟ: ___ 4

-P

t ɍ ʁɟɞɧɨʁɲɤɨɥɢ ɭɩɪɜɨɦ ɪɚɡɪɟɞɭ ɢɦɚ 167 ɭɱɟɧɢɤɚ, ɚ ɭɞɪɭɝɨɦ ɪɚɡɪɟɞɭ ɢɦɚ 138 ɭɱɟɧɢɤɚ.ɍ ɬɪɟʄɟɦ ɪɚɡɪɟɞɭ ɢɦɚ ɡɚ 58 ɦɚʃɟɧɟɝɨ ɭɩɪɜɨɦ, ɚ ɭɱɟɬɜɪɬɨɦ ɪɚɡɪɟɞɭ ɡɚ 29 ɭɱɟɧɢɤɚɜɢɲɟ ɧɟɝɨ ɭɞɪɭɝɨɦ ɪɚɡɪɟɞɭ. Ʉɨɥɢɤɨ ɭ ɬɨʁɲɤɨɥɢ ɢɦɚ ɭɱɟɧɢɤɚ ɭ ɬɪɟʄɟɦ ɢ ɱɟɬɜɪɬɨɦ ɪɚɡɪɟɞɭ? Ɋɟɲɟʃɟ: ___ 10 t ɍ ɜɨɡɭʁɟɛɢɥɨ 318ɩɭɬɧɢɤɚ. ɇɚ ɩɪɜɨʁɫɬɚɧɢɰɢ ʁɟ ɢɡɚɲɥɨ 97ɩɭɬɧɢɤɚ, ɚ ɭɲɥɨ 89 ɩɭɬɧɢɤɚ. Ʉɨɥɢɤɨɩɭɬɧɢɤɚʁɟ ɬɚɞɚɛɢɥɨ ɭɜɨɡɭ?

8

t Ɇɚɪɤɨɜɢɪɨɞɢɬɟʂɢ ɫɟɛɚɜɟ ɩɱɟɥɚɪɫɬɜɨɦ. ɍ ɬɨɤɭ ɝɨɞɢɧɟɩɪɨɞɚɥɢ ɫɭ 346 kg ɥɢɜɚɞɫɤɨɝ ɦɟɞɚ ɢ 288 kg ɛɚɝɪɟɦɨɜɨɝɦɟɞɚ. ɒɭɦɫɤɨɝ ɦɟɞɚɩɪɨɞɚɥɢ ɫɭ ɡɚ 33 kg ɦɚʃɟɧɟɝɨ ɥɢɜɚɞɫɤɨɝ. Ʉɨɥɢɤɨɫɭ ɭɤɭɩɧɨ ɤɢɥɨɝɪɚɦɚ ɦɟɞɚ ɩɪɨɞɚɥɢ" Ɋɟɲɟʃɟ: ___

7

U KA

Ɋɟɲɟʃɟ: ___

ED

310

954

195

947

205

77

742

276

65

663

536

70


ɋȺȾȺ ɁɇȺɆ ɆɇɈȽɈ ȼɂɒȿ Ʉʂɭɱɧɟɪɟɱɢ ɫɚɛɢɪɚʃɟɢɨɞɭɡɢɦɚʃɟ ɞɨ0, ɡɚɞɚɰɢ ɫɚ ɞɜɟ ɨɩɟɪɚɰɢʁɟ

ɋȺȻɂɊȺɆ ɌɊɈɐɂɎɊȿɇȿ ȻɊɈȳȿȼȿ ɉɂɋɆȿɇɂɆ ɉɈɋɌɍɉɄɈɆ ɋɚɛɢɪɤɟ ɡɚɩɢɫɭʁɟɦ ʁɟɞɚɧɢɫɩɨɞɞɪɭɝɨɝ, ɚɥɢ ɬɚɤɨɞɚɫɭʁɟɞɢɧɢɰɟ ɡɚɩɢɫɚɧɟ ɢɫɩɨɞ ʁɟɞɢɧɢɰɚ, ɞɟɫɟɬɢɰɟ ɢɫɩɨɞɞɟɫɟɬɢɰɚ, ɚ ɫɬɨɬɢɧɟ ɢɫɩɨɞɫɬɨɬɢɧɚ ɉɪɜɨ ɫɚɛɢɪɚɦ ʁɟɞɢɧɢɰɟ, ɡɚɬɢɦ ɞɟɫɟɬɢɰɟ ɢ ɧɚ ɤɪɚʁɭɫɬɨɬɢɧɟ.

ɋ Ⱦ

ȳ

1

5 2

3 4

8 5

7

8

3

ȳ 7 2 9

Ȼɟɡ ɬɚɛɥɢɰɟ ɢɡɝɥɚɞɚ ɨɜɚɤɨ

ȳ

1

1

538 + 245 783

+

1 1

8 6

5 3

3

4

8

437 +352 789

1

185 + 163 348

+

ɋ

Ⱦ

ȳ

1

1

3 3

5 6

9 4

7

2

3

1 1

359 + 364 723

O

+

+

Ⱦ 3 5 8

R

ɋ Ⱦ

ɋ 4 3 7

L

400 + 30 + 7 + 300 + 50 + 2 700 + 80 + 9

TA

ɋȾȳ

437 +352 789

ɈȾɍɁɂɆȺɆ ɌɊɈɐɂɎɊȿɇȿ ȻɊɈȳȿȼȿ ɉɂɋɆȿɇɂɆ ɉɈɋɌɍɉɄɈɆ

-P

ɍɦɚʃɢɥɚɰɡɚɩɢɫɭʁɟɦ ɢɫɩɨɞɭɦɚʃɟɧɢɤɚɧɚ ɫɥɟɞɟʄɢ ɧɚɱɢɧ ʁɟɞɢɧɢɰɟ ɡɚɩɢɫɭʁɟɦ ɢɫɩɨɞʁɟɞɢɧɢɰɚ, ɞɟɫɟɬɢɰɟ ɢɫɩɨɞɞɟɫɟɬɢɰɚ, ɚɫɬɨɬɢɧɟ ɢɫɩɨɞɫɬɨɬɢɧɚ.

ɋȾȳ

600 + 90 + 8 – 300 – 40 – 5 300 + 50 + 3

698 –345 353 ɋ Ⱦ

ȳ 14

ED

6

U KA

ɉɪɜɨ ɨɞɭɡɢɦɚɦ ʁɟɞɢɧɢɰɟ, ɡɚɬɢɦɞɟɫɟɬɢɰɟ ɢ ɧɚ ɤɪɚʁɭ ɫɬɨɬɢɧɟ

6 2 4

7 3 3

674 – 238 436

4 8 6

ɋ

Ⱦ

2

15

3 1 1

5 8 7

358 – 185 173

ȳ

8 5 3

ɋ 6 3 3

Ⱦ 9 4 5

ȳ 8 5 3

Ȼɟɡ ɬɚɛɥɢɰɟ ɢɡɝɥɚɞɚ ɨɜɚɤɨ

ɋ Ⱦ

ȳ

ɋ Ⱦ

8

12

14

3

9 7 1

3 9 3

4 6 8

4

10 10

5 3 1

0 8 1

934 – 796 138

ȳ

698 –345 353 ɏ ɋ

Ⱦ

9

9

9

0 5 5

10 10 10

1 –

0 7 2

0 3 6

. 9 10

. 9 9 10

500 – 385 115

1000 – 738 262

ɁȺȾȺɐɂ ɋȺ Ⱦȼȿ ɈɉȿɊȺɐɂȳȿ  ɋȺȻɂɊȺȵȿ ɂ ɈȾɍɁɂɆȺȵȿ 800 – 483 + 276 = 317 + 276 = 593 Ɣ ɍ ɢɡɪɚɡɭɛɟɡ ɡɚɝɪɚɞɚ, ɫɚɛɢɪɚɦ ɢɨɞɭɡɢɦɚɦ ɨɧɢɦ ɪɟɞɨɦ ɤɚɤɨʁɟ ɡɚɩɢɫɚɧɨ 800 – (483 + 276) = 800 – 759 = 41 Ɣ ɍ ɢɡɪɚɡɭɫɚɡɚɝɪɚɞɚɦɚ, ɩɪɜɨ ɨɛɚɜʂɚɦ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ ɤɨʁɟɫɟɧɚɥɚɡɟ ɭ ɡɚɝɪɚɞɚɦɚ.

71

ȳ 0 8 2


ɉɊɈȼȿɊȺȼȺɆɈ ɇȺɍɑȿɇɈ Ʉʂɭɱɧɟɪɟɱɢ ɫɚɛɢɪɚʃɟɢɨɞɭɡɢɦɚʃɟ ɞɨ0, ɡɚɞɚɰɢ ɫɚ ɞɜɟ ɨɩɟɪɚɰɢʁɟ

ɉɨɩɭɧɢɬɚɛɥɢɰɟ ɚ

246

429

715

658

m

800

520

311

762

b

647

481

187

328

n

437

269

232

578

a+b

ɂɡɪɚɱɭɧɚʁ 3 8 6 2 4 5 + 9 5

2 4 3 3 7 2 + 2 8 4

4 1 7 1 8 4 + 3 9 6

1 9 9 2 9 9 + 3 9 9

5 0 9 1 2 6 + 1 8 7

L

2.

m–n

TA

1.

R

3. ȳɟɥɟɧɚʁɟ ɤɭɩɢɥɚ ɝɭɦɟɧɟ ɱɢɡɦɢɰɟ ɡɚ 655ɞɢɧɚɪɚ ɢ ɤɢɲɨɛɪɚɧɡɚ 148ɞɢɧɚɪɚ. Ɋɚɱɭɧʁɟ ɩɥɚɬɢɥɚɧɨɜɱɚɧɢɰɨɦ ɨɞ 1000ɞɢɧɚɪɚ. Ʉɨɥɢɤɨ ɢɡɧɨɫɢȳɟɥɟɧɢɧ ɤɭɫɭɪ"

-P

O

ɂɡɪɚɡ ___________________________________________

Ɉɞɝɨɜɨɪ _____________________________________________ ɍʁɟɞɧɨɦ ɜɨʄʃɚɤɭʁɟ ɭɛɪɚɧɨ 325 kg ɬɪɟɲɚʃɚ ɢ ɡɚ 188 kg ɜɢɲɟ ɜɢɲɚʃɚ Ʉɨɥɢɤɨʁɟ ɤɢɥɨɝɪɚɦɚ ɭɛɪɚɧɨ ɬɪɟɲɚʃɚ ɢɜɢɲɚʃɚ"

U KA

4.

ɂɡɪɚɡ___________________________________________ Ɉɞɝɨɜɨɪ ____________________________________

ED

____________________________________________

5. Ⱦɜɚɩɥɢɜɚɱɚ ɫɟɧɚɥɚɡɟɧɚ ɪɚɫɬɨʁɚʃɭ ɨɞɩɨɥɚ ɤɢɥɨɦɟɬɪɚ.ɍ ɢɫɬɨ ɜɪɟɦɟɩɨɱɟɥɢ ɫɭɞɚɩɥɢɜɚʁɭʁɟɞɚɧɞɪɭɝɨɦ ɭ ɫɭɫɪɟɬ. Ʉɚɞɚ ʁɟ ʁɟɞɚɧ ɨɞ ʃɢɯɩɪɟɩɥɢɜɚɨ 186 m, ɞɪɭɝɢ ʁɟ ɡɚ ɬɨ ɢɫɬɨ ɜɪɟɦɟ ɩɪɟɩɥɢɜɚɨ 238 m. Ʉɨɥɢɤɨʁɟ ɬɚɞɚɛɢɥɨ ɪɚɫɬɨʁɚʃɟ ɢɡɦɟɻɭʃɢɯ" _____________________________________ Ɉɞɝɨɜɨɪ ____________________________________________________________ 6. ɍɩɢɲɢ ɭɛɟɥɚɩɨʂɚ ɰɢɮɪɟ ɤɨʁɟɧɟɞɨɫɬɚʁɭ.

7 0 8 – 2 5 2

6 7 + 3 6 7 4

8 –

2

7 2 5 4

ɂɧɬɟɪɧɟɬ ɚɞɪɟɫɚɧɚ ɤɨʁɨʁɦɨɠɟɲ ɞɚ ɩɪɨɧɚɻɟɲ ɫɥɢɱɧɟ ɡɚɞɚɬɤɟ https// dms.rs/kengur/zadaci/

72

3 6 + 3 4 8 0


ГЕОМЕТРИЈСКЕ ФИГУРЕ

TA

L

śřŎŅőōŎŗ

R

ŖʼnŜŠőŅŎš

O

ŭũŷŸűƁŮƁŷźŷŪűŶŮŸŹũūŷżŬũŷŶűųũűųūũŭŹũŻũ

-P

ŭũſŹŻũƁŸŹũūŷżŬũŷŶűųűųūũŭŹũŻųŷŹűźŻŮƓűŬŮŷŵŮŻŹűƐźųűŸŹűŪŷŹ

U KA

ŭũŷŭŹŮŭűƁŷŪűŵŸŹũūŷżŬũŷŶűųũűųūũŭŹũŻũŸŷŵŷƓżŷŪŹũźſũ ŭũŸŹũūűƁŵŷŭŮŴŮŸŹũūŷżŬũŷŶűųũűųūũŭŹũŻũ űŷŭƒűžźũźŻũūƑũƁŹũŰŴűƀűŻŮŽűŬżŹŮ

um

L

m

ip s

ED

ŮŴŮŵŮŶŻŮŻŹŷżŬŴũ  ŭũŹũŰŴűųżƐŮƁūŹźŻŮŻŹŷżŬŴŷūũŸŹŮŵũŭżůűŶũŵũźŻŹũŶűſũ m Lor e ore ŭũųŷŶźŻŹżűƁŮƁŻŹŷżŬũŷųŷŹűźŻŮƓűŬŮŷŵŮŻŹűƐźųűŸŹűŪŷŹ ŭũŷŭŹŮŭűƁŷŪűŵŻŹŷżŬŴũŸŷŵŷƓżŷŪŹũźſũ

ŭũŸŹũūűƁŵŷŭŮŴŮŻŹŷżŬŴũűŷŭƒűžźũźŻũūƑũƁŹũŰŴűƀűŻŮŽűŬżŹŮ ŭũŸŹŮźŴűųũūũƁŬŮŷŵŮŻŹűƐźųŮŽűŬżŹŮŶũųūũŭŹũŻŶŷƐŵŹŮůű


ɉɊȺȼɈɍȽȺɈɇɂɄ ɄȼȺȾɊȺɌ ɌɊɈɍȽȺɈ Ʉʂɭɱɧɟɪɟɱɢ: ɩɪɚɜɨɭɝɚɨɧɢɤɤɜɚɞɪɚɬ ɬɪɨɭɝɚɨɩɨɧɚɜʂɚʃɟ ɝɪɚɞɢɜɚ ɞɪɭɝɨɝ ɪɚɡɪɟɞɚ

1. ɉɨɫɦɚɬɪɚʁ ɰɪɬɟɠɟ. ɚ ɉɥɚɜɨɦɛɨʁɨɦ ɨɛɨʁɭɧɭɬɪɚɲʃɭ ɨɛɥɚɫɬ ɩɪɚɜɨɭɝɚɨɧɢɤɚ. ɛ ɐɪɜɟɧɨɦ ɛɨʁɨɦɩɨɞɟɛʂɚʁɫɬɪɚɧɢɰɟ ɤɜɚɞɪɚɬɚ. ɜ)ɀɭɬɨɦ ɛɨʁɨɦ ɨɛɨʁɭɧɭɬɪɚɲʃɭ ɨɛɥɚɫɬ ɬɪɨɭɝɥɚ ɚ ɡɟɥɟɧɨɦɩɨɞɟɛʂɚʁʃɟɝɨɜɟɫɬɪɚɧɢɰɟ.

ɞɭɠɢ ɝɟɨɦɟɬɪɢʁɫɤɟ ɬɚɱɤɟ ɢɡɥɨɦʂɟɧɢɦ ɩɪɚɜɟ

Ɣ ɉɪɚɜɨɭɝɚɨɧɢɤ

TA

ɨɛɢɦ

L

ɜ) ɍɫɜɚɤɨʁ ɪɟɱɟɧɢɰɢ ɢɡɨɫɬɚɜʂɟɧɚ ʁɟɩɨʁɟɞɧɚ ɪɟɱɉɪɨɧɚɻɢ ɢɯ ɦɟɻɭɩɨɧɭɻɟɧɢɦɪɟɱɢɦɚ ɢɧɚɩɢɲɢ ɧɚ ɨɞɝɨɜɚɪɭʁɭʄɟ ɦɟɫɬɨ.

ɤɜɚɞɪɚɬ ɢ ɬɪɨɭɝɚɨɫɭ ______________ɮɢɝɭɪɟ.

ɭɧɭɬɪɚɲʃɟ ɨɛɥɚɫɬɢ oɝɪɚɧɢɱɟɧɟ ɫɭ ɡɚɬɜɨɪɟɧɢɦ ________________ ɥɢɧɢʁɚɦɚ. ɍɤɭɩɧɚ ɞɭɠɢɧɚ ɡɚɬɜɨɪɟɧɟ ɢɡɥɨɦʂɟɧɟ ɥɢɧɢʁɟɩɪɟɞɫɬɚɜʂɚ ________________ ɝɟɨɦɟɬɪɢʁɫɤɢɯɮɢɝɭɪɚ.

R

Ɣ ȵɢɯɨɜɟ

-P

Ɉ ɜ) ɬɪɨɭɝɥɚ.

U KA

S ɛ) ɩɪɚɜɨɭɝɚɨɧɢɤɚ;

O

2. ɇɚ ɧɚɰɪɬɚɧɟ ɩɪɚɜɟ (ɩɨɦɨʄɭ ɲɟɫɬɚɪɚ) ɧɚɞɨɜɟɠɢ ɫɬɪɚɧɢɰɟ: ɚ) ɤɜɚɞɪɚɬɚ;

ȓ

ȟ

m

Ɇ Ɣ ɒɬɚɩɪɟɞɫɬɚɜʂɚɞɭɠɢɧɚɫɜɚɤɟ ɢɡɥɨɦʂɟɧɟɥɢɧɢʁɟ" Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨɢɫɩɪɟɞɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ. ɚ) ɨɛɢɦ ɮɢɝɭɪɟ ɛ) ɞɭɠɢɧɭ ɮɢɝɭɪɟ ɜ ɲɢɪɢɧɭɮɢɝɭɪɟ ɝ ɩɨɜɪɲɢɧɭɮɢɝɭɪɟ

ED

3. ɋɚɛɢɪɚʁɭʄɢ ɞɭɠɢɧɟ ɫɬɪɚɧɢɰɚ ɢɡɪɚɱɭɧɚʁ ɚ) ɨɛɢɦ ɩɪɚɜɨɭɝɚɨɧɢɤɚ ABCD ɱɢʁɟ ɫɭɫɬɪɚɧɢɰɟ: AB = 6FPBC = 3 cmCD = 6 cmDA = 3 cm; _______________________________________ ɛ) ɨɛɢɦ ɤɜɚɞɪɚɬɚ MSNR ɱɢʁɚ ʁɟ ɫɬɪɚɧɢɰɚ 7cm; ______________________________________ ɜ) ɨɛɢɦ ɬɪɨɭɝɥɚ ɈɊɄ ɱɢʁɟ ɫɭɫɬɪɚɧɢɰɟ: ɈɊ = 10 cm ɊɄ = 8 cm ɄɈ = 6 cm. _______________________________________ 4. ɇɚɰɪɬɚʁ ɧɚ ɤɜɚɞɪɚɬɧɨʁ ɦɪɟɠɢ: ɚ ɩɪɚɜɨɭɝɚɨɧɢɤɱɢʁɟɫɭɫɬɪɚɧɢɰɟ 4 cm ɢ 2 cm.

74

ɛ ɤɜɚɞɪɚɬɱɢʁɟɫɭɫɬɪɚɧɢɰɟ 2 cm.


ɉɊȺȼɈɍȽȺɈɇɂɄɂ ɄȼȺȾɊȺɌ Ʉʂɭɱɧɟɪɟɱɢ: ɝɟɨɦɟɬɪɢʁɫɤɟɮɢɝɭɪɟ, ɱɟɬɜɨɪɨɭɝɚɨ ɩɪɚɜɨɭɝɚɨɧɢɤ ɤɜɚɞɪɚɬ, ɟɥɟɦɟɧɬɢ ɩɪɚɜɨɭɝɚɨɧɢɤɚ

1. ɉɨɫɦɚɬɪɚʁ ɧɚɰɪɬɚɧɭɮɢɝɭɪɭ ɢɞɨɩɭɧɢɪɟɱɟɧɢɰɟ Ɣ ɍɧɭɬɪɚɲʃɚ ɨɛɥɚɫɬ ɮɢɝɭɪɟɧɚɫɥɢɰɢɨɝɪɚɧɢɱɟɧɚʁɟ ɡɚɬɜɨɪɟɧɨɦ _____________ɥɢɧɢʁɨɦ ɤɨʁɚɫɟ ɫɚɫɬɨʁɢɢɡɱɟɬɢɪɢ ________. Ɣ ɍɧɭɬɪɚɲʃɨɫɬ ɮɢɝɭɪɟʁɟ ɨɛɨʁɟɧɚ ___________ɛɨʁɨɦ

TA

L

Ɏɢɝɭɪɚ ɤɨʁɭ ɨɝɪɚɧɢɱɚɜɚ ɡɚɬɜɨɪɟɧɚ ɢɡɥɨɦʂɟɧɚ ɥɢɧɢʁɚɤɨʁɭɱɢɧɟɱɟɬɢɪɢ ɞɭɠɢ,ɧɚɡɢɜɚ ɫɟ ɱɟɬɜɨɪɨɭɝɚɨ. ɑɟɬɜɨɪɨɭɝɚɨɱɢɧɟ ɡɚɬɜɨɪɟɧɚ ɢɡɥɨɦʂɟɧɚ ɥɢɧɢʁɚ ɢ ʃɟɧɚ ɭɧɭɬɪɚɲʃɨɫɬ 2. ɍɨɱɢ ɭɝɥɨɜɟɧɚɰɪɬɚɧɨɝ ɩɪɚɜɨɭɝɚɨɧɢɤɚ. ɉɪɨɜɟɪɢɩɨɦɨʄɭ ɬɪɨɭɝɚɨɧɢɤɚ ɞɚ ɥɢ ɫɭ ɬɢ ɭɝɥɨɜɢɩɪɚɜɢ ɑɟɬɜɨɪɨɭɝɚɨ ɤɨɦɟɫɭɫɜɢ ɭɝɥɨɜɢɩɪɚɜɢ ɡɨɜɟɫɟ ɩɪɚɜɨɭɝɚɨɧɢɤ. D C DAB, B

BCA ɢ

CDA.

t Ɍɚɱɤɟ Ⱥ, ȼ, ɋ ɢ D ɫɭ ɬɟɦɟɧɚ ɩɪɚɜɨɭɝɚɨɧɢɤɚ.

O

A

ABC,

R

t ɍɝɥɨɜɢɧɚɰɪɬɚɧɨɝɩɪɚɜɨɭɝɚɨɧɢɤɚɫɭ:

ȾɭɠɢAB, BC, CD ɢ DA ɫɭ ɫɬɪɚɧɢɰɟ ɩɪɚɜɨɭɝɚɨɧɢɤɚ.

A

B

t ɋɬɪɚɧɢɰɟ ɩɪɚɜɨɭɝɚɨɧɢɤɚ ɤɨʁɟ ɢɦɚʁɭʁɟɞɧɨ ɡɚʁɟɞɧɢɱɤɨ ɬɟɦɟ ɧɚɡɢɜɚʁɭɫɟ ɫɭɫɟɞɧɟ ɫɬɪɚɧɢɰɟ. Ɉɧɟɫɭ ɦɟɻɭɫɨɛɧɨ ɧɨɪɦɚɥɧɟ ɢ ɪɚɡɥɢɱɢɬɟɩɨɞɭɠɢɧɢ

-P

C

t ɍɩɪɚɜɨɭɝɚɨɧɢɤɭ ABCD ɡɟɥɟɧɨɦɛɨʁɨɦ ɨɡɧɚɱɟɧʁɟʁɟɞɚɧɩɚɪ ɫɭɫɟɞɧɢɯɫɬɪɚɧɢɰɚ. Ɍɨɫɭɫɬɪɚɧɢɰɟ Ⱥȼ ɢ ȼɋ (Ⱥȼ ŏ ȼɋ).

U KA

D

3. ɂɦɟɧɭʁɢɧɚɩɢɲɢʁɨɲ3ɩɚɪɚɫɭɫɟɞɧɢɯɫɬɪɚɧɢɰɚɧɚɰɪɬɚɧɨɝɩɪɚɜɨɭɝɚɨɧɢɤɚ ABCD. Ʉɨɪɢɫɬɢ ɡɧɚɤŏ ɢ ɬɚɤɨ ɡɚɩɢɲɢ ʃɢɯɨɜɦɟɻɭɫɨɛɧɢɨɞɧɨɫ ___________________________________________________________________________

ED

D

A

C

B

t ɋɬɪɚɧɢɰɟ ɩɪɚɜɨɭɝɚɨɧɢɤɚ ɤɨʁɟ ɫɟɧɚɥɚɡɟʁɟɞɧɚ ɧɚɫɩɪɚɦɞɪɭɝɟ ɧɚɡɢɜɚʁɭ ɫɟ ɧɚɫɩɪɚɦɧɟ ɫɬɪɚɧɢɰɟ. ɍ ɩɪɚɜɨɭɝɚɨɧɢɤɭ ABCD ɧɚɫɩɪɚɦɧɟɫɬɪɚɧɢɰɟ ɫɭ __ ɢ __, __ ɢ __. ɇɚɫɩɪɚɦɧɟ ɫɬɪɚɧɢɰɟɫɭ ɦɟɻɭɫɨɛɧɨ ɩɚɪɚɥɟɥɧɟ ɢ ʁɟɞɧɚɤɟ ɩɨɞɭɠɢɧɢ AB II CD ɢ AB = CD

BC II AD ɢ BC = AD

ɉɪɚɜɨɭɝɚɨɧɢɤɤɨɦɟɫɭɫɜɟɫɬɪɚɧɢɰɟ ʁɟɞɧɚɤɟɞɭɠɢɧɟɧɚɡɢɜɚ ɫɟ ɤɜɚɞɪɚɬ. S

O

MN = NO = OS = SM 4. Ɉɩɢɲɢ ɨɫɨɛɢɧɟɧɚɰɪɬɚɧɨɝ ɤɜɚɞɪɚɬɚ MNOS.

M

N ȿɥɟɦɟɧɬɢɩɪɚɜɨɭɝɚɨɧɢɤɚ ɤɜɚɞɪɚɬɚ ɫɭ: 4 ɫɬɪɚɧɢɰɟ, 4 ɬɟɦɟɧɚ ɢ 4 ɭɝɥɚ.

75


É&#x2030;É&#x160;ȺȟÉ&#x2C6;É?ȽȺÉ&#x2C6;É&#x2021;É&#x201A;É&#x201E;É&#x201A; É&#x201E;ȟȺȞÉ&#x160;ČşÉ&#x152; É&#x201E;Ę&#x201A;ɭɹɧÉ&#x;ÉŞÉ&#x;ɹɢ: É?É&#x;ɨɌÉ&#x;ÉŹÉŞÉ˘Ę ÉŤÉ¤É&#x;ɎɢÉ?É­ÉŞÉ&#x;, ÉąÉ&#x;ÉŹÉ&#x153;ɨɪɨɭÉ?É&#x161;ɨ ÉŠÉŞÉ&#x161;É&#x153;ɨɭÉ?É&#x161;ɨɧɢɤ ɤÉ&#x153;É&#x161;É&#x17E;ÉŞÉ&#x161;ÉŹ, É&#x;ÉĽÉ&#x;ÉŚÉ&#x;ɧɏɢ ÉŠÉŞÉ&#x161;É&#x153;ɨɭÉ?É&#x161;ɨɧɢɤÉ&#x161;

É&#x2021;É&#x161;É°ÉŞÉŹÉ&#x161;ɧĘ É&#x; ÉŠÉŞÉ&#x161;É&#x153;ɨɭÉ?É&#x161;ɨɧɢɤOSRP. P

2.

É&#x201E;ɨɼɢɤɨɧÉ&#x161;É°ÉŞÉŹÉ&#x;É É­ ɢɌÉ&#x161;:

R

O

S

L

1.

É&#x161;) É&#x152;É&#x;ÉŚÉ&#x;ɧÉ&#x161;ÉŠÉŞÉ&#x161;É&#x153;ɨɭÉ?É&#x161;ɨɧɢɤÉ&#x161;ÉŤÉ­ ÉŹÉ&#x161;ɹɤÉ&#x;: __, __, __ ɢ __. É&#x203A;) É&#x2039;ÉŹÉŞÉ&#x161;ɧɢɰÉ&#x;ÉŠÉŞÉ&#x161;É&#x153;ɨɭÉ?É&#x161;ɨɧɢɤÉ&#x161;ÉŤÉ­É&#x17E;É­É É˘ ___, ___, ___ ɢ ___.

TA

É&#x161;) ÉŠÉŞÉ&#x161;É&#x153;ɨɭÉ?É&#x161;ɨɧɢɤÉ&#x161;" ___ É&#x203A;) ɤÉ&#x153;É&#x161;É&#x17E;ÉŞÉ&#x161;ÉŹÉ&#x161;" ___

T

D

R

3. É&#x2030;ɨɍɌÉ&#x161;ÉŹÉŞÉ&#x161;Ę É°ÉŞÉŹÉ&#x;É É˘É&#x17E;ɨɊɭɧɢ

t É&#x2039;É­ÉŤÉ&#x;É&#x17E;ɧÉ&#x; ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x; ɧÉ&#x161;É°ÉŞÉŹÉ&#x161;ɧɨÉ?ÉŠÉŞÉ&#x161;É&#x153;ɨɭÉ?É&#x161;ɨɧɢɤÉ&#x161;ÉŤÉ­:

N

É&#x2C6;ɧÉ&#x;ÉŤÉ­ _______________ɊɨÉ&#x17E;É­É É˘É§É˘

-P

M

O

MN ɢ ND, ___ ɢ ___, ___ ɢ ___, ___ ɢ ___.

t É&#x2021;É&#x161;ÉŤÉŠÉŞÉ&#x161;ɌɧÉ&#x;ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x;ÉŤÉ­: ___ ɢ ___, ___ ɢ ___. É&#x2C6;ɧÉ&#x; ÉŤÉ­ _______________ ɊɨÉ&#x17E;É­É É˘É§É˘

U KA

4. É&#x2021;É&#x161;É°ÉŞÉŹÉ&#x161;ɧɨɌ ɤÉ&#x153;É&#x161;É&#x17E;ÉŞÉ&#x161;ÉŹÉ­ ɨÉ&#x203A;É&#x;ÉĽÉ&#x;É É˘ ÉŹÉ&#x;ÉŚÉ&#x;ɧÉ&#x161;, É&#x161; ÉĄÉ&#x161;ɏɢɌ É&#x17E;ɨɊɭɧɢÉŞÉ&#x;ÉąÉ&#x;ɧɢɰÉ&#x;. t É&#x2039;ÉŹÉŞÉ&#x161;ɧɢɰÉ&#x; ɤÉ&#x153;É&#x161;É&#x17E;ÉŞÉ&#x161;ÉŹÉ&#x161;ÉŤÉ­É&#x17E;ɭɠɢ: _______________________.

t É&#x201E;É&#x153;É&#x161;É&#x17E;ÉŞÉ&#x161;ÉŹ Ę É&#x;ÉŠÉŞÉ&#x161;É&#x153;ɨɭÉ?É&#x161;ɨɧɢɤɤɨɌÉ&#x;ÉŤÉ­ÉŤÉ&#x153;É&#x;ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x; ____________________ É&#x17E;É­É É˘É§É&#x;.

5. É&#x2021;É&#x161;É°ÉŞÉŹÉ&#x161;ɧĘ É&#x; ɤÉ&#x153;É&#x161;É&#x17E;ÉŞÉ&#x161;ÉŹABCD. É&#x161;) É&#x2021;É&#x161;ɊɢɲɢɧÉ&#x161;ɥɢÉ&#x153;É&#x; Ę&#x192;É&#x;É?ɨÉ&#x153;ɢɯ É­É?ɼɨÉ&#x153;É&#x161;

ED

D

C

______________________________________________

A B É&#x203A;) É&#x201E;É¨Ę É&#x; ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x; ɤÉ&#x153;É&#x161;É&#x17E;ÉŞÉ&#x161;ÉŹÉ&#x161; ɨÉ&#x203A;ÉŞÉ&#x161;ÉĄÉ­Ę É­ÉŠÉŞÉ&#x161;É&#x153;É&#x; É­É?ɼɨÉ&#x153;É&#x;" É É&#x161;É¨É¤ÉŞÉ­É É˘ ɍɼɨÉ&#x153;ɨ ɢɍɊɪÉ&#x;É&#x17E; ÉŹÉ&#x161;ɹɧɨÉ? ɨÉ&#x17E;É?ɨÉ&#x153;ɨɪÉ&#x161; É&#x161; ɧÉ&#x161;ÉŤÉŠÉŞÉ&#x161;ɌɧÉ&#x;

É&#x203A;) ÉŤÉ­ÉŤÉ&#x;É&#x17E;ɧÉ&#x;

6. É&#x201E;ɨɼɢɤɨĘ É&#x; ɤÉ&#x153;É&#x161;É&#x17E;ÉŞÉ&#x161;ÉŹÉ&#x161;ɊɪɢɤÉ&#x161;ÉĄÉ&#x161;ɧÉ&#x161;ɨ ɧÉ&#x161; ɍɼɢɰɢ" É? ÉŹÉ&#x161;É&#x203A;É&#x;ɼɢ ÉŤÉ&#x161;É&#x203A;ÉŞÉ¨Ę É&#x;É&#x153;ɢɌÉ&#x161;, ɨÉ&#x203A;É¨Ę ɊɨĘ&#x201A;É&#x;ÉŤÉ&#x161; ÉŹÉ&#x161;ɹɧɢɌ ɨÉ&#x17E;É?ɨÉ&#x153;ɨɪɨɌ

8 10 11 12 13 14

É&#x201A;ɧɏÉ&#x;ɪɧÉ&#x;ÉŹ É&#x161;É&#x17E;ÉŞÉ&#x;ÉŤÉ&#x161; ɧÉ&#x161; É¤É¨Ę É¨Ę ÉŚÉ¨É É&#x;ɲ É&#x17E;É&#x161; ɊɪɨɧÉ&#x161;ÉťÉ&#x;ɲ ɍɼɢɹɧÉ&#x; ÉĄÉ&#x161;É&#x17E;É&#x161;ɏɤÉ&#x;: https:// dms.rs/kengur/zadaci/

76


ɍɉɈɊȿȭɂȼȺȵȿȾɍɀɂ; ȽɊȺɎɂɑɄɈ ɇȺȾɈȼȿɁɂȼȺȵȿȾɍɀɂ ɉɈɆɈȶɍ ɒȿɋɌȺɊȺ Ʉʂɭɱɧɟɪɟɱɢ: ɭɩɨɪɟɻɢɜɚʃɟ ɞɭɠɢ, ɝɪɚɮɢɱɤɨ ɧɚɞɨɜɟɡɢɜɚʃɟ ɞɭɠɢ ɩɨɦɨʄɭ ɲɟɫɬɚɪɚ

Ⱦɭɠɢ ɦɨɠɟɦɨɞɚ ɭɩɨɪɟɻɭʁɟɦɨ. D

ɚ) ɂɡɦɟɪɢɦɨʃɢɯɨɜɟ ɞɭɠɢɧɟɥɟʃɢɪɨɦ, ɚ ɡɚɬɢɦɢɯ ɭɩɨɪɟɞɢɦɨ: A

B

M

AB = 3 cm

N

S

T

MN = 2 cm AB = CD,

t ɍɩɨɪɟɻɭʁɟɦɨ:

C

ST = 3 cm 5 mm

CD = 3 cm

MN < AB < ST.

N

O

C

D

R

TA

M

L

ɛ) ɍɩɨɪɟɻɭʁɟɦɨʃɢɯɨɜɟ ɞɭɠɢɧɟɩɨɦɨʄɭɲɟɫɬɚɪɚ:

M

T

R

S

-P

O

M ɍ ɨɬɜɨɪ ɲɟɫɬɚɪɚ ɭɡɦɟɦɨɞɭɠCD. N ɂɝɥɭɲɟɫɬɚɪɚ ɡɚɛɨɞɟɦɨ ɭ ɬɚɱɤɭ Ɇ.ɍɨɱɚɜɚɦɨɞɚʁɟ CD < ɆɌ. O ɇɚ ɢɫɬɢ ɧɚɱɢɧɭɩɨɪɟɻɭʁɟɦɨɞɭɠɢCD ɢ RS. ɍɨɱɚɜɚɦɨɞɚʁɟ CD > RS. 1. ɍɩɨɪɟɞɢ ɩɨɦɨʄɭɲɟɫɬɚɪɚɧɚɰɪɬɚɧɟ ɞɭɠɢ ɚ ɂɦɟɧɭʁɧɚʁɤɪɚʄɭ ɢɧɚʁɞɭɠɭ ɞɭɠ.

M

U KA

Ⱥ

ɛ) Ʉɨʁɟ ɞɭɠɢ ɢɦɚʁɭʁɟɞɧɚɤɟɞɭɠɢɧɟ?

C

S

B

L

N

P

‡ Ⱦɭɠɢ ɦɨɠɟɦɨɞɚ ɩɪɟɧɨɫɢɦɨɧɚ ɨɞɪɟɻɟɧɭɩɪɚɜɭ. ȾɭɠȺȼ ɩɪɟɧɨɫɢɦɨɧɚɩɪɚɜɭ m ɧɚ ɫɥɟɞɟʄɢ ɧɚɱɢɧ.

ED

t ɇɚ ɩɪɚɜɨʁ m ɨɞɪɟɞɢɦɨʁɟɞɧɭ ɬɚɱɤɭ. Ɉɡɧɚɱɢɦɨʁɟ ɫɥɨɜɨɦɈ.

O

Ⱥ

ȼ

t ɍ ɨɬɜɨɪɲɟɫɬɚɪɚ ɭɡɦɟɦɨɞɭɠȺȼ. ɂɝɥɭ ɲɟɫɬɚɪɚ ɡɚɛɨɞɟɦɨ ɭ ɬɚɱɤɭ Ɉ, ɚ ɨɥɨɜɤɨɦ ɲɟɫɬɚɪɚ ɨɡɧɚɱɢɦɨ ɬɚɱɤɭ Ɇ.

m

m

O O ȾɭɠɈɆ ɧɚɫɬɚɥɚ ʁɟɩɪɟɧɨɲɟʃɟɦ ɞɭɠɢȺȼ ɧɚ ɩɪɚɜɭ m .

M

m

2. ɇɚɰɪɬɚʁ ɞɭɠ PF ɢ ɩɪɚɜɭ n . ɉɪɟɧɟɫɢɧɚɩɪɢɤɚɡɚɧɧɚɱɢɧɞɭɠPF ɧɚ ɩɪɚɜɭ n . ‡ Ʉɨɪɢɲʄɟʃɟɦ ɲɟɫɬɚɪɚ, ɞɭɠɢ ɦɨɠɟɦɨ ʁɟɞɧɨɫɬɚɜɧɨ ɢ ɥɚɤɨ ɧɚɞɨɜɟɡɢɜɚɬɢ ʁɟɞɧɭɧɚɞɪɭɝɭ. ɉɪɟɧɨɫɢɦɨɞɭɠɢȺɋ ɢ RP ʁɟɞɧɭ ɡɚɞɪɭɝɨɦ, ɚɥɢ ɬɚɤɨ ɞɚɫɟ ɬɚɱɤɟ ɋ ɢ R ɩɪɟɤɥɨɩɟ. Ⱥ

ɋ

R

P

m O

S

AC = OS

RP = SN

N

3. ɇɚɰɪɬɚʁ ɬɪɢ ɞɭɠɢ ɪɚɡɥɢɱɢɬɟɞɭɠɢɧɟ, ɚ ɡɚɬɢɦ ɢɯ ɩɨɦɨʄɭɲɟɫɬɚɪɚ ɧɚɞɨɜɟɠɢ ʁɟɞɧɭɧɚɞɪɭɝɭ.

77


ɐɊɌȺȵȿ ɉɊȺȼɈɍȽȺɈɇɂɄȺ ɂ ɄȼȺȾɊȺɌȺ ɌɊɈɍȽȺɈɇɂɄɈɆ ɂ ɅȿȵɂɊɈɆ Ʉʂɭɱɧɟɪɟɱɢ: ɰɪɬɚʃɟ ɩɪɚɜɨɭɝɚɨɧɢɤɚɢɤɜɚɞɪɚɬɚɬɪɨɭɝɚɨɧɢɤɨɦ ɢ ɥɟʃɢɪɨɦ

D

25 mm

‡ ɇɚɰɪɬɚʄɟɦɨɩɪɚɜɨɭɝɚɨɧɢɤɱɢʁɟ ɫɭ ɫɭɫɟɞɧɟ ɫɬɪɚɧɢɰɟ 5 cm ɢ 25 mm.

M ɉɨɦɨʄɭ ɬɪɨɭɝɚɨɧɢɤɚ

TA

P ɇɚ ɤɪɚɤɭ ɤɨʁɢʁɟɩɚɪɚɥɟɥɚɧɫɚ ɫɬɪɚɧɢɰɨɦAD, ɨɡɧɚɱɢɦɨ ɬɚɱɤɭ ɋ.

U KA

-P

O

O ɍ ɬɟɦɟɧɭ ȼ ɩɨɦɨʄɭ ɬɪɨɭɝɚɨɧɢɤɚ ɧɚɰɪɬɚɦɨʁɨɲʁɟɞɚɧɩɪɚɜɭɝɚɨ.

B

Q ɇɚ ɤɪɚʁɭɫɩɨʁɢɦɨ ɬɚɱɤɟ ɋ ɢ D.

ED A

B

R

A

D

B

L

D

A

A 5 cm

N ɇɚ ʁɟɞɧɨɦ ɤɪɚɤɭ ɨɡɧɚɱɢɦɨ ɞɭɠ ɞɭɠɢɧɟ 5 cm, ɚɧɚ ɞɪɭɝɨɦ ɞɭɠ ɞɭɠɢɧɟ 25 mm. Ɉɡɧɚɱɢɦɨ ɬɚɱɤɟ B ɢ D.

ɧɚɰɪɬɚɦɨ ɩɪɚɜ ɭɝɚɨ. Ɉɛɟɥɟɠɢɦɨ ɬɟɦɟ ɫɥɨɜɨɦ Ⱥ.

D

C

D

C

A

B

1. ɇɚ ɢɫɬɢɧɚɱɢɧɧɚɰɪɬɚʁɩɪɚɜɨɭɝɚɨɧɢɤ ɱɢʁɟɫɭɫɟɞɧɟ ɫɬɪɚɧɢɰɟ ɢɦɚʁɭɞɭɠɢɧɟ:

C

ɚ) 6 cm ɢ 4 cm; ɛ) 45 mm ɢ 35 mm; ɜ) 8 cm ɢ 65 mm;

B

ɝ) 1 dm ɢ 2 cm.

‡ Ɂɧɚɲɞɚ ʁɟ ɤɜɚɞɪɚɬ ɩɪɚɜɨɭɝɚɨɧɢɤɱɢʁɟɫɭɫɜɟɫɬɪɚɧɢɰɟʁɟɞɧɚɤɟ ɞɭɠɢɧɟ. Ɂɚɬɨ ɫɟ ɤɜɚɞɪɚɬ ɰɪɬɚ ɧɚ ɢɫɬɢ ɧɚɱɢɧɫɚɦɨ ɲɬɨɫɟ ɭɜɟɤ ɨɞɦɟɪɚɜɚ ɢɫɬɚɞɭɠɢɧɚɫɬɪɚɧɢɰɟ. 2. ɇɚɰɪɬɚʁɤɜɚɞɪɚɬɱɢʁɚʁɟ ɫɬɪɚɧɢɰɚ ɞɭɠɢɧɟ: ɚ) 5 cm; ɛ) 35 mm; ɜ) 6 dm.

78


ɐɊɌȺȵȿ ɉɊȺȼɈɍȽȺɈɇɂɄȺ ɂ ɄȼȺȾɊȺɌȺ ɒȿɋɌȺɊɈɆ ɂ ɌɊɈɍȽȺɈɇɂɄɈɆ Ʉʂɭɱɧɟɪɟɱɢ: ɰɪɬɚʃɟ ɩɪɚɜɨɭɝɚɨɧɢɤɚɢɤɜɚɞɪɚɬɚɲɟɫɬɚɪɨɦ ɢ ɬɪɨɭɝɚɨɧɢɤɨɦ

‡ ɇɚɰɪɬɚʄɟɦɨɩɪɚɜɨɭɝɚɨɧɢɤɱɢʁɟ ɫɭ ɫɭɫɟɞɧɟ ɫɬɪɚɧɢɰɟ 5 cm ɢ 25 mm.

M ɇɚɰɪɬɚɦɨɞɭɠɢ ɱɢʁɟ ɫɭ

N ɇɚɰɪɬɚɦɨɩɪɚɜɭɝɚɨ ɩɨɦɨʄɭ ɬɪɨɭɝɚɨɧɢɤɚ.

ɞɭɠɢɧɟʁɟɞɧɚɤɟɫɭɫɟɞɧɢɦ ɫɬɪɚɧɢɰɚɦɚɩɪɚɜɨɭɝɚɨɧɢɤɚ Ⱥȼ ɢ ȼɋ.

D

C 25 mm

A 5 cm B

D ȼ

TA

Ⱥ

L

A

O ɇɚ ɤɪɚɤɟ ɩɪɚɜɨɝɭɝɥɚ (ɩɨɦɨʄɭɲɟɫɬɚɪɚ) ɩɪɟɧɟɫɟɦɨ ɞɭɠɢɧɟ ɧɚɰɪɬɚɧɢɯɫɬɪɚɧɢɰɚ Ⱥȼ ɢ AD. ɇɚ ɬɚʁɧɚɱɢɧ ɞɨɛɢɥɢ ɫɦɨ ɬɟɦɟɧɚ B ɢ D.

O

R

P ɂɡ ɬɟɦɟɧɚ ȼ ɧɚɰɪɬɚɦɨɞɟɨ ɤɪɭɠɧɢɰɟ ɱɢʁɢʁɟ ɩɨɥɭɩɪɟɱɧɢɤ ɫɬɪɚɧɢɰɚ ȼɋ (AD = ȼɋ). Ɂɚɬɢɦ ɢɡ ɢɡ ɬɟɦɟɧɚD ɧɚɰɪɬɚɦɨɞɟɨ ɤɪɭɠɧɢɰɟ ɱɢʁɢʁɟɩɨɥɭɩɪɟɱɧɢɤɫɬɪɚɧɢɰɚ DC (AB = DC). ɇɚ ɬɚʁɧɚɱɢɧɞɨɛɢɥɢɫɦɨ ɬɟɦɟ ɋ. D

C

U KA

-P

D

Ⱥ

ȼ

Q D

Ⱥ

ȼ

C

ED

ɇɚ ɤɪɚʁɭɞɭɠɢɦɚɫɩɨʁɢɦɨ ɬɟɦɟɧɚȼ ɢ C, ɋ ɢ D.

A

B

ɇɚ ɬɚʁɧɚɱɢɧɞɨɛɢɥɢɫɦɨ ɞɪɭɝɟɞɜɟ ɫɭɫɟɞɧɟ ɫɬɪɚɧɢɰɟ BC ɢ CD.

1. ɇɚɰɪɬɚʁɩɪɚɜɨɭɝɚɨɧɢɤɱɢʁɟɫɭɫɭɫɟɞɧɟ ɫɬɪɚɧɢɰɟ: a) 7 cm ɢ 5 cm; ɛ) 8 cm ɢ 65 mm;

2. ɇɚɰɪɬɚʁ ɤɜɚɞɪɚɬ ɱɢʁɚ ʁɟ ɫɬɪɚɧɢɰɚ: a) 5 cm; ɛ) 7 cm; ɜ) 55 mm.

Ɂɚɛɚɜɢɬɟ ɫɟ ɩɪɚɜʂɟʃɟɦ ɦɨɞɟɥɚɩɪɚɜɨɭɝɚɨɧɢɤɚ ɢɤɜɚɞɪɚɬɚ ɢ ɪɚɡɥɢɱɢɬɢɯɮɢɝɭɪɚ... Ɣ

ɇɚɩɪɚɜʂɟɧɟ ɞɟɥɨɜɟ ɦɨɠɟɬɟ ɞɚɫɩɚʁɚɬɟɩɨɦɨʄɭ ɥɨɩɬɢɰɚɨɞ ɩɥɚɫɬɟɥɢɧɚ ɢɥɢ ɥɟɩɢɥɚ.

ɫɥɚɦɱɢɰɟ

ɱɚɱɤɚɥɢɰɟ

79

ɤɚɪɬɨɧ


ɐɊɌȺȵȿɉɊȺȼɈɍȽȺɈɇɂɄȺ ɂ ɄȼȺȾɊȺɌȺ Ʉʂɭɱɧɟɪɟɱɢ: ɰɪɬɚʃɟ ɩɪɚɜɨɭɝɚɨɧɢɤɚɢɤɜɚɞɪɚɬɚ

1. ɇɚɰɪɬɚʁɩɨɦɨʄɭ ɬɪɨɭɝɚɨɧɢɤɚ ɢ ɥɟʃɢɪɚ ɤɜɚɞɪɚɬ ɱɢʁɚɫɬɪɚɧɢɰɚ ɢɦɚɞɭɠɢɧɭ 35 mm. Ɉɛɟɥɟɠɢ ʃɟɝɨɜɚ ɬɟɦɟɧɚ

2. ɇɚɰɪɬɚɧɚ ɞɭɠ OS ʁɟ ɫɬɪɚɧɢɰɚ ɩɪɚɜɨɭɝɚɨɧɢɤɚ MNOS. ȵɟɧɟ ɫɭɫɟɞɧɟ ɫɬɪɚɧɢɰɟɫɭɞɜɚ ɩɭɬɚ ɤɪɚʄɟ. ɇɚɰɪɬɚʁɬɚʁɩɪɚɜɨɭɝɚɨɧɢɤɩɨɦɨʄɭ ɬɪɨɭɝɚɨɧɢɤɚ ɢɥɟʃɢɪɚ. S

4. ɇɚɰɪɬɚʁɩɨɦɨʄɭɲɟɫɬɚɪɚɢ ɬɪɨɭɝɚɨɧɢɤɚɩɪɚɜɨɭɝɚɨɧɢɤABCD, ɬɚɤɨɞɚɞɭɠɢɧɚʃɟɝɨɜɢɯ ɫɭɫɟɞɧɢɯ ɫɬɪɚɧɢɰɚɛɭɞɟʁɟɞɧɚɤɚɞɭɠɢɧɢ ɧɚɰɪɬɚɧɢɯɞɭɠɢ.

O

ɇɚɰɪɬɚʁ ɩɨɦɨʄɭɲɟɫɬɚɪɚ ɢ ɬɪɨɭɝɚɨɧɢɤɚ ɤɜɚɞɪɚɬ ROPG ɱɢʁɚ ʁɟ ɫɬɪɚɧɢɰɚɞɭɠɢɧɟ 5ɫm.

U KA

-P

3.

R

TA

L

Ɉ

Ⱥ ȼ

ɋ

ED

ȼ

5. ɇɚɰɪɬɚɧɟ ɫɭɞɜɟ ɩɪɚɜɟ ɤɨʁɟ ɫɟ ɫɟɤɭ. ɉɪɨɢɡɜɨʂɧɢɦɨɬɜɨɪɨɦ ɲɟɫɬɚɪɚɧɚɰɪɬɚʁ ɤɪɭɠɧɢɰɭɫɚɰɟɧɬɪɨɦ ɭ ɬɚɱɤɢ Ɉ.Ɍɚɱɤɟ ɩɪɟɫɟɤɚ ɤɪɭɠɧɢɰɟ ɢɩɪɚɜɢɯɫɩɨʁɞɭɠɢɦɚ. Ɉɛɟɥɟɠɢ ɬɟɦɟɧɚɧɚɰɪɬɚɧɨɝɩɪɚɜɨɭɝɚɨɧɢɤɚ.

6. ɇɚ ɢɫɬɢ ɧɚɱɢɧɤɚɨ ɭɩɪɟɬɯɨɞɧɨɦ ɡɚɞɚɬɤɭ, ɧɚɰɪɬɚʁɤɜɚɞɪɚɬ. a

b

m n

GeoGebra ɉɨɦɨʄɭ ɚɥɚɬɤɟ

ɰɪɬɚɲɩɪɚɜɨɭɝɚɨɧɢɤɢ ɤɜɚɞɪɚɬ (ɦɧɨɝɨɭɝɚɨ).

80


ɈȻɂɆ ɉɊȺȼɈɍȽȺɈɇɂɄȺ Ʉʂɭɱɧɟɪɟɱɢ: ɨɛɢɦ ɩɪɚɜɨɭɝɚɨɧɢɤɚ

Ɣ Ɇɚɪɤɨɜɢɪɨɞɢɬɟʂɢ ɢɦɚʁɭɜɨʄʃɚɤɱɢʁɚʁɟɩɨɜɪɲ ɨɛɥɢɤɚɩɪɚɜɨɭɝɚɨɧɢɤɚ. ɋɭɫɟɞɧɟ ɫɬɪɚɧɢɰɟ ɬɟɩɨɜɪɲɢɢɦɚʁɭ ɞɭɠɢɧɟ 50 m ɢ 20 m. Ʉɨɥɢɤɨ ʁɟɩɨɬɪɟɛɧɨ ɦɟɬɚɪɚ ɠɢɰɟ ɞɚ ɫɟ ɬɚʁɜɨʄʃɚɤ ɨɝɪɚɞɢ ɫɚ ɫɜɢɯɫɬɪɚɧɚ" Ⱦɭɠɢɧɚ ɠɢɰɟ ɤɨʁɚʁɟɩɨɬɪɟɛɧɚ ɞɚ ɫɟɜɨʄʃɚɤ ɨɝɪɚɞɢ,ɩɪɟɞɫɬɚɜʂɚ ɨɛɢɦɩɪɚɜɨɭɝɚɨɧɢɤɚ. ɇɚɰɪɬɚʄɟɦɨ ɫɤɢɰɭɜɨʄʃɚɤɚ.

Ɂɧɚɲ ɞɚɫɟ ɨɛɢɦɩɪɚɜɨɭɝɚɨɧɢɤɚ ɨɞɪɟɻɭʁɟ ɫɚɛɢɪɚʃɟɦɞɭɠɢɧɚɫɜɢɯʃɟɝɨɜɢɯɫɬɪɚɧɢɰɚ:

50 m

__ m + 50 m + __ m + 20 m = ___ m

20 m

L

20 m

Ɣ Ⱦɚɛɢɫɟ ɜɨʄʃɚɤ ɨɝɪɚɞɢɨ ɫɚɫɜɢɯɫɬɪɚɧɚ, ɩɨɬɪɟɛɧɨ ʁɟ ___ m ɠɢɰɟ

b

Ɇ

N

a

ɋɬɪɚɧɢɰɭ Ȏ ɧɚɡɢɜɚɦɨ ɞɭɠɢɧɚɩɪɚɜɨɭɝɚɨɧɢɤɚ ɋɬɪɚɧɢɰɭ b ɧɚɡɢɜɚɦɨ ɲɢɪɢɧɚ ɩɪɚɜɨɭɝɚɨɧɢɤɚ.

1. Ɉɞɪɟɞɢɨɛɢɦɧɚɰɪɬɚɧɨɝ ɩɪɚɜɨɭɝɚɨɧɢɤɚ ɝɪɚɮɢɱɤɢɦ ɧɚɞɨɜɟɡɢɜɚʃɟɦɞɭɠɢ ɫɬɪɚɧɢɰɟɩɪɚɜɨɭɝɚɨɧɢɤɚ ɲɟɫɬɚɪɨɦ ɩɪɟɧɟɫɢɧɚɩɨɥɭɩɪɚɜɭ Sn). ɋɜɚɤɭɩɪɟɧɟɬɭɫɬɪɚɧɢɰɭ ɨɛɟɥɟɠɢ ɨɞɝɨɜɚɪɚʁɭʄɢɦ ɫɥɨɜɨɦ(Ȏ ɢɥɢ b). ɒɬɚ ɭɨɱɚɜɚɲ"

n

U KA

S

R

b

Ɣ Ɂɧɚɲ ɞɚ ɩɪɚɜɨɭɝɚɨɧɢɤ ɨɝɪɚɧɢɱɚɜɚ ɡɚɬɜɨɪɟɧɚ ɢɡɥɨɦʂɟɧɚ ɥɢɧɢʁɚ ɤɨʁɭɱɢɧɟɱɟɬɢɪɢ ɞɭɠɢ.

O

O

-P

a

E

TA

50 m

Ⱥɤɨɫɭɫɟɞɧɟ ɫɬɪɚɧɢɰɟɩɪɚɜɨɭɝɚɨɧɢɤɚ ɨɛɟɥɟɠɢɦɨɫɥɨɜɢɦɚ Ȏ ɢ b, ɚ ɨɛɢɦɫɥɨɜɨɦɈ, ɬɚɞɚ ɨɛɢɦɛɢɥɨ ɤɨɝ ɩɪɚɜɨɭɝɚɨɧɢɤɚ ɦɨɠɟɦɨ ɢɡɪɚɱɭɧɚɬɢ ɧɚ ɫɥɟɞɟʄɢɧɚɱɢɧ Ɉ=Ȏ+Ȏ+b+b Ʉɚɤɨʁɟ Ȏ + Ȏ = 2 · Ȏ ɢ b + b = 2 · b, ɦɨɠɟɦɨ ɡɚɩɢɫɚɬɢɞɚʁɟ: Ɉ = 2 · Ȏ + 2 · b

ED

ɂɥɢ ʁɨɲɤɪɚʄɟ: O = 2 · (Ȏ + b)

2. ɉɪɢɦɟɧɢɨɛɪɚɡɚɰ ɢ ɢɡɪɚɱɭɧɚʁɨɛɢɦɩɪɚɜɨɭɝɚɨɧɢɤɚ, ɤɚɨɲɬɨʁɟɩɨɤɚɡɚɧɨɧɚɩɪɢɦɟɪɭ. Ȏ = 7 cm b = 5 cm

ɚ) Ȏ = 8 cm b = 5 ɫm

ɛ) Ȏ = 15 ɫm b = 3 cm

ɜ) Ȏ = 9 dm b = 6 dm

O = 2 · (Ȏ + b) Ɉ = 2 · (7 + 5) cm Ɉ = 2 · 12 cm Ɉ = 24 cm 3. Ɉɛɢɦ ɩɪɚɜɨɭɝɚɨɧɢɤɚ ȺȼȿɈ ɢɡɧɨɫɢ 20ɫm, ɚʃɟɝɨɜɚɞɭɠɢɧɚ ʁɟ 6 ɫm.ɇɚɰɪɬɚʁɞɭɠɌɋ ɤɨʁɚ ɩɪɟɞɫɬɚɜʂɚ ʃɟɝɨɜɨɛɢɦ. ɇɚɞɨɜɟɠɢ ɞɭɠɢɧɟɩɨɡɧɚɬɟɫɬɪɚɧɢɰɟ (ɞɜɚ ɩɭɬɚɩɨ 6 ɫm). ɒɬɚ ɩɪɟɞɫɬɚɜʂɚ ɩɪɟɨɫɬɚɥɢ ɞɟɨɞɭɠɢɌɋ" Ɉɞɪɟɞɢ ɲɢɪɢɧɭɩɪɚɜɨɭɝɚɨɧɢɤɚ ȺȼȿɈ

81


ɈȻɂɆ ɉɊȺȼɈɍȽȺɈɇɂɄȺ Ʉʂɭɱɧɟɪɟɱɢ ɨɛɢɦ ɩɪɚɜɨɭɝɚɨɧɢɤɚ

1. ɂɡɪɚɱɭɧɚʁɨɛɢɦɩɪɚɜɨɭɝɚɨɧɢɤɚ ɱɢʁɟɫɭɫɭɫɟɞɧɟ ɫɬɪɚɧɢɰɟ ɛ) Ȏ = 1 dm 8 cm b = 12 cm

ɜ) Ȏ = 65 mm b = 5 cm

______________________________________________

TA

2. ɉɨɜɪɲ ɫɬɨɥʃɚɤɚʁɟ ɨɛɥɢɤɚɩɪɚɜɨɭɝɚɨɧɢɤɚɱɢʁɚʁɟɞɭɠɢɧɚ 2 m, ɚɲɢɪɢɧɚ 15 dm. Ʉɪɨʁɚɱɢɰɚ ɠɟɥɢ ɞɚɫɬɚɜɢɭɤɪɚɫɧɭ ɬɪɚɤɭɞɭɠ ɢɜɢɰɚ ɬɨɝɚɫɬɨɥʃɚɤɚ. Ʉɨɥɢɤɨ ɦɟɬɚɪɚ ɬɪɚɤɟ ɤɪɨʁɚɱɢɰɚ ɬɪɟɛɚ ɞɚ ɤɭɩɢ"

L

ɚ) Ȏ = 6 cm b = 3 cm

R

Ɉɞɝɨɜɨɪ _______________________________________________

________________

O

ɐɟɧɚ ʁɟɞɧɨɝ ɦɟɬɪɚ ɬɪɚɤɟ ʁɟ 135ɞɢɧɚɪɚ. Ʉɨɥɢɤɢ ʄɟ ɛɢɬɢɪɚɱɭɧɡɚ ɤɭɩʂɟɧɭ ɬɪɚɤɭ? Ɉɞɝɨɜɨɪ_________________________________________

E

-P

3. ɂɡɦɟɪɢɞɭɠɢɧɟ ɫɬɪɚɧɢɰɚɧɚɰɪɬɚɧɨɝɩɪɚɜɨɭɝɚɨɧɢɤɚ ɢ ɢɡɪɚɱɭɧɚʁʃɟɝɨɜɨɛɢɦ O

___________

U KA

___________ M

N

ED

4. Ɉɛɢɦ ʁɟɞɧɨɝ ɩɪɚɜɨɭɝɚɨɧɢɤɚ ɢɡɧɨɫɢ16ɫm, ɚ ɞɭɠɢɧɚ ʁɟɞɧɟ ɨɞ ʃɟɝɨɜɢɯ ɫɭɫɟɞɧɢɯ ɫɬɪɚɧɢɰɚ ʁɟ 3 ɫm. ɇɚɰɪɬɚʁɞɭɠ ɤɨʁɚ ɩɪɟɫɬɚɜʂɚʃɟɝɨɜɨɛɢɦ. Ⱦɜɚ ɩɭɬɚɧɚɞɨɜɟɠɢ ɞɭɠɢɧɭɩɨɡɧɚɬɟɫɬɪɚɧɢɰɟ. ɇɚ ɨɫɧɨɜɭɩɪɟɨɫɬɚɥɨɝɞɟɥɚɞɭɠɢ, ɨɞɪɟɞɢ ɞɭɠɢɧɭɞɪɭɝɟ ɫɭɫɟɞɧɟ ɫɬɪɚɧɢɰɟ ɬɨɝ ɩɪɚɜɨɭɝɚɨɧɢɤɚ.

Ⱦɭɠɢɧɚɞɪɭɝɟ ɫɭɫɟɞɧɟ ɫɬɪɚɧɢɰɟɩɪɚɜɨɭɝɚɨɧɢɤɚ ʁɟ _______. 5. ɉɨɜɪɲ ɞɧɚ ɛɚɡɟɧɚ ɢɦɚ ɨɛɥɢɤ ɩɪɚɜɨɭɝɚɨɧɢɤɚɞɭɠɢɧɟ 12 m, ɚʃɟɝɨɜɨɛɢɦ ɢɡɧɨɫɢ 40 m. Ʉɨɥɢɤɚʁɟɲɢɪɢɧɚ ɬɨɝɛɚɡɟɧɚ? Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨɢɫɩɪɟɞ ɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ Ɣ Ʉɨɪɢɫɬɢ ɩɨɞɚɬɤɟ ɫɚ ɰɪɬɟɠɚ.

a =?

O = 40 m b = 12 m

a =?

ɚ) 5 m

ɛ) 6 m

82

ɜ) 7 m

ɝ) 8 m


ɈȻɂɆ ɉɊȺȼɈɍȽȺɈɇɂɄȺ Ʉʂɭɱɧɟɪɟɱɢ: ɨɛɢɦ ɩɪɚɜɨɭɝɚɨɧɢɤɚ

2. Ⱦɭɠɢɧɚɩɪɚɜɨɭɝɚɨɧɢɤɚ ʁɟ 8 cm, ɚ ɲɢɪɢɧɚʁɟ ɡɚ 3 cm ɤɪɚʄɚ ɨɞɞɭɠɢɧɟ. ɂɡɪɚɱɭɧɚʁɨɛɢɦ ɬɨɝɩɪɚɜɨɭɝɚɨɧɢɤɚ.

Ɉɛɢɦ ɩɪɚɜɨɭɝɚɨɧɢɤɚʁɟ ________.

Ɉɛɢɦ ɩɪɚɜɨɭɝɚɨɧɢɤɚ ʁɟ ________.

L

1. Ʉɨɥɢɤɨ ɢɡɧɨɫɢɨɛɢɦ ɩɪɚɜɨɭɝɚɨɧɢɤɚ, ɚɤɨɫɭɞɭɠɢɧɟʃɟɝɨɜɢɯɫɭɫɟɞɧɢɯ ɫɬɪɚɧɢɰɚ 9 cm ɢ 6 cm?

b = _________

TA

3. ɂɡɪɚɱɭɧɚʁɨɛɢɦɩɪɚɜɨɭɝɚɨɧɢɤɚ ɱɢʁɚ ʁɟ ɫɬɪɚɧɰɚ b = 16 dm, ɚ ɫɬɪɚɧɢɰɚ а ʁɟ ɞɜɚ ɩɭɬɚɞɭɠɚ. a = ____________________

b

R

Ȏ

O

4. ɋɩɨɪɬɫɤɢ ɬɟɪɟɧɢɦɚ ɨɛɥɢɤ ɩɪɚɜɨɭɝɚɨɧɢɤɚɞɭɠɢɧɟ 30 m ɢ ɲɢɪɢɧɟ 20 m. ɚ) Ɉɤɨ ɬɟɪɟɧɚ ɬɪɟɛɚɩɨɫɬɚɜɢɬɢ ɠɢɱɚɧɭ ɨɝɪɚɞɭɫɚɫɜɢɯɫɬɪɚɧɚ Ʉɨɥɢɤɨ ʄɟɫɟ ɦɟɬɚɪɚ ɠɢɰɟ ɭɩɨɬɪɟɛɢɬɢ ɡɚ ɨɝɪɚɻɢɜɚʃɟ ɨɜɨɝɬɟɪɟɧɚ?

-P

____________________________________________________________ Ɉɞɝɨɜɨɪ: ______________________________________________________

U KA

ɛ) ɇɚ ɫɜɚɤɚ 2 m ɨɤɨ ɨɜɨɝɬɟɪɟɧɚ ɦɨɪɚɞɚ ɫɟɩɨɫɬɚɜɢ ɩɨ ʁɟɞɚɧɛɟɬɨɧɫɤɢ ɫɬɭɛ. Ʉɨɥɢɤɨ ʄɟɫɬɭɛɨɜɚ ɛɢɬɢ ɭɩɨɬɪɟɛʂɟɧɨ?

___________________ Ɉɞɝɨɜɨɪ: _______________________________________

ED

5. ɂɡɪɚɱɭɧɚʁɨɛɢɦ ɩɪɚɜɨɭɝɚɨɧɢɤɚ ɱɢʁɚ ʁɟ ɫɬɪɚɧɰɚ а = 267 mm, ɚɫɬɪɚɧɢɰɚ b ʁɟ ɬɪɢ ɩɭɬɚ ɤɪɚʄɚ. Ȏ = ___________

b = ____________________

b

Ȏ

6.

Ɉɛɢɦ ɩɪɚɜɨɭɝɚɨɧɢɤɚ ɢɡɧɨɫɢ144 cm, ɚ ɭɤɭɩɧɚ ɞɭɠɢɧɚɞɜɟ ɩɚɪɚɥɟɧɟ ɫɬɪɚɧɢɰɟ ʁɟ98 cm. ɚ) ɇɚɰɪɬɚʁɫɤɢɰɭɩɪɚɜɨɭɝɚɨɧɢɤɚ ɭ ɭɧɟɫɢɩɨɡɧɚɬɟɩɨɞɚɬɤɟ. ɛ ɂɡɪɚɱɭɧɚʁɞɭɠɢɧɟ ɫɭɫɟɞɧɢɯɫɬɪɚɧɢɰɚ ɬɨɝɩɪɚɜɨɭɝɚɨɧɢɤɚ.

83


ɈȻɂɆ ɄȼȺȾɊȺɌȺ Ʉʂɭɱɧɟɪɟɱɢ: ɨɛɢɦ ɤɜɚɞɪɚɬɚ

D

Ȏ

Ȏ

C Ȏ

Ⱥ

B

Ȏ

Ɣ Ɂɧɚɲ ɞɚʁɟ ɤɜɚɞɪɚɬ ɩɪɚɜɨɭɝɚɨɧɢɤɱɢʁɟɫɭɫɜɟɫɬɪɚɧɢɰɟ ʁɟɞɧɚɤɟɞɭɠɢɧɟ. Ɂɚɬɨ ɫɬɪɚɧɢɰɟ ɤɜɚɞɪɚɬɚ ɨɛɟɥɟɠɚɜɚɦɨ ɢɫɬɢɦɫɥɨɜɨɦ. 1. Ɉɞɪɟɞɢ ɨɛɢɦɧɚɰɪɬɚɧɨɝ ɤɜɚɞɪɚɬɚ ɝɪɚɮɢɱɤɢɦ ɧɚɞɨɜɟɡɢɜɚʃɟɦ ɞɭɠɢ ɫɬɪɚɧɢɰɟ ɤɜɚɞɪɚɬɚɲɟɫɬɚɪɨɦɩɪɟɧɢɫɢɧɚ ɩɨɥɭɩɪɚɜɭ En). ɋɜɚɤɭɩɪɟɧɟɬɭɫɬɪɚɧɢɰɭ ɨɛɟɥɟɠɢ ɫɥɨɜɨɦ Ȏ. Ʉɨɥɢɤɨʁɟ ɩɭɬɚ ɨɛɢɦ ɤɜɚɞɪɚɬɚɞɭɠɢ ɨɞ ʃɟɝɨɜɟ ɫɬɪɚɧɢɰɟ?

TA

L

n ȿ ɍɨɱɚɜɚɦɨɞɚ ʁɟ ɨɛɢɦ ɤɜɚɞɪɚɬɚ 4ɩɭɬɚɜɟʄɢɨɞɞɭɠɢɧɟʃɟɝɨɜɟ ɫɬɪɚɧɢɰɟ. Ɂɚɬɨ ɨɛɢɦ ɤɜɚɞɪɚɬɚ ɦɨɠɟɦɨɞɚ ɢɡɪɚɱɭɧɚɜɚɦɨɩɨɦɨʄɭ ɨɛɪɚɫɰɚ: Ɉ = 4 · Ȏ Ʉɚɤɨʁɟ Ȏ = 2 cm, ɨɛɢɦ ɤɜɚɞɪɚɬɚʁɟ Ɉ = 4 Ȏ = 4 __ cm = __ cm. 1. ɂɡɦɟɪɢ ɫɬɪɚɧɢɰɭɧɚɰɪɬɚɧɨɝ ɤɜɚɞɪɚɬɚ ɢ ɢɡɪɚɱɭɧɚʁʃɟɝɨɜɨɛɢɦ. C

R

D

2. Ɉɛɢɦ ɤɜɚɞɪɚɬɚʁɟ 144 cm. ɂɡɪɚɱɭɧɚʁ ɞɭɠɢɧɭʃɟɝɨɜɟ ɫɬɪɚɧɢɰɟ. Ȏ

Ȏ

O

Ȏ

A

B

________________________

U KA

3. ɂɡɪɚɱɭɧɚʁɨɛɢɦ ɤɜɚɞɪɚɬɚɱɢʁɚ ɫɬɪɚɧɢɰɚ ɢɦɚɞɭɠɢɧɭ 117 mm.

-P

Ȏ

Ɋɚɱɭɧɚɲɨɜɚɤɨ: 4·Ȏ=Ɉ 4 · Ȏ = ___ cm Ȏ = 144 cm : 4 Ȏ = __ cm

ɋɬɪɚɧɢɰɚ ɤɜɚɞɪɚɬɚʁɟ __ cm.

4. ɂɡɪɚɱɭɧɚʁɫɬɪɚɧɢɰɭ ɤɜɚɞɪɚɬɚɱɢʁɢ ʁɟ ɨɛɢɦ 108 mm.

ED

5. ɋɬɪɚɧɢɰɚʁɟɞɧɨɝ ɤɜɚɞɪɚɬɚʁɟ 5 cm. Ʉɨɥɢɤɨɩɭɬɚʁɟɜɟʄɢɨɛɢɦɞɪɭɝɨɝ ɤɜɚɞɪɚɬɚ ɱɢʁɚ ʁɟ ɫɬɪɚɧɢɰɚ 2ɩɭɬɚɞɭɠɚ? ________________________________________________________________ Ɉɞɝɨɜɨɪ: ________________________________________________________ 6. ɒɤɨɥɫɤɨɞɜɨɪɢɲɬɟ ʁɟ ɨɛɥɢɤɚ ɤɜɚɞɪɚɬɚ, ɫɬɪɚɧɢɰɟ 15 m. Ʉɨɥɢɤɚʁɟ ɞɭɠɢɧɚ ɠɢɱɚɧɟ ɨɝɪɚɞɟ ɤɨʁɨɦ ʁɟ ɬɨ ɞɜɨɪɢɲɬɟ ɨɝɪɚɻɟɧɨ ɫɚ 3ɫɬɪɚɧɟ? ___________________________________ Ɉɞɝɨɜɨɪ: _____________________________________________________________ 7. Ɉɛɢɦ ɤɜɚɞɪɚɬɚʁɟɞɧɚɤʁɟ ɨɛɢɦɭɩɪɚɜɨɭɝɚɨɧɢɤɚɱɢʁɟ ɫɭ ɫɭɫɟɞɧɟ ɫɬɪɚɧɢɰɟ 32 mm ɢ 18 mm. Ʉɨɥɢɤɚ ʁɟɞɭɠɢɧɚɫɬɪɚɧɢɰɟ ɤɜɚɞɪɚɬɚ? Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞ ɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ.

84

ɚ) 20 mm

ɛ) 25 mm

ɜ) 35 mm

ɝ) 15 mm


ɈȻɂɆ ɄȼȺȾɊȺɌȺ Ʉʂɭɱɧɟɪɟɱɢ: ɨɛɢɦ ɤɜɚɞɪɚɬɚ

1. ɂɡɪɚɱɭɧɚʁɞɭɠɢɧɭ ɨɛɢɦɚ ɤɜɚɞɪɚɬɚ, ɚɤɨʁɟʃɟɝɨɜɚ ɫɬɪɚɧɢɰɚ: ɛ) a = 13 cm;

a) a = 7 dm;

ɜ) a = 136 mm.

_________________

__________________

__________________________

_________________

__________________

__________________________

L

3. Ⱦɭɠɢɧɚɩɪɚɜɨɭɝɚɨɧɢɤɚʁɟ 5 cm, ɚɲɢɪɢɧɚ 3 cm. ɇɚɰɪɬɚʁɤɜɚɞɪɚɬ ɤɨʁɢɢɦɚ ɢɫɬɢ ɨɛɢɦ

-P

O

R

TA

2. ɇɚɰɪɬɚʁɤɜɚɞɪɚɬABCD ɱɢʁɢʁɟ ɨɛɢɦ 12 cm.

4. ɂɡɪɚɱɭɧɚʁɞɭɠɢɧɭɫɬɪɚɧɢɰɟ ɤɜɚɞɪɚɬɚɱɢʁɢ ʁɟ ɨɛɢɦ: ɛ) Ɉ = 60 cm;

ɜ) Ɉ = 472 mm.

U KA

ɚ) Ɉ = 32 cm;

ED

5. Ʉɜɚɞɪɚɬ ʁɟɫɚɞɜɟ ɩɪɚɜɟ ɩɨɞɟʂɟɧɧɚ 4 ɦɚʃɚ ɤɜɚɞɪɚɬɚ ɨɞ ɤɨʁɢɯ ɫɜɚɤɢ ɢɦɚ ɨɛɢɦ 32 cm. Ʉɨɥɢɤɢʁɟ ɨɛɢɦ ɜɟɥɢɤɨɝ ɤɜɚɞɪɚɬɚ?

Ɉɞɝɨɜɨɪ: _____________________________________________________ 6. Ⱥɤɨɫɜɚɤɭɫɬɪɚɧɢɰɭ ɤɜɚɞɪɚɬɚ ɭɦɚʃɢɦɨ ɡɚ 6 cm,ɞɨɛɢʄɟɦɨ ɤɜɚɞɪɚɬ ɱɢʁɢʁɟ ɨɛɢɦ 24 cm. Ʉɨɥɢɤɢʁɟ ɨɛɢɦɩɪɜɨɛɢɬɧɨɝ ɤɜɚɞɪɚɬɚ?

Ɉɞɝɨɜɨɪ: __________________________________________________________

85


ɆȺɌȿɆȺɌɂɑɄȺɉȺɅɂȾɊȼɐȺ Ʉʂɭɱɧɟɪɟɱɢ: ɦɚɬɟɦɚɬɢɱɤɚ ɩɚɥɢɞɪɜɰɚ, ɤɜɚɞɪɚɬ

Ɂɚɛɚɜɢɬɟ ɫɟɩɪɚɜʂɟʃɟɦ ɦɨɞɟɥɚ ɤɜɚɞɪɚɬɚ ɩɨɦɨʄɭɩɚɥɢɞɪɜɚɰɚ... Ⱦɨɛɢʁɟɧɚ ɪɟɲɟʃɚ ɭɩɨɪɟɞɢɬɟɫɚ ɨɫɬɚɥɢɦ ɱɥɚɧɨɜɢɦɚ ɝɪɭɩɟ 2. ɉɨɫɬɚɜɢɩɚɥɢɞɪɜɰɚ ɤɚɨɲɬɨʁɟ ɩɨɤɚɡɚɧɨɧɚɰɪɬɟɠɭ. Ɂɚɬɢɦ ɭɤɥɨɧɢ 5ɩɚɥɢɞɪɜɚɰɚ, ɬɚɤɨɞɚ ɨɫɬɚɧɭ 3ʁɟɞɧɚɤɚ ɤɜɚɞɪɚɬɚ.

U KA

-P

O

R

TA

L

1. Ɉɞ 20ɩɚɥɢɞɪɜɚɰɚɫɚɫɬɚɜɢ 5 ɤɜɚɞɪɚɬɚ ɤɚɨɲɬɨ ʁɟɩɨɤɚɡɚɧɨ ɧɚɰɪɬɟɠɭ. Ɂɚɬɢɦ ɩɪɟɦɟɫɬɢ 4ɩɚɥɢɞɪɜɰɚ, ɬɚɤɨɞɚɞɨɛɢʁɟɲ 7 ɤɜɚɞɪɚɬɚ.

4. ɉɨɫɬɚɜɢɩɚɥɢɞɪɜɰɚ ɤɚɤɨ ʁɟ ɩɨɤɚɡɚɧɨ ɧɚɰɪɬɟɠɭ. ɉɪɟɦɟɫɬɢ 3ɩɚɥɢɞɪɜɰɚ, ɬɚɤɨɞɚɞɨɛɢʁɟɲ 3 ɤɜɚɞɪɚɬɚ.

ED

3. ɉɨɫɬɚɜɢ ɩɚɥɢɞɪɜɰɚ ɤɚɨɲɬɨʁɟɩɨɤɚɡɚɧɨ ɧɚɰɪɬɟɠɭ. ɉɪɟɦɟɫɬɢ ɫɚɦɨ 2 ɩɚɥɢɞɪɜɰɚ, ɬɚɤɨɞɚ ɞɨɛɢʁɟɲ 5ʁɟɞɧɚɤɢɯ ɤɜɚɞɪɚɬɚ.

5. Ɉɞɩɚɥɢɞɪɜɚɰɚɫɥɨɠɢ 5 ɤɜɚɞɪɚɬɚ ɤɚɨɲɬɨʁɟ ɩɨɤɚɡɚɧɨ ɧɚ ɰɪɬɟɠɭ. ɉɪɟɦɟɫɬɢ 4ɩɚɥɢɞɪɜɰɚ, ɬɚɤɨɞɚɞɨɛɢʁɟɲ 4ɧɨɜɚ ɤɜɚɞɪɚɬɚ ɢɫɬɟ ɜɟɥɢɱɢɧɟ

86


ɌɊɈɍȽȺɈ; ȼɊɋɌȿ ɌɊɈɍȽɅȺ Ʉʂɭɱɧɟɪɟɱɢ: ɬɪɨɭɝɚɨ, ɟɥɟɦɟɧɬɢ ɬɪɨɭɝɥɚ, ɧɟʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ, ʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ,ʁɟɞɧɚɤɨɤɪɚɤɢ

1. ɉɨɫɦɚɬɪɚʁɬɪɨɭɝɚɨɧɚɫɥɢɰɢ ɢ ɞɨɩɭɧɢɪɟɱɟɧɢɰɟ Ɣ ɍɧɭɬɪɚɲʃɚ ɨɛɥɚɫɬɬɪɨɭɝɥɚ ɨɝɪɚɧɢɱɟɧɚʁɟ ɡɚɬɜɨɪɟɧɨɦ _____________ɥɢɧɢʁɨɦ ɤɨʁɚɫɟ ɫɚɫɬɨʁɢɢɡ _____ɞɭɠɢ. Ɣ ɍɧɭɬɪɚɲʃɨɫɬɬɪɨɭɝɥɚ ʁɟ ɨɛɨʁɟɧɚ ___________ɛɨʁɨɦ

Ź ȾɭɠɢȺȼ, Ź

ȼɋȺ.

TA

Ź

ȼɋ ɢ ɋȺ ɢ ɧɚɡɢɜɚʁɭɫɟ ɫɬɪɚɧɢɰɟ ɬɪɨɭɝɥɚ. Ɍɚɱɤɟ Ⱥ, ȼ ɢ ɋ ɫɭ ɬɟɦɟɧɚ ɬɪɨɭɝɥɚ. ɋɬɪɚɧɢɰɟ ɬɪɨɭɝɥɚ ɨɛɪɚɡɭʁɭ 3ɭɝɥɚ: ɋȺȼ, Ⱥȼɋ ɢ

L

Ɣ Ɍɪɨɭɝɚɨɱɢɧɟ ɡɚɬɜɨɪɟɧɚ ɢɡɥɨɦʂɟɧɚ __________ ɢʃɟɧɚ ɭɧɭɬɪɚɲʃɨɫɬ

ȿɥɟɦɟɧɬɢɬɪɨɭɝɥɚɫɭ: 3ɫɬɪɚɧɢɰɟ, 3 ɬɟɦɟɧɚ ɢ 3 ɭɝɥɚ.

R

Ɍɪɨɭɝɚɨɫɟ ɨɛɟɥɟɠɚɜɚɨɡɧɚɤɚɦɚ ɬɟɦɟɧɚ. Ƚɨɪɟɧɚɰɪɬɚɧɢ ɬɪɨɭɝɚɨ ɡɚɩɢɫɭʁɟɦɨ Ⱥȼɋ.

a c

a

U KA

b

ʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ ɬɪɨɭɝɚɨ

-P

ɧɟʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ ɬɪɨɭɝɚɨ

O

Ɣ ɉɪɟɦɚɞɭɠɢɧɚɦɚɫɬɪɚɧɢɰɚ, ɪɚɡɥɢɤɭʁɟɦɨ:

ɋɬɪɚɧɢɰɟɬɪɨɭɝɥɚ MOR ɫɭ ɪɚɡɥɢɱɢɬɟ ɞɭɠɢɧɟ. Ɂɚɬɨɢɯ ɨɛɟɥɟɠɚɜɚɦɨ ɪɚɡɥɢɱɢɬɢɦ ɫɥɨɜɢɦɚ (ɧɚ ɩɪɢɦɟɪ: Ȏ, b, c).

a

a

ɋɜɟ ɫɬɪɚɧɢɰɟɬɪɨɭɝɥɚ Ⱥȼɋ ɫɭʁɟɞɧɚɤɟ ɞɭɠɢɧɟ. Ɂɚɬɨɢɯ ɨɛɟɥɟɠɚɜɚɦɨ ɢɫɬɢɦ ɫɥɨɜɨɦ (ɧɚ ɩɪɢɦɟɪ ɫɥɨɜɨɦ Ȏ).

ʁɟɞɧɚɤɨɤɪɚɤɢ ɬɪɨɭɝɚɨ

b

b a

Ⱦɜɟ ɫɬɪɚɧɢɰɟɬɪɨɭɝɥɚ DNS ɫɭ ʁɟɞɧɚɤɟ ɞɭɠɢɧɟ. Ɂɨɜɭ ɫɟɤɪɚɰɢ. Ɉɛɟɥɟɠɚɜɚɦɨɢɯ ɢɫɬɢɦ ɫɥɨɜɨɦ (ɧɚ ɩɪɢɦɟɪ ɫɥɨɜɨɦ b).

ED

1. Ɇɟɪɟʃɟɦ ɭɬɜɪɞɢ ɞɭɠɢɧɟɫɬɪɚɧɢɰɚɧɚɰɪɬɚɧɢɯ ɬɪɨɭɝɥɨɜɚ. ɂɦɟɧɭʁɢɯ ɢɪɚɡɜɪɫɬɚʁ ɭ ɬɚɛɟɥɭ.

ʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ

ɌɊɈɍȽȺɈ ʁɟɞɧɚɤɨɤɪɚɤɢ

87

ɧɟʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ


ɌɊɈɍȽȺɈ; ȼɊɋɌȿ ɌɊɈɍȽɅȺ Ʉʂɭɱɧɟɪɟɱɢ: ɬɪɨɭɝɚɨ, ɟɥɟɦɟɧɬɢ ɬɪɨɭɝɥɚ, ɧɟʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ,ʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ,ʁɟɞɧɚɤɨɤɪɚɤɢ

1. ɇɚɰɪɬɚɧʁɟ ɬɪɨɭɝɚɨ ɢ 5 ɬɚɱɚɤɚ.Ʉɨʁɟ ɬɚɱɤɟɩɪɢɩɚɞɚʁɭ ɧɚɰɪɬɚɧɨɦ ɬɪɨɭɝɥɭ? Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ.

ɛ) Ɉ, Ɇ, ɋ

ɜ) ȿ, Ɇ, Ɉ

ɝ) ɋ, Ɇ, ȿ

ɞ ȿ, Ɇ, Ʉ

ɻ) ɋ, Ɉ, Ʉ

L

ɚ) Ʉ, ɋ, ȿ

ȼ

TA

2. ɇɚɰɪɬɚɧʁɟ ɬɪɨɭɝɚɨ ANB. Ⱦɨɩɢɲɢ ɲɬɚɧɟɞɨɫɬɚʁɟ

Ø Ɍɟɦɟɧɚ ɬɪɨɭɝɥɚɫɭ ɬɚɱɤɟ: __, __ ɢ __.

Ø ɋɬɪɚɧɢɰɟ ɬɪɨɭɝɥɚɫɭ ɞɭɠɢ: ___, ___ ɢ ___.

A

N

a

____,

____ɢ

____.

R

Ø ɍɝɥɨɜɢɫɭ:

c

Ø Ɍɪɨɭɝɚɨɱɢʁɟɫɭɫɜɟɫɬɪɚɧɢɰɟ ɪɚɡɥɢɱɢɬɟ ɞɭɠɢɧɟ ɡɨɜɟ ɫɟ ______________________ ɬɪɨɭɝɚɨ.

O

b

U KA

-P

3. ɂɡɦɟɪɢɞɭɠɢɧɟ ɫɬɪɚɧɢɰɚɧɚɰɪɬɚɧɨɝ ɬɪɨɭɝɥɚ Ⱥȼɋ. Ⱦɨɩɢɲɢ ɲɬɚɧɟɞɨɫɬɚʁɟ. ɋ Ⱥȼ = __________ Ø Ɍɪɨɭɝɚɨ Ⱥȼɋ ɫɟ ɡɨɜɟ ȼɋ = __________ ______________________ ɬɪɨɭɝɚɨ. ɋȺ = __________

Ⱥ

ȼ

4. ɂɡɦɟɪɢ ɞɭɠɢɧɟɫɬɪɚɧɢɰɚɧɚɰɪɬɚɧɨɝ ɬɪɨɭɝɥɚ SRT. Ⱦɨɩɢɲɢ ɲɬɚɧɟɞɨɫɬɚʁɟ.

ED

T

S

R

SR = __________ RT = __________

Ø Ɍɪɨɭɝɚɨ SRT ɫɟ ɡɨɜɟ ______________________ ɬɪɨɭɝɚɨ.

TS = __________

5. ɍɩɢɲɢɧɚ ɥɢɧɢʁɭɛɪɨʁɬɪɨɭɝɥɨɜɚ ɤɨʁɟɭɨɱɚɜɚɲ ɧɚ ɰɪɬɟɠɭ. ɚ)

ɛ)

ɜ)

88


ɐɊɌȺȵȿɌɊɈɍȽɅȺ Ʉʂɭɱɧɟɪɟɱɢ: ɰɪɬɚʃɟ ɬɪɨɭɝɥɚ ɧɟʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ, ʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ,ʁɟɞɧɚɤɨɤɪɚɤɢ

‡ ɇɚɰɪɬɚʄɟɦɨɧɟʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ ɬɪɨɭɝɚɨ Ⱥȼɋ ɱɢʁɟɫɭɫɬɪɚɧɢɰɟ: Ⱥȼ = 35 mm ȼɋ = 30 mm ɋȺ = 20 mm M ɉɪɜɨ ɧɚɰɪɬɚɦɨ N ɒɟɫɬɚɪɨɦ ɨɞɦɟɪɢɦɨ O Ɉɬɜɨɪɨɦ ɲɟɫɬɚɪɚ ɞɭɠɢɧɭ ɫɬɪɚɧɢɰɟȼɋ. Ɂɚɛɨɞɟɦɨ ɢɝɥɭ ɲɟɫɬɚɪɚ ɭɬɚɱɤɭ ȼ ɢ ɰɪɬɚɦɨ ɞɟɨ ɤɪɭɠɧɢɰɟ

ɨɞɦɟɪɢɦɨɫɬɪɚɧɢɰɭ ɋȺ. Ɂɚɛɨɞɟɦɨ ɢɝɥɭ ɲɟɫɬɚɪɚ ɭ ɬɚɱɤɭ Ⱥ ɢ ɰɪɬɚɦɨ ɞɟɨ ɤɪɭɠɧɢɰɟɌɚɤɨɞɨɛɢʁɚɦɨ ɬɚɱɤɭ ɋ.

P ɉɪɚɜɢɦ ɥɢɧɢʁɚɦɚ ɫɩɚʁɚɦɨɬɚɱɤɭ ɋ ɫɚɬɚɱɤɚɦɚ Ⱥ ɢ ȼ. Ɍɚɤɨ ɫɦɨ ɞɨɛɢɥɢ ɬɪɨɭɝɚɨ Ⱥȼɋ.

TA

L

ɞɭɠ ɞɭɠɢɧɟ4 cm. Ʉɪɚʁʃɟɬɚɱɤɟɞɭɠɢ ɨɛɟɥɟɠɢɦɨ ɫɥɨɜɢɦɚ Ⱥ ɢ ȼ.

R

1. ɇɚɰɪɬɚʁ ɬɪɨɭɝɚɨ MBD ɱɢʁɟ ɫɭɫɬɪɚɧɢɰɟ 4 cm, 2 cm ɢ 3 cm.

-P

O

2. ɉɨ ɢɫɬɨɦ ɩɨɫɬɭɩɤɭɧɚɰɪɬɚʁ ʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ ɬɪɨɭɝɚɨ RST, ɱɢʁɚʁɟɫɬɪɚɧɢɰɚ 3 cm. Ɍ 3 cm

3 cm

R 3 cm S

U KA

3. ɉɨ ɢɫɬɨɦ ɩɨɫɬɭɩɤɭɧɚɰɪɬɚʁ ʁɟɞɧɚɤɨɤɪɚɤɢ ɬɪɨɭɝɚɨ Ⱥȼɋ ɱɢʁɢɫɭ ɤɪɚɰɢ ɞɭɠɢɧɟ 3 cm, ɚ ɬɪɟʄɚ ɫɬɪɚɧɢɰɚ ʁɟ 2 cm. ɋ 3 cm

3 cm

ED

Ⱥ 2 ɫm ȼ

Ɂɚɛɚɜɢɬɟ ɫɟɫɚɜɢʁɚʃɟɦɢ ɫɟɱɟʃɟɦ ɯɚɪɬɢʁɟ. ɉɪɚɜɢɬɟ ɦɨɞɟɥɟ ɬɪɨɭɝɥɨɜɚ ɢ ɪɚɡɥɢɱɢɬɟɮɢɝɭɪɟ... Ɣ ɉɪɨɭɱɢɬɟ ɩɪɢɤɚɡɚɧ ɩɨɫɬɭɩɚɤ ɭ ɤɨɪɚɤɚ ɢ ɧɚɩɪɚɜɢɬɟ ɨɛɟɥɟɠɢɜɚɱɟ ɡɚ ɤʃɢɝɭ ɢɥɢ ɫɜɟɫɤɭ.

M

P

N

Q

Ɣ

O

R

89

ɉɪɚɜɢɬɟ ɦɨɞɟɥɟ ɬɪɨɭɝɥɨɜɚ ɨɞ ɪɚɡɥɢɱɢɬɢɯ ɦɚɬɟɪɢʁɚɥɚ. ɋɚɫɬɚɜɢɬɟɨɞ ʃɢɯ ɪɢɛɢɰɟ ɡɚ ɜɚɲ ɡɢɞɧɢ ɚɤɜɚɪɢʁɭɦ, ɭɤɪɚɫɟɡɚ ʁɟɥɤɭ ɢɥɢ ɧɟɤɟ ɞɪɭɝɟ ɮɢɝɭɪɟ.


ɐɊɌȺȵȿ ɌɊɈɍȽɅȺ Ʉʂɭɱɧɟɪɟɱɢ: ɰɪɬɚʃɟ ɬɪɨɭɝɥɚ ɧɟʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ, ʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ ʁɟɞɧɚɤɨɤɪɚɤɢ

TA

L

1. ɇɚɰɪɬɚʁɬɪɨɭɝɚɨ Ⱥȼɋ ɱɢʁɟ ɫɭɫɬɪɚɧɢɰɟɞɭɠɢɧɟ 4 cm, 5 cm ɢ 3 cm.

-P

O

R

2. ɇɚɰɪɬɚʁɮɢɝɭɪɭ ɤɨʁɚ ʁɟ ɫɚɫɬɚɜʂɟɧɚ ɢɡ 3ʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɚ ɬɪɨɭɝɥɚɱɢʁɟɫɭ ɫɬɪɚɧɢɰɟ ɞɭɠɢɧɟ 4 cm.

ED

U KA

3. ɇɚɰɪɬɚʁʁɟɞɧɚɤɨɤɪɚɤɢ ɬɪɨɭɝɚɨ RPS ɱɢʁɚ ʁɟʁɟɞɧɚ ɫɬɪɚɧɢɰɚ 3 cm. Ⱦɪɭɝɟɞɜɟʁɟɞɧɚɤɟɫɬɪɚɧɢɰɟ ɢɦɚʁɭ ɞɭɠɢɧɭ 4 cm.

4. ɇɚɰɪɬɚʁ ʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɚ ɬɪɨɭɝɥɚ, ɬɚɤɨɞɚ ɢɦ ʁɟ ɧɚɰɪɬɚɧɚ ɞɭɠȺȼ ɡɚʁɟɞɧɢɱɤɚ ɫɬɪɚɧɢɰɚ.

5. ɇɚɰɪɬɚʁ ʁɟɞɧɚɤɨɤɪɚɤɚ ɬɪɨɭɝɥɚ ɬɚɤɨ ɞɚ ɢɦ ʁɟɧɚɰɪɬɚɧɚɞɭɠST ɡɚʁɟɞɧɢɱɤɚɫɬɪɚɧɢɰɚ.

ȼ

T

Ⱥ

S

GeoGebra ɉɨɦɨʄɭ ɚɥɚɬɤɟ

ɰɪɬɚɲɬɪɨɭɝɚɨ ɦɧɨɝɨɭɝɚɨ).

90


É&#x2C6;ČťÉ&#x201A;É&#x2020;É&#x152;É&#x160;É&#x2C6;É?Č˝É&#x2026;Čş É&#x201E;Ę&#x201A;ɭɹɧÉ&#x;ÉŞÉ&#x;ɹɢ: ɨÉ&#x203A;ɢɌ ɏɪɨɭÉ?ÉĽÉ&#x161; ɧÉ&#x;Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨɍɏɪÉ&#x161;ɧɢɹɧɢ Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨɍɏɪÉ&#x161;ɧɢɹɧɢ,Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨɤɪÉ&#x161;ɤɢ

ČźÉ&#x;ɍɧÉ&#x161; Ę É&#x; ɨÉ&#x17E;ÉŤÉĽÉ&#x161;ɌɹɢɰÉ&#x161; ÉĄÉ&#x161; ɍɨɤ ɧÉ&#x161;ÉŠÉŞÉ&#x161;É&#x153;ɢɼÉ&#x161; ɌɨÉ&#x17E;É&#x;ÉĽ ɏɪɨɭÉ?ÉĽÉ&#x161;. É&#x2039;ÉŹÉŞÉ&#x161;ɧɢɰÉ&#x161; ɌɨÉ&#x17E;É&#x;ÉĽÉ&#x161;É°ÉŞÉ&#x153;É&#x;ɧÉ&#x;É&#x203A;É¨Ę É&#x;Ę É&#x; 33 mm, ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x161;ÉŠÉĽÉ&#x161;É&#x153;É&#x; É&#x203A;É¨Ę É&#x; Ę É&#x; 29 mm, É&#x161;ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x161; ÉĄÉ&#x;ÉĽÉ&#x;ɧÉ&#x; É&#x203A;É¨Ę É&#x;Ę É&#x; 20 mm. É&#x201A;ÉĄÉŞÉ&#x161;ɹɭɧÉ&#x161;Ę É­É¤É­ÉŠÉ§É­ É&#x17E;É­É É˘É§É­ ɭɊɨɏɪÉ&#x;É&#x203A;Ę&#x201A;É&#x;ɧɢɯ ÉŤÉĽÉ&#x161;ɌɹɢɰÉ&#x161;ÉĄÉ&#x161; ɢɥɪÉ&#x161;É&#x17E;É­ ɏɨÉ? ɌɨÉ&#x17E;É&#x;ÉĽÉ&#x161;. É É§É&#x161;ɲ É&#x17E;É&#x161;Ę É&#x; ÉĄÉ&#x203A;ɢɪÉ&#x17E;ɭɠɢɧÉ&#x161; ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x161; ɏɪɨɭÉ?ÉĽÉ&#x161;Ę É&#x;É&#x17E;ɧÉ&#x161;ɤĘ&#x192;É&#x;É?ɨÉ&#x153;ɨɌ ɨÉ&#x203A;ɢɌɭ. É É§É&#x161;ɹɢ, ɭɤɭɊɧÉ&#x161; É&#x17E;ɭɠɢɧÉ&#x161; ɭɊɨɏɪÉ&#x;É&#x203A;Ę&#x201A;É&#x;ɧɢɯÉŤÉĽÉ&#x161;ɌɹɢɰÉ&#x161; Ę É&#x; (33 + __ + __) mm = ___ mm. É&#x2039; É&#x2021;É&#x161;É°ÉŞÉŹÉ&#x161;ɼɢ ɍɌɨ ɏɪɨɭÉ?É&#x161;ɨ ȺȟÉ&#x2039;, ɢɍɏɢɯÉ&#x17E;ɢɌÉ&#x;É§ÉĄÉ˘Ę É&#x161; ɤÉ&#x161;ɨ ɌɨÉ&#x17E;É&#x;ÉĽ ɨÉ&#x17E; ÉŤÉĽÉ&#x161;ɌɹɢɰÉ&#x161;.É&#x2039;ÉŹÉŞÉ&#x161;ɧɢɰɭÉ°ÉŞÉ&#x153;É&#x;ɧÉ&#x; É&#x203A;É¨Ę É&#x; ɨÉ&#x203A;É&#x;ÉĽÉ&#x;ɠɢɼɢɍɌɨ ɍɼɨÉ&#x153;ɨɌ Č&#x17D;,ÉŠÉĽÉ&#x161;É&#x153;É­ɍɼɨÉ&#x153;ɨɌb, É&#x161; ÉĄÉ&#x;ÉĽÉ&#x;ɧɭɍɼɨÉ&#x153;ɨɌČ&#x;.

Č&#x17D;

Čş

L

b

TA

Ć&#x201D;

c

Čź

É&#x201E;É&#x161;É&#x17E;É&#x161;ÉŤÉ­ɊɨɥɧÉ&#x161;ÉŹÉ&#x; É&#x17E;É­É É˘É§É&#x;ÉŤÉ&#x153;ɢɯÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x161;ɧÉ&#x;Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨɍɏɪÉ&#x161;ɧɢɹɧɨÉ? ɏɪɨɭÉ?ÉĽÉ&#x161;, Ę&#x192;É&#x;É?ɨÉ&#x153;ɨÉ&#x203A;ɢɌ ɌɨɠÉ&#x;ɌɨÉ&#x17E;É&#x161; ɢɥɪÉ&#x161;ɹɭɧÉ&#x161;ɌɨɊɨɌɨĘ&#x201E;É­ ɨÉ&#x203A;ÉŞÉ&#x161;ÉŤÉ°É&#x161;: É&#x2C6; = Č&#x17D; + b + c

R

É&#x2C6;É&#x203A;ɢɌɏɪɨɭÉ?ÉĽÉ&#x161; ȺȟÉ&#x2039;ɢɥɧɨɍɢ: É&#x2C6; = Č&#x17D; + b + c = (__ + __ + __) mm = ___ mm.

O

1. É&#x201A;ÉĄÉŞÉ&#x161;ɹɭɧÉ&#x161;Ę É­ÉŤÉŚÉ&#x;ɧɨɢ ÉĄÉ&#x161;ɊɢɲɢɨÉ&#x203A;ɢɌ ɧÉ&#x;Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨɍɏɪÉ&#x161;ɧɢɹɧɨÉ? ɏɪɨɭÉ?ÉĽÉ&#x161;, É&#x161;ɤɨÉŤÉ­Ę&#x192;É&#x;É?ɨÉ&#x153;É&#x; ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x;: É&#x203A;) Č&#x17D; = 1 dm, b = 7 cm, c = 9 cm. É&#x2C6; = _______. É&#x161;) Č&#x17D; = 6ÉŤm, b = 5ÉŤm, c = 4ÉŤm; É&#x2C6; = _______.

-P

É&#x201E;É&#x161;É&#x17E;É&#x161; je ɊɨɥɧÉ&#x161;ÉŹÉ&#x161;É&#x17E;É­É É˘É§a ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x;Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨɍɏɪÉ&#x161;ɧɢɹɧɨÉ? ɏɪɨɭÉ?ÉĽÉ&#x161;, Ę&#x192;É&#x;É?ɨÉ&#x153;ɨÉ&#x203A;ɢɌ ɌɨɠÉ&#x;ɌɨÉ&#x17E;É&#x161; ɢɥɪÉ&#x161;ɹɭɧÉ&#x161;ɌɨɊɨɌɨĘ&#x201E;É­ ɨÉ&#x203A;ÉŞÉ&#x161;ÉŤÉ°É&#x161;: É&#x2C6; = Č&#x17D; + Č&#x17D; + Č&#x17D; ɢɼɢɤɪÉ&#x161;Ę&#x201E;É&#x;: É&#x2C6; = 3 Č&#x17D; P

U KA

2. É&#x201A;ÉĄÉŚÉ&#x;ɪɢ É&#x17E;É­É É˘É§É&#x; ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x161; ɏɪɨɭÉ?ÉĽÉ&#x161; É&#x2C6;SP ɢ ɢɥɪÉ&#x161;ɹɭɧÉ&#x161;Ę Ę&#x192;É&#x;É?ɨÉ&#x153;ɨÉ&#x203A;ɢɌ. _____________________________

Č&#x17D;

_____________________________

O

Č&#x17D; S

Č&#x17D;

ED

3. É&#x201A;ÉĄÉŞÉ&#x161;ɹɭɧÉ&#x161;Ę É­ÉŤÉŚÉ&#x;ɧɨ ɢ ÉĄÉ&#x161;Ɋɢɲɢ ɨÉ&#x203A;ɢɌĘ É&#x;É&#x17E;ɧÉ&#x161;ɤɨɍɏɪÉ&#x161;ɧɢɹɧɨÉ? ɏɪɨɭÉ?ÉĽÉ&#x161;, É&#x161;ɤɨĘ É&#x;Ę&#x192;É&#x;É?ɨÉ&#x153;É&#x161; ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x161;: É&#x161;) Č&#x17D; = 9ÉŤm; É&#x203A;) Č&#x17D; = 1 dm; É&#x153;) Č&#x17D; = 35 mm; É?) Č&#x17D; = 2 dm 8 cm. É&#x2C6; = _______

É&#x2C6; = _______

É&#x2C6; = _______

É&#x2C6; = _______

É&#x201E;É&#x161;É&#x17E;É&#x161;ÉŤÉ­ɊɨɥɧÉ&#x161;ÉŹÉ&#x;É&#x17E;É­É É˘É§É&#x;ÉŤÉ&#x153;ɢɯÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x161;Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨɤɪÉ&#x161;ɤɨÉ? ɏɪɨɭÉ?ÉĽÉ&#x161;, Ę&#x192;É&#x;É?ɨÉ&#x153;ɨÉ&#x203A;ɢɌ ɌɨɠÉ&#x;ɌɨÉ&#x17E;É&#x161; ɢɥɪÉ&#x161;ɹɭɧÉ&#x161;ɌɨɊɨɌɨĘ&#x201E;É­ ɨÉ&#x203A;ÉŞÉ&#x161;ÉŤÉ°É&#x161;: É&#x2C6; = Č&#x17D; + b + b ɢɼɢɤɪÉ&#x161;Ę&#x201E;É&#x;: É&#x2C6; = É&#x161; + 2  b S

4. É&#x201A;ÉĄÉŚÉ&#x;ɪɢ É&#x17E;É­É É˘É§É&#x;ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x161; ɏɪɨɭÉ?ÉĽÉ&#x161; MTS ɢ ɢɥɪÉ&#x161;ɹɭɧÉ&#x161;Ę Ę&#x192;É&#x;É?ɨÉ&#x153;ɨÉ&#x203A;ɢɌ. _____________________________

b

b

_____________________________ M

Č&#x17D;

T

5. É&#x201A;ÉĄÉŞÉ&#x161;ɹɭɧÉ&#x161;Ę É­ÉŤÉŚÉ&#x;ɧɨ ɢ ÉĄÉ&#x161;ɊɢɲɢɨÉ&#x203A;ɢɌĘ É&#x;É&#x17E;ɧÉ&#x161;ɤɨɤɪÉ&#x161;ɤɨÉ? ɏɪɨɭÉ?ÉĽÉ&#x161;, É&#x161;ɤɨÉŤÉ­Ę&#x192;É&#x;É?ɨÉ&#x153;É&#x; ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x;: É&#x161;) Č&#x17D; = 5 ÉŤm, ɤɪÉ&#x161;ɤb = 8 ÉŤm; É&#x203A;) Č&#x17D; = 30 mm, ɤɪÉ&#x161;ɤ b = 55 mm; É&#x153;) Č&#x17D; = 65 mm, ɤɪÉ&#x161;ɤ b = 45 mm. É&#x2C6; = ________________

É&#x2C6; = ___________________

91

É&#x2C6; = __________________


É&#x2C6;ČťÉ&#x201A;É&#x2020;É&#x152;É&#x160;É&#x2C6;É?Č˝É&#x2026;Čş É&#x201E;Ę&#x201A;ɭɹɧÉ&#x;ÉŞÉ&#x;ɹɢ: ɨÉ&#x203A;ɢɌ ɏɪɨɭÉ?ÉĽÉ&#x161; ɧÉ&#x;Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨɍɏɪÉ&#x161;ɧɢɹɧɢ Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨɍɏɪÉ&#x161;ɧɢɹɧɢ, Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨɤɪÉ&#x161;ɤɢ

1. É&#x2030;ɪɢɌÉ&#x;ɧɢ ɨÉ&#x203A;ÉŞÉ&#x161;ÉĄÉ&#x161;É° ɢɢɥɪÉ&#x161;ɹɭɧÉ&#x161;Ę ɨÉ&#x203A;ɢɌ ɏɪɨɭÉ?ÉĽÉ&#x161;ÉąÉ˘Ę É&#x; ÉŤÉ­ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x;: É&#x161;) Č&#x17D; = 3 cm, b = 6 cm ɢ Č&#x; = 5 cm;

É&#x203A;) Č&#x17D; = 45 mm, b = 56 mm ɢ Č&#x; = 35 mm.

É&#x2C6; = ___________________________

É&#x2C6; = ___________________________

É&#x2C6; = ___________________________

É&#x2C6; = ___________________________

2. É&#x201A;ÉĄÉŞÉ&#x161;ɹɭɧÉ&#x161;Ę ɨÉ&#x203A;ɢɌĘ É&#x;É&#x17E;ɧÉ&#x161;ɤɨɍɏɪÉ&#x161;ɧɢɹɧɨÉ? ɏɪɨɭÉ?ÉĽÉ&#x161;, É&#x161;ɤɨĘ É&#x; Ę&#x192;É&#x;É?ɨÉ&#x153;É&#x161; ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x161;: É&#x161;) Č&#x17D; = 27ÉŤm;

É&#x203A;) Č&#x17D; = 18 dm;

É&#x153; Č&#x17D; = 68 mm;

É?) Č&#x17D; = 5 dm 3 cm.

É&#x2C6; = _______

É&#x2C6; = _______

É&#x2C6; = _______

É&#x2C6; = 3 ¡ __ÉŤm

É&#x2C6; = _______

É&#x2C6; = _______

É&#x2C6; = _______

É&#x2C6; = _______

É&#x2C6; = _______

É&#x2C6; = _______

É&#x2C6; = _______

TA

L

É&#x2C6;=3¡Č&#x201E;

3. É&#x201A;ÉĄÉŞÉ&#x161;ɹɭɧÉ&#x161;Ę É&#x17E;É­É É˘É§É­ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x;Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨɍɏɪÉ&#x161;ɧɢɹɧɨÉ? ɏɪɨɭÉ?ÉĽÉ&#x161;, É&#x161;ɤɨĘ É&#x; Ę&#x192;É&#x;É?ɨÉ&#x153;ɨÉ&#x203A;ɢɌ: É&#x161;) É&#x2C6; = 144 mm;

R

É&#x161;) É&#x2C6; = 75 mm;

O=3¡a 36 mm = 3 ¡ a

O = _____

a = 36 mm : __

a = ___________

a = __ mm

a = __ mm

O = _____

-P

______________

O

É&#x161;) É&#x2C6; = 36 mm;

É&#x161;) É&#x2C6; = 165 mm. ______________

______________

______________

a = ___________

______________

a = __ mm

_____________

U KA

4. É&#x2030;ɪɢɌÉ&#x;ɧɢɨÉ&#x203A;ÉŞÉ&#x161;ÉĄÉ&#x161;É° ɢɢɥɪÉ&#x161;ɹɭɧÉ&#x161;Ę ɨÉ&#x203A;ɢɌ Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨɤɪÉ&#x161;ɤɨÉ? ɏɪɨɭÉ?ÉĽÉ&#x161;, É&#x161;ɤɨÉŤÉ­Ę&#x192;É&#x;É?ɨÉ&#x153;É&#x; ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x;: É&#x161;) Č&#x17D; = 4 ÉŤm, ɤɪÉ&#x161;ɤ b = 9 ÉŤm; É&#x203A;) Č&#x17D; = 2 ÉŤm 5mm b = 50 mm;

É&#x153;) Č&#x17D; = 7 cm, ɤɪÉ&#x161;ɤ b = 1 dm 2 cm.

É&#x2C6; = ____________

É&#x2C6; = ____________

É&#x2C6; = ____________

É&#x2C6; = ____________

É&#x2C6; = ____________

É&#x2C6; = ____________

É&#x2C6; = ____________

É&#x2C6; = ____________

ED

É&#x2C6; = ____________

5. É&#x2C6;É&#x203A;ɢɌ Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɨɤɪÉ&#x161;ɤɨÉ? ɏɪɨɭÉ?ÉĽÉ&#x161; ɢɥɧɨɍɢ19 cm. ČžÉ­É É˘É§É&#x161;Ę É&#x;É&#x17E;ɧÉ&#x; ɨÉ&#x17E;Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɢɯÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x161;Ę É&#x; 7 cm. É&#x201E;ɨɼɢɤÉ&#x161;Ę É&#x; É&#x17E;ɭɠɢɧÉ&#x161; ÉŹÉŞÉ&#x;Ę&#x201E;É&#x;ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x;?

b

b = 7 cm

O = 19 cm b = 7 cm Č&#x17D;=?

O=a+2¡b 19 cm = Č&#x17D; + 2 ¡ 7 cm Č&#x17D; = ___ cm â&#x20AC;&#x201C; ___ cm Č&#x17D; = ___ cm

a=? É&#x2C6;É&#x17E;É?ɨÉ&#x153;ɨɪ: ________________________________________ 6. É&#x201A;ÉĄÉŞÉ&#x161;ɹɭɧÉ&#x161;Ę ɧÉ&#x;ɊɨɥɧÉ&#x161;ÉŹÉ­ÉŤÉŹÉŞÉ&#x161;ɧɢɰɭĘ É&#x;É&#x17E;ɧÉ&#x161;ɤɨɤɪÉ&#x161;ɤɨÉ? ɏɪɨɭÉ?ÉĽÉ&#x161;, ɤÉ&#x161;É&#x17E;É&#x161;Ę É&#x;ɊɨɥɧÉ&#x161;ÉŹ Ę&#x192;É&#x;É?ɨÉ&#x153;ɨÉ&#x203A;ɢɌ ɢ Ę É&#x;É&#x17E;ɧÉ&#x161; ɨÉ&#x17E;Ę É&#x;É&#x17E;ɧÉ&#x161;ɤɢɯ ÉŤÉŹÉŞÉ&#x161;ɧɢɰÉ&#x161; ɤɪÉ&#x161;ɤ b): É&#x161;) O = 22 cm, b = 6 cm; ______________________________________________________ É&#x203A;) O = 1 dm, b = 34 mm. ______________________________________________________

92


ɉɊȿɋɅɂɄȺȼȺȵȿ ȽȿɈɆȿɌɊɂȳɋɄɂɏ ɎɂȽɍɊȺ ɇȺ ɄȼȺȾɊȺɌɇɈȳ ɆɊȿɀɂ Ʉʂɭɱɧɟɪɟɱɢ: ɩɪɟɫɥɢɤɚɜɚʃɟ ɝɟɨɦɟɬɪɢʁɫɤɢɯ ɮɢɝɭɪɚ ɧɚ ɤɜɚɞɪɚɬɧɨʁ ɦɪɟɠɢ ɭ ɨɞɧɨɫɭ ɧɚ ɞɚɬɭ ɩɪɚɜɭ

1. Ⱦɭɲɚɧʁɟ ɧɚɰɪɬɚɨɞɜɚ ɦɚɝɚɪɰɚ. ɉɚɠʂɢɜɨɩɨɫɦɚɬɪɚʁ ɫɥɢɤɭ. ɒɬɚʁɟ ɤɨɞ ɨɜɚ ɞɜɚ ɰɪɬɟɠɚ ɪɚɡɥɢɱɢɬɨ? Ɂɚɨɤɪɢɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ ɚ) ɭɲɢ ɛ ɜɟɥɢɱɢɧɚ ɝ) ʃɭɲɤɚ

TA

ɞ) ɨɛɥɢɤ

L

ɜ) ɪɟɩ

ɻ ɩɨɥɨɠɚʁ

ɪɟɤɥɚɞɚ ɢɦ ʁɟ ɬɟɥɨɩɨɬɩɭɧɨ ɢɫɬɨ, ɚɥɢ ɞɚ ɡɚɭɡɢɦɚʁɭ ɪɚɡɥɢɱɢɬ ɩɨɥɨɠɚʁɭ ɨɞɧɨɫɭɧɚ ɩɪɚɜɭɥɢɧɢʁɭ. ȾɚɥɢʁɟɆɢɧɢɧ ɨɞɝɨɜɨɪ ɬɚɱɚɧ" Ɣ ɒɬɚ ɦɢɫɥɢɲɤɚɤɨʁɟ Ⱦɭɲɚɧɭɫɩɟɨɞɚɧɚɰɪɬɚ ɨɜɚɞɜɚ ɦɚɝɚɪɰɚ?

R

Ɣ Ɇɢɧɚʁɟ

O

ɇɚ ɨɜɨʁɫɥɢɰɢ ɭɨɱɚɜɚɦɨɞɚʁɟ Ⱦɭɲɚɧɡɚɰɪɬɚʃɟ ɤɨɪɢɫɬɢɨ ɤɜɚɞɪɚɬɧɭ ɦɪɟɠɭ ɢɩɪɚɜɭɥɢɧɢʁɭ.

-P

Ⱦɭɲɚɧʁɟɩɪɜɢɰɪɬɟɠɩɪɟɫɥɢɤɚɨ ɧɚ ɫɭɩɪɨɬɧɭɫɬɪɚɧɭɩɪɜɟ ɥɢɧɢʁɟ.

U KA

Ɍɚɤɨʁɟɞɨɛɢɨɞɜɚ ɢɫɬɚɰɪɬɟɠɚ, ɤɨʁɢɦɚʁɟ ɫɚɦɨ ɪɚɡɥɢɱɢɬ ɩɨɥɨɠɚʁ

ɇɚ ɤɜɚɞɪɚɬɧɨʁɦɪɟɠɢ ɦɨɠɟɦɨɩɪɟɫɥɢɤɚɬɢ ɮɢɝɭɪɭ ɭ ɨɞɧɨɫɭɧɚɧɚɰɪɬɚɧɭɩɪɚɜɭɥɢɧɢʁɭ.

ED

1. ɉɨɦɨʄɭɩɪɚɜɟ ɥɢɧɢʁɟ,ɩɨɞɟɥɢ ɫɜɚɤɭɮɢɝɭɪɭɧɚɞɜɚ ʁɟɞɧɚɤɚɞɟɥɚ.

2. ɉɪɟɫɥɢɤɚʁɢ ɬɢ ɧɚɰɪɬɚɧɟ ɮɢɝɭɪɟ ɭ ɨɞɧɨɫɭɧɚɞɚɬɭɩɪɚɜɭ. ɉɨɝɥɟɞɚʁɩɪɢɦɟɪ.

93


ɉɊȿɋɅɂɄȺȼȺȵȿȽȿɈɆȿɌɊɂȳɋɄɂɏ ɎɂȽɍɊȺ ɇȺ ɄȼȺȾɊȺɌɇɈȳ ɆɊȿɀɂ Ʉʂɭɱɧɟɪɟɱɢ: ɩɪɟɫɥɢɤɚɜɚʃɟ ɝɟɨɦɟɬɪɢʁɫɤɢɯ ɮɢɝɭɪɚ ɧɚ ɤɜɚɞɪɚɬɧɨʁ ɦɪɟɠɢ ɭ ɨɞɧɨɫɭ ɧɚ ɞɚɬɭ ɩɪɚɜɭ

ɨɡɧɚɱɢɩɪɟɫɥɢɤɚɧɟ ɮɢɝɭɪɟ. Ɏɢɝɭɪɟ ɤɨʁɟ ɧɢɫɭɩɪɟɫɥɢɤɚɧɟ ɨɡɧɚɱɢ ɫɚ

.

TA

L

1. Ɂɧɚɤɨɦ

3. Ⱦɚɥɢɢɫɩɪɟɤɢɞɚɧɚ ɥɢɧɢʁɚ ɞɟɥɢ ɮɢɝɭɪɭɧɚ ɞɜɚ ʁɟɞɧɚɤɚɞɟɥɚ? Ɉɞɝɨɜɨɪɢ ɫɚ „ȾȺ” ɢɥɢ„ɇȿ”.

U KA

-P

O

R

2. ɉɨɜɟɠɢɥɢɧɢʁɨɦɨɞɝɨɜɚɪɚʁɭʄɟ ɩɨɥɨɜɢɧɟ ɮɢɝɭɪɚ.

ED

4. ɉɪɟɫɥɢɤɚʁ ɞɪɭɝɢ ɞɟɨɮɢɝɭɪɟ ɭ ɨɞɧɢɫɭ ɧɚ ɞɚɬɭɩɪɚɜɭ.

5. Ɏɢɝɭɪɟ ɧɚ ɰɪɬɟɠɭɩɨɦɟɪɢ ɧɚɞɟɫɧɨ, ɬɚɤɨ ɲɬɨ ʄɟɲɢɯ ɧɚɰɪɬɚɬɢ ɧɚ ɭɞɚʂɟɧɨɫɬɢɞɜɟ ɞɭɠɢɧɟ ɫɬɪɚɧɢɰɟ ɤɜɚɞɪɚɬɚ ɫɚ ɤɜɚɞɪɚɬɧɟ ɦɪɟɠɟ. ɉɨɝɥɟɞɚʁɩɪɢɦɟɪ.

7. ɇɚɰɪɬɚʁɭ ɫɜɟɫɰɢɧɚ ɤɜɚɞɪɚɬɢʄɟ ɩɪɚɜɨɭɝɚɨɧɢɤ ɤɜɚɞɪɚɬ ɢ ɬɪɨɭɝɚɨ. ɉɨɦɟɪɢ ɬɟɮɢɝɭɪɟ ɧɚ ɥɟɜɨ, ɬɚɤɨɲɬɨ ʄɟɲɢɯ ɧɚɰɪɬɚɬɢ ɧɚ ɭɞɚʂɟɧɨɫɬɢɬɪɢ ɞɭɠɢɧɟ ɫɬɪɚɧɢɰɟ ɤɜɚɞɪɚɬɚɫɚ ɤɜɚɞɪɚɬɧɟ ɦɪɟɠɟ.

94


ɋȺȾȺ ɁɇȺɆ ɆɇɈȽɈ ȼɂɒȿ Ʉʂɭɱɧɟɪɟɱɢ: ɩɪɚɜɨɭɝɚɨɧɢɤ, ɤɜɚɞɪɚɬ, ɬɪɨɭɝɚɨ, ɩɪɟɫɥɢɤɚɜɚʃɟ ɝɟɨɦɟɬɪɢʁɫɤɢɯ ɮɢɝɭɪɚ ɧɚ ɤɜɚɞɪɚɬɧɨʁ ɦɪɟɠɢ

Źɉɪɚɜɨɭɝɚɨɧɢɤ

ʁɟɝɟɨɦɟɬɪɢʁɫɤɚ ɮɢɝɭɪɚ ɤɨʁɭ ɱɢɧɟ ɡɚɬɜɨɪɟɧɚ ɢɡɥɨɦʂɟɧɚ ɥɢɧɢʁɚɢ ʃɟɧɚ ɭɧɭɬɪɚɲʃɨɫɬ. Ɍɚ ɡɚɬɜɨɪɟɧɚ ɢɡɥɨɦʂɟɧɚɥɢɧɢʁɚɫɟ ɫɚɫɬɨʁɢ ɢɡ 4 ɞɭɠɢ. ɉɪɚɜɨɭɝɚɨɧɢɤʁɟ ɱɟɬɜɨɪɨɭɝɚɨ ɤɨʁɢ ɢɦɚ 4 ɩɪɚɜɚ ɭɝɥɚ. ɍɝɥɨɜɢ ɩɪɚɜɨɭɝɚɨɧɢɤɚɧɚ ɰɪɬɟɠɭ ɫɭ: DAB, ABC, BCD ɢ CDA.

a

D

C

ɤɨʁɟɨɝɪɚɧɢɱɚɜɚʁɭ ɩɪɚɜɨɭɝɚɨɧɢɤɧɚɡɢɜɚʁɭ ɫɟ ɫɬɪɚɧɢɰɟ ɩɪɚɜɨɭɝɚɨɧɢɤɚAB, BC, CD ɢ DA. b ŹɌɚɱɤɟɭ ɤɨʁɢɦɚ ɫɟɫɚɫɬɚʁɭ ɫɬɪɚɧɢɰɟ ɧɚɡɢɜɚʁɭ ɫɟɬɟɦɟɧɚ ɩɪɚɜɨɭɝɚɨɧɢɤɚ Ɍɨ ɫɭ ɬɚɱɤɟ: A, B, C ɢ D.

b

B

a

L

A

ŹȾɭɠɢ

ɫɬɪɚɧɢɰɟ ɢɦɚʁɭ ɡɚʁɟɞɧɢɱɤɨ ɬɟɦɟ. Ɇɟɻɭɫɨɛɧɨɫɭ ɧɨɪɦɚɥɧɟɢɪɚɡɥɢɱɢɬɟ ɩɨ ɞɭɠɢɧɢ. Ɍɨ ɫɭ ɫɬɪɚɧɢɰɟ: AB ɢ BC, BC ɢ CD, CD ɢ DA, DA ɢ AB. Źɇɚɫɩɪɚɦɧɟ ɫɬɪɚɧɢɰɟ ɫɟ ɧɚɥɚɡɟ ʁɟɞɧɚ ɧɚɫɩɪɚɦ ɞɪɭɝɟ. Ɇɟɻɭɫɨɛɧɨɫɭ ɩɚɪɚɥɟɥɧɟ ɢ ʁɟɞɧɚɤɟ ɩɨ ɞɭɠɢɧɢ. ɇɚɫɩɪɚɦɧɟ ɫɬɪɚɧɢɰɟɫɭ: AB ɢ DC, AD ɢ BC. Ź Ɉɛɢɦ ɩɪɚɜɨɭɝɚɨɧɢɤɚɦɨɠɟɦɨ ɞɚɨɞɪɟɞɢɦɨɩɨɦɨʄɭ ɨɛɪɚɫɰɚ: Ɉ = 2 · (Ȏ + b).

Ȏ

R

C

Ȏ

ŹɄɜɚɞɪɚɬ Ź Ɉɛɢɦ

Ȏ

ʁɟ ɩɪɚɜɨɭɝɚɨɧɢɤ ɤɨʁɢ ɢɦɚ ɫɜɟ ɫɬɪɚɧɢɰɟ ʁɟɞɧɚɤɟ ɞɭɠɢɧɟ. ɤɜɚɞɪɚɬɚ ɦɨɠɟɦɨ ɞɚɨɞɪɟɞɢɦɨ ɩɨɦɨʄɭ ɨɛɪɚɫɰɚ: Ɉ = 4  Ȏ.

O

D

TA

Źɋɭɫɟɞɧɟ

ȿɥɟɦɟɧɬɢ ɩɪɚɜɨɭɝɚɨɧɢɤɚ(ɤɜɚɞɪɚɬɚ) ɫɭ: 4 ɫɬɪɚɧɢɰɟ, ɬɟɦɟɧɚ ɢ 4 ɭɝɥɚ.

B

Ȏ

-P

Ⱥ

ʁɟɝɟɨɦɟɬɪɢʁɫɤɚ ɮɢɝɭɪɚ ɤɨʁɭ ɱɢɧɟ ɡɚɬɜɨɪɟɧɚ ɢɡɥɨɦʂɟɧɚ ɥɢɧɢʁɚɢ ʃɟɧɚɭɧɭɬɪɚɲʃɨɫɬ Ɍɚɡɚɬɜɨɪɟɧɚ ɢɡɥɨɦʂɟɧɚ ɥɢɧɢʁɚ ɫɟɫɚɫɬɨʁɢ ɢɡ 3 ɞɭɠɢ.

U KA

ŹɌɪɨɭɝɚɨ

Ź Ⱦɭɠɢ Ź

a

b

Ź

Ⱥȼ, ȼɋ ɢ ɋȺ ɧɚɡɢɜɚʁɭ ɫɟɫɬɪɚɧɢɰɟɬɪɨɭɝɥɚ Ɍɚɱɤɟ Ⱥ, ȼ ɢ ɋ ɫɭ ɬɟɦɟɧɚ ɬɪɨɭɝɥɚ. ɋɬɪɚɧɢɰɟɬɪɨɭɝɥɚ ɨɛɪɚɡɭʁɭ 3 ɭɝɥɚ: ɋȺȼ, Ⱥȼɋ ɢ

ȼɋȺ.

ȿɥɟɦɟɧɬɢ ɬɪɨɭɝɥɚ ɫɭ: ɫɬɪɚɧɢɰɟ, 3 ɬɟɦɟɧɚ ɢ 3 ɭɝɥɚ.

ȕ

ED

 ɉɪɟɦɚ ɞɭɠɢɧɚɦɚ ɫɬɪɚɧɢɰɚ ɪɚɡɥɢɤɭʁɟɦɨ ɬɪɢ ɜɪɫɬɟ ɬɪɨɭɝɥɨɜɚ ɧɟʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ

ʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ P

ɋ

Ȏ

b

Ⱥ

ȟ

Ɉ=a+b+c

Ɣ

Ȏ ȼ

O

ʁɟɞɧɚɤɨɤɪɚɤɢ S

Ȏ Ȏ

Ɉ = 3 a

Ɂɧɚɦɞɚ ɧɚ ɤɜɚɞɪɚɬɧɨʁɦɪɟɠɢ ɩɪɟɫɥɢɤɚɦ ɝɟɨɦɟɬɪɢʁɫɤɭ ɮɢɝɭɪɭ.

95

b

b S

M

Ȏ

T

Ɉ = a + 2 b


ɉɊɈȼȿɊȺȼȺɆɈ ɇȺɍɑȿɇɈ Ʉʂɭɱɧɟɪɟɱɢ ɩɪɚɜɨɭɝɚɨɧɢɤ, ɤɜɚɞɪɚɬ, ɬɪɨɭɝɚɨ, ɩɪɟɫɥɢɤɚɜɚʃɟ ɝɟɨɦɟɬɪɢʁɫɤɢɯ ɮɢɝɭɪɚ ɧɚ ɤɜɚɞɪɚɬɧɨʁ ɦɪɟɠɢ

1. ɉɨɦɨʄɭɲɟɫɬɚɪɚ ɢɥɟʃɢɪɚɧɚɰɪɬɚʁ ɚ ɩɪɚɜɨɭɝɚɨɧɢɤAMST, ɱɢʁɟ ɫɭɫɭɫɟɞɧɟ ɫɬɪɚɧɢɰɟɞɭɠɢɧɟ 4 cm ɢ 3 cm;

TA

L

ɛ ɤɜɚɞɪɚɬȺȼɋD, ɱɢʁɚʁɟɫɬɪɚɧɢɰɚ ɞɭɠɢɧɟ 3 cm.

2. ɂɡɪɚɱɭɧɚʁɨɛɢɦɩɪɚɜɨɭɝɚɨɧɢɤɚ, ɚɤɨʁɟ ɚ) Ȏ = 12 cm ɛ) Ȏ = 6 dm 4 cm b = 7 cm b = 9 cm

ɛ) Ɉ = 68 cm;

ɜ) O = 512 mm.

U KA

ɚ) Ɉ = 2 dm;

ɛ) Ȏ = 58 cm

O

R

ɚ) Ȏ = 7 dm

-P

4. ɂɡɪɚɱɭɧɚʁɫɬɪɚɧɢɰɭ ɤɜɚɞɪɚɬɚ ɱɢʁɢʁɟ ɨɛɢɦ

3. ɂɡɪɚɱɭɧɚʁɨɛɢɦ ɤɜɚɞɪɚɬɚ, ɚɤɨʁɟ

5. ɉɪɟɦɚɞɚɬɢɦ ɩɨɞɚɰɢɦɚ ɭ ɬɚɛɟɥɢ,ɧɚɰɪɬɚʁɨɞɝɨɜɚɪɚʁɭʄɟ ɬɪɨɭɝɥɨɜɟ ɢɨɞɪɟɞɢ ʃɢɯɨɜɟ ɨɛɢɦɟ. ɛ) ʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ ɬɪɨɭɝɚɨ Ȏ = 3 cm

ɜ) ʁɟɞɧɚɤɨɤɪɚɤɢ ɬɪɨɭɝɚɨ Ȏ = 2 cm, ɤɪɚɤ b = 3 cm

ED

ɚ ɧɟʁɟɞɧɚɤɨɫɬɪɚɧɢɱɧɢ ɬɪɨɭɝɚɨ Ȏ = 5 cm, b = 4 cm, c = 25 mm

Ɉ = ______________________

Ɉ = ____________________

6. ɉɪɟɫɥɢɤɚʁ ɧɚɰɪɬɚɧɟ ɮɢɝɭɪɟ ɭ ɨɞɧɨɫɭɧɚɞɚɬɭɩɪɚɜɭ.

96

Ɉ=


TA

L

МНОЖЕЊЕ И ДЕЉЕЊЕ ДО 1000 

O

R

ōřŜŌőōŎŗ

-P

ŖʼnŜŠőŅŎš

U KA

ŭũŸűźŵŮŶűŵŸŷźŻżŸųŷŵŵŶŷůűƁ ŻŹŷſűŽŹŮŶŮŪŹŷƐŮūŮƐŮŭŶŷſűŽŹŮŶűŵŪŹŷƐŮūűŵũ

ED

ŭũŸűźŵŮŶűŵŸŷźŻżŸųŷŵŭŮŴűƁ ŻŹŷſűŽŹŮŶŮŪŹŷƐŮūŮƐŮŭŶŷſűŽŹŮŶűŵŪŹŷƐŮūűŵũ ŭũŹŮƁũūũƁŰũŭũŻųŮźũŭūŮűŻŹűŷŸŮŹũſűƐŮ

ŭũŸŹűŵŮŶűƁŸŹũūűŴũŷŹŮŭŷźŴŮŭżŹũƀżŶźųűžŷŸŮŹũſűƐũ żŵũŻŮŵũŻűƀųűŵűŰŹũŰűŵũ ŷźūŷƐźŻūűŵũŹũƀżŶźųűžŷŸŮŹũſűƐũŵŶŷůŮƒũűŭŮƑŮƒũ ŭũŹŮƁũūũƁƐŮŭŶũƀűŶŮźũŶŮŸŷŰŶũŻűŵƀűŶűŷſŮŵ ŭũŸŹűŵŮŶűƁźŻŮƀŮŶũŰŶũƒũżŹũŰŴűƀűŻűŵŰũŭũſűŵũ


ɉɂɋɆȿɇɈ ɆɇɈɀȿȵȿɌɊɈɐɂɎɊȿɇɈȽ ȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ: 243 · 2; 216 · 3 Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

ɇɚɭɱɢɥɢ ɫɦɨ ɤɚɤɨɞɚ ɪɚɱɭɧɚɦɨ ɩɪɨɢɡɜɨɞ ɛɪɨʁɟɜɚ ɭɫɦɟɧɢɦɩɨɫɬɭɩɤɨɦ.

Ɣ

ɉɪɢɦɟʃɭʁɟɦɫɜɨʁɫɬɜɨ ɦɧɨɠɟʃɚ ɡɛɢɪɚɛɪɨʁɟɦ

243 · 2 = (200 + 40 + 3) · 2 = (200 · 2) + (40 · 2) + (3 · 2) = 400 + 80 + 6 = 486 ɉɪɜɨ ɦɧɨɠɢɦɨɫɬɨɬɢɧɟ, ɡɚɬɢɦ ɞɟɫɟɬɢɰɟ ɢɧɚ ɤɪɚʁɭʁɟɞɢɧɢɰɟ.

ȳ

2

4

3

4

8

6

2 · 3 = 6, ɰɢɮɪɭ 6 ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞʁɟɞɢɧɢɰɚ 

2

2 · 4 = 8, ɰɢɮɪɭ 8 ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞɞɟɫɟɬɢɰɚ.

O

· 2 0 1 3 4 · 2 0 2 1 3 · 3 0 4 3 2 · 2 0 2 1 2 · 4

3

-P

2

243·2 486

2 · 2 = 4, ɰɢɮɪɭ 4 ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞɫɬɨɬɢɧɚ.

1. ɂɡɪɚɱɭɧɚʁɩɪɨɢɡɜɨɞɟ ɧɚɝɨɪɟɩɪɢɤɚɡɚɧɧɚɱɢɧ 1

Ȼɟɡ ɬɚɛɥɢɰɟ

R

ɋ Ⱦ

TA

L

Ɍɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɟɥɚɤɲɟ ɢɛɪɠɟ ɦɧɨɠɢɦɨ ʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦɩɢɫɦɟɧɢɦ ɩɨɫɬɭɩɤɨɦ ɂ ɬɨ, ɨɜɚɤɨ: ɩɪɜɨ ɦɧɨɠɢɦɨ ʁɟɞɢɧɢɰɟ, ɡɚɬɢɦ ɞɟɫɟɬɢɰɟ ɢɧɚ ɤɪɚʁɭ ɫɬɨɬɢɧɟ.

ɋ Ⱦ

ȳ

2

1

6

6

4

8

·

3

U KA

‡ ɐɟɧɚʁɟɞɧɨɝ ɪɚɧɰɚɢɡɧɨɫɢ 216 ɞɢɧɚɪɚ. Ʉɨɥɢɤɨɞɢɧɚɪɚ ʁɟ ɬɪɝɨɜɚɰɩɪɢɦɢɨ, ɤɚɞɚʁɟ ɩɪɨɞɚɨ 3 ɬɚɤɜɚ ɪɚɧɰɚ? 3 · 6ȳ = 18ȳ 1Ⱦ 8ȳ ɐɢɮɪɭ 8 ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞʁɟɞɢɧɢɰɚ, ɚ 1 ɞɟɫɟɬɢɰɭɞɨɞɚʁɟɦɨɞɟɫɟɬɢɰɚɦɚ. 3 · 1Ⱦ = 3Ⱦ, 3Ⱦ + 1Ⱦ = 4Ⱦ . ɐɢɮɪɭ 4 ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞɞɟɫɟɬɢɰɚ.

Ȼɟɡ ɬɚɛɥɢɰɟ

3 · 2ɋ= 6ɋɐɢɮɪɭ 6 ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞɫɬɨɬɢɧɚ.

ED

216·3 648

Ɣ

Ɍɪɝɨɜɚɰʁɟ ɡɚ ɬɪɢɩɪɨɞɚɬɚ ɪɚɧɰɚ ɩɪɢɦɢɨ ___ ɞɢɧɚɪɚ.

2. ɂɡɪɚɱɭɧɚʁɩɪɨɢɡɜɨɞɟ ɧɚɝɨɪɟɩɪɢɤɚɡɚɧɧɚɱɢɧ 2

3

7

 2

0

1

0

9

 6

0

2

1

6

 4

3. Ɉɞɪɟɞɢ ɛɪɨʁɤɨʁɢʁɟ: ɚ) 6ɩɭɬɚɜɟʄɢɨɞɛɪɨʁɚ 107?

0

4

2

8

 2

0

2

1

5

 3

ɛ) 3ɩɭɬɚɜɟʄɢɨɞɛɪɨʁɚ 229?

Ɍɨʁɟɛɪɨʁ ___.

Ɍɨʁɟɛɪɨʁ ___.

4. ɉɨɥɚ ɤɢɥɨɝɪɚɦɚ ɫɚɥɚɦɟ ɤɨɲɬɚ 419 ɞɢɧɚɪɚ. Ʉɨɥɢɤɨ ɤɨɲɬɚ 1 kg ɬɟɫɚɥɚɦɟ" Ɉɞɝɨɜɨɪ: _______________________________________________

98


ɉɂɋɆȿɇɈ ɆɇɈɀȿȵȿɌɊɈɐɂɎɊȿɇɈȽ ȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ 243 · 2; 216 · 3 Ʉʂɭɱɧɟɪɟɱɢ ɦɧɨɠɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

L

1. ɂɡɪɚɱɭɧɚʁɩɪɨɢɡɜɨɞɟ ɧɚ ɩɭɡɥɚɦɚ, a ɡɚɬɢɦ ɢɯ ɨɛɨʁɪɚɡɥɢɱɢɬɢɦ ɛɨʁɚɦɚ.

270

375

250

R

265

Ɍɚɱɚɧɨɞɝɨɜɨɪ ɡɚɨɤɪɭɠɢ ɰɪɜɟɧɨɦɛɨʁɨɦ.

TA

2. ɇɚ ʁɟɞɧɨɦɞɟɱʁɟɦ ɤɚɧɚɥɭɩɪɟɞɜɢɻɟɧɨ ɜɪɟɦɟ ɡɚ ɲɤɨɥɫɤɢɩɪɨɝɪɚɦ ʁɟ 125 ɦɢɧɭɬɚ, ɚɜɪɟɦɟ ɡɚɰɪɬɚɧɟɮɢɥɦɨɜɟ ʁɟ ɬɪɢ ɩɭɬɚɞɭɠɟ. Ʉɨɥɢɤɨ ɦɢɧɭɬɚʁɟ ɩɪɟɞɜɢɻɟɧɨ ɡɚ ɰɪɬɚɧɟɮɢɥɦɨɜɟ?

3. ȳɟɥɟɧɚ ʁɟ ɩɪɨɱɢɬɚɥɚ 237ɫɬɪɚɧɚ ʁɟɞɧɟ ɤʃɢɝɟ, ɚ ɬɨʁɟ ɩɨɥɨɜɢɧɚ ɰɟɥɟ ɤʃɢɝɟ. Ʉɨɥɢɤɨ ɫɬɪɚɧɚ ɢɦɚ ɤʃɢɝɚ ɤɨʁɭȳɟɥɟɧɚ ɱɢɬɚ? 464

474

414

O

ɉɨʂɟɫɚɬɚɱɧɢɦɨɞɝɨɜɨɪɨɦ ɨɛɨʁ ɠɭɬɨɦ ɛɨʁɨɦ.

444

-P

4. ɐɟɧɚʁɟɞɧɟ ɭɥɚɡɧɢɰɟ ɡɚ Ɂɨɨ-ɜɪɬ ʁɟ 215ɞɢɧɚɪɚ. Ʉɨɥɢɤɨɞɢɧɚɪɚ ɬɪɟɛɚ ɞɚ ɢɡɞɜɨʁɢ ɱɟɬɜɨɪɨɱɥɚɧɚɩɨɪɨɞɢɰɚ ɡɚɩɨɫɟɬɭɁɨɨ-ɜɪɬɭ? ɉɪɟɰɪɬɚʁɩɨʂɚɫɚɧɟɬɚɱɧɢɦɨɞɝɨɜɨɪɨɦ.

U KA

860

805

680

870

5. Ⱥɥɛɭɦ ɡɚ ɮɨɬɨɝɪɚɮɢʁɟ ɢɦɚ 116ɫɬɪɚɧɚ. ɇɚɫɜɚɤɭɫɬɪɚɧɭ ɦɨɝɭ ɞɚɫɟɫɬɚɜɟ 4ɮɨɬɨɝɪɚɮɢʁɟ.Ʉɨɥɢɤɨ ʄɟɮɨɬɨɝɪɚɮɢʁɚ ɛɢɬɢ ɭ ɚɥɛɭɦɭ ɤɚɞɚ ɫɟ ɨɧɩɨɩɭɧɢ"

ED

Ɍɚɱɚɧɨɞɝɨɜɨɪ ɡɚɨɤɪɭɠɢ ɩɥɚɜɨɦ ɛɨʁɨɦ.

414

474

454

464

6. ɂɡɜɪɲɢɦɧɨɠɟʃɚ. ɉɪɨɧɚɻɢ ɭ ɬɚɛɟɥɢ ɞɨɛɢʁɟɧɟɛɪɨʁɟɜɟ ɢ ɢɡɧɚɞʃɢɯɧɚɩɢɲɢɨɞɝɨɜɚɪɚʁɭʄɚ ɢɦɟɧɚ.Ɍɚɤɨ ʄɟɲɫɚɡɧɚɬɢ ɡɚɧɢɦʂɢɜɨɫɬɢ ɨɧɟɤɢɦɫɬɚɧɨɜɧɢɰɢɦɚɛɚɪɚ ɢ ʁɟɡɟɪɚ. 2

1

9

·

3

ɦɚɥɢ ɝʃɭɪɚɰ

3

2

6

·

ɜɨɞɨɦɚɪ

3

4

3

8

·

ɛɚɪɫɤɚ ɫɨɜɚ

2

1

9

·

3

ɜɢɥɢɧɤɨʃɢɰ

Ʌɟɬɢ ɤɚɨ ɯɟɥɢɤɨɩɬɟɪ ɂɚɤɨɠɢɜɟ ɭɫɚɦʂɟɧɨ, ɦɚɥɟ ɍɯɜɚʄɟɧɭ ɪɢɛɭ ɩɪɜɨ ɧɚɩɪɟɞ, ɧɚɡɚɞ, ɝɨɪɟ, ɝɪɭɩɟ ɧɚɡɢɜɚʁɭ „ɩɚɪɥɚɦɟɧɬ” ɨɲɚɦɭɬɢ ɭɞɚɪɚʁɭʄɢʁɟɨ ɞɨɥɟ ɢɥɢ ɭ ɦɟɫɬɭ. ʁɟɪ ɫɭ ɬɨ ɜɪɥɨ ɦɭɞɪɟ ɩɬɢɰɟ ɞɪɜɨ, ɚɨɧɞɚ ʁɟɩɪɨɝɭɬɚ.

99

2

Ɋɨɧɟ ɧɚ ɞɭɛɢɧɢ ɞɨ 4 m ɢ ɬɚɤɨ ɩɪɟɥɚɡɟ ɜɟɥɢɤɟɪɚɡɞɚʂɢɧɟ


ɉɂɋɆȿɇɈ ɆɇɈɀȿȵȿɌɊɈɐɂɎɊȿɇɈȽ ȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ: 241 · 4; 165 · 5 Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

‡ ɍɩɪɨɞɚɜɧɢɰɢɫɭɜɟɧɢɪɚ ɭʁɟɞɧɨɦ ɦɟɫɟɰɭɩɪɨɞɚɬ ʁɟ 241ɫɚɬ ɢ 4ɩɭɬɚɜɢɲɟ ɨɩɚɧɚɤɚ. Ʉɨɥɢɤɨʁɟ ɩɪɨɞɚɬɨ ɨɩɚɧɚɤɚ?

2

4

1

9

6

4

4 · 1ȳ = 4ȳ ɰɢɮɪɭ 4 ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞʁɟɞɢɧɢɰɚ. ·

4

4 · 4Ⱦ = 16Ⱦ 1ɋ6Ⱦ. ɐɢɮɪɭ 6 ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞɞɟɫɟɬɢɰɚ ɚ 1ɫɬɨɬɢɧɭɞɨɞɚʁɟɦɨɫɬɨɬɢɧɚɦɚ. 4 · 2ɋ = 8ɋ 8ɋ+ 1ɋ= 9ɋ. ɐɢɮɪɭ 9 ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞɫɬɨɬɢɧɚ

Ȼɟɡ ɬɚɛɥɢɰɟ

2 4 1 4 964

L

ȳ

 ɉɪɨɞɚɬɨʁɟ ___ ɨɩɚɧɚɤɚ.

1. ɂɡɪɚɱɭɧɚʁɞɚɬɟɩɪɨɢɡɜɨɞɟ ɧɚ ɝɨɪɟɩɪɢɤɚɡɚɧɧɚɱɢɧ 7

·

2

3

0

1

9

·

1

6

0

1

7

·

2

4

0

2

9

·

3

R

1

TA

ɋ Ⱦ

3

0

1

8

·

1

5

O

2. ȳɟɞɧɚ ɫɤɢʁɚɲɤɚɫɬɚɡɚ ɢɦɚɞɭɠɢɧɭ 240 m ɚ ɞɪɭɝɚ ɫɬɚɡɚʁɟ 4ɩɭɬɚɞɭɠɚ. Ʉɨɥɢɤɚ ʁɟɞɭɠɢɧɚɞɪɭɝɟɫɬɚɡɟ?

-P

Ɉɞɝɨɜɨɪ: _________________________________

‡ ɐɟɧɚʁɟɞɧɨɝɫɥɚɞɨɥɟɞɚ ʁɟ 165 ɞɢɧɚɪɚ. Ʉɨɥɢɤɢ ʄɟ ɪɚɱɭɧɛɢɬɢ ɡɚɩɟɬ ɬɚɤɜɢɯɫɥɚɞɨɥɟɞɚ? Ⱦ

ȳ

3

2

0

0

0

1 8

6 2

5 5

·

5

5 5ȳ = 2ȳ 2Ⱦ 5ȳ. ɐɢɮɪɭ ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞʁɟɞɢɧɢɰɚ ɚ 2ɞɟɫɟɬɢɰɟ

U KA

ɋ

ɞɨɞɚʁɟɦɨɞɟɫɟɬɢɰɚɦɚ.

5 6Ⱦ= 30Ⱦ 3Ⱦ + 2Ⱦ= 32Ⱦ 3ɋ 2Ⱦ. ɐɢɮɪɭ ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɞɟɫɟɬɢɰɚ ɚ ɫɬɨɬɢɧɟɞɨɞɚʁɟɦɨ ɫɬɨɬɢɧɚɦɚ.

Ȼɟɡ ɬɚɛɥɢɰɟ

ED

165·5 825

5  1ɋ = 5ɋ5ɋ + 3ɋ = 8ɋ. ɐɢɮɪɭ ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɫɬɨɬɢɧɚ

 Ɋɚɱɭɧɡɚɩɟɬ ɫɥɚɞɨɥɟɞɚ ʄɟɛɢɬɢ ___ɞɢɧɚɪɚ.

3. Ɉɞɪɟɞɢ ɩɪɨɢɡɜɨɞɟɩɢɫɦɟɧɢɦɩɨɫɬɭɩɤɨɦ 1

5

7

·

4

0

2

3

8

·

3

0

1

9

8

·

5

0

2

9

9

·

3

0

1

4. Ɣ ɍʁɟɞɧɨɦ ɯɨɬɟɥɭɫɟɧɚɥɚɡɢ 148 ɨɞɪɚɫɥɢɯ ɨɫɨɛɚ ɢ 3 ɩɭɬɚɜɢɲɟɞɟɰɟ. Ʉɨɥɢɤɨʁɟɞɟɰɟɫɦɟɲɬɟɧɨ ɭ ɬɨɦ ɯɨɬɟɥɭ? Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ. ɚ) 244 ɛ) 344 ɜ 444 ɝ) 424 ɞ) 414 Ɣ ɇɚ ɩɥɚɠɢɫɟɧɚɥɚɡɢ 158ɫɭɧɰɨɛɪɚɧɚ ɚ ɢɫɩɨɞɫɜɚɤɨɝɩɨ 2ɥɟɠɚʂɤɟ. Ʉɨɥɢɤɨ ɧɚ ɬɨʁɩɥɚɠɢ ɢɦɚɥɟɠɚʂɤɢ? Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ ɚ) 316 ɛ) 326 ɜ) 306 ɝ) 336 ɞ) 346 5. ɍɫɜɚ ɬɪɢ ɩɪɚɡɧɚɩɨʂɚ ɭɩɢɲɭ ɢɫɬɭɰɢɮɪɭɬɚɤɨɞɚ ɦɧɨɠɟʃɟɛɭɞɟ ɬɚɱɧɨ. ·

= 176

100

7

8

·

5


ɉɂɋɆȿɇɈ ɆɇɈɀȿȵȿɌɊɈɐɂɎɊȿɇɈȽ ȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ 241 · 4; 165 · 5 Ʉʂɭɱɧɟɪɟɱɢ ɦɧɨɠɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

1.

ɂɡɪɚɱɭɧɚʁ 4

2.

8

·

2

2

0

1

6

·

1

6

0

1

8

2

·

4

0

1

4

2

·

4

0

2

8

3

·

3

Ɇɢɥɢɰɚ ɢ ɋɨʃɚ ɤɭɩɭʁɭɫɭɜɟɧɢɪɟ. ɉɪɨɰɟɧɢ ɢɡɧɨɫɟ ɪɚɱɭɧɚ, ɚ ɡɚɬɢɦ ɩɪɨɜɟɪɢ ɪɚɱɭɧɚʃɟɦ. ɚ) Ⱦɚɥɢʄɟ Ɇɢɥɢɰɢ ɛɢɬɢ ɞɨɜɨʂɧɨ 900ɞɢɧɚɪɚɞɚ ɤɭɩɢ ɱɟɬɢɪɢ ɦɚɝɧɟɬɚ? ɛ ɧɟʄɟ, ɧɟɞɨɫɬɚʁɚʄɟʁɨʁ28ɞɢɧɚɪɚ ɜ)ɧɟʄɟ, ɧɟɞɨɫɬɚʁɚʄɟʁɨʁ8ɞɢɧɚɪɚ

TA

ɚ) ɯɨʄɟ, ɪɚɱɭɧʁɟ ɬɚɱɧɨ 900ɞɢɧɚɪɚ ɜ) ɯɨʄɟ, ɪɚɱɭɧʁɟ ɦɚʃɢɨɞ 900ɞɢɧɚɪɚ

L

Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨɢɫɩɪɟɞɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ

ɇɚ ʁɟɞɧɨɦɬɭɪɧɢɪɭ ɭ ɤɚɪɚɬɟɭʁɟ 155 ɭɱɟɫɧɢɤɚ ɢ 6ɩɭɬɚɜɢɲɟ ɝɥɟɞɚɥɚɰɚ. Ʉɨɥɢɤɨ ɢɦɚ ɝɥɟɞɚɥɚɰɚ?

O

3.

R

ɚ) Ⱦɚɥɢʄɟ ɋɨʃɢɛɢɬɢ ɞɨɜɨʂɧɨ 950ɞɢɧɚɪɚɞɚ ɤɭɩɢɞɜɚɛɪɨɞɚ ɢʁɟɞɚɧɦɚɝɧɟɬ" ɚ) ɯɨʄɟ, ɪɚɱɭɧʁɟ ɬɚɱɧɨ 950ɞɢɧɚɪɚ ɛ ɧɟʄɟ, ɧɟɞɨɫɬɚʁɚʄɟʁɨʁ16ɞɢɧɚɪɚ ɜ) ɯɨʄɟ, ɪɚɱɭɧʁɟ ɦɚʃɢɨɞ 950ɞɢɧɚɪɚ ɜ)ɧɟʄɟ, ɧɟɞɨɫɬɚʁɚʄɟʁɨʁ10ɞɢɧɚɪɚ

-P

Ɉɞɝɨɜɨɪ ___________________________________________________

U KA

4. ɇɚ ɰɪɬɟɠɢɦɚɫɭɧɟɩɪɚɜɢɥɧɨ ɩɨɪɟɻɚɧɢɞɨɝɚɻɚʁɢ ɢɡ ɛɚʁɤɟ Ɇɚɱɚɤɭɱɢɡɦɚɦɚ. Ɋɟɲɢ ɡɚɞɚɬɤɟ ɢɞɨɛɢʁɟɧɟɛɪɨʁɟɜɟɩɪɨɧɚɻɢɧɚɰɪɬɟɠɢɦɚ.ɍɩɢɲɢ ɭ ɨɞɝɨɜɚɪɚʁɭʄɟ ɛɪɨʁɟɜɟ ɨɞ 1 ɞɨ 8.Ɍɚɤɨ ʄɟɲɞɨɛɢɬɢ ɬɚɱɚɧ ɪɟɞɨɫɥɟɞɞɨɝɚɻɚʁɚ ɨɜɟ ɥɟɩɟ ɛɚʁɤɟ. 6

9

·

5

2

3

6

·

3

1

9

7

·

5

3

2

7

·

3

3

6

5

·

2

2

5

9

·

3

1

1

8

·

7

4

5

8

·

2

ED

1

101


ɁȺȾȺɐɂ ɋȺ Ⱦȼȿ ɈɉȿɊȺɐɂȳȿ – ɆɇɈɀȿȵȿ ɂ ɋȺȻɂɊȺȵȿ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɨ 1000, ɡɚɞɚɰɢ ɫɚ ɞɜɟ ɨɩɟɪɚɰɢʁɟ, ɦɧɨɠɟʃɟ ɢ ɫɚɛɢɪɚʃɟ

Ɍɜɨʁɟɩɪɟɬɯɨɞɧɨ ɡɧɚʃɟ... ɍ ɦɚɬɟɦɚɬɢɱɤɢɦ ɢɡɪɚɡɢɦɚ ɨɩɟɪɚɰɢʁɚ ɦɧɨɠɟʃɚ ɢɦɚ ɩɪɟɞɧɨɫɬ ɭ ɨɞɧɨɫɭɧɚɫɚɛɢɪɚʃɟ ɢɨɞɭɡɢɦɚʃɟ. ɉɪɜɨɫɟ ɦɧɨɠɢ, ɚ ɡɚɬɢɦɫɚɛɢɪɚ ɢ ɨɞɭɡɢɦɚ. 50 + 3 · 8 = 50 + 24 = 74. Ɉɜɨ ɩɪɚɜɢɥɨɩɪɢɦɟʃɭʁɟɦɨ ɢ ɭ ɦɚɬɟɦɚɬɢɱɤɢɦ ɢɡɪɚɡɢɦɚɱɢʁɚʁɟɜɪɟɞɧɨɫɬɜɟʄɚ ɨɞ 100.

ɉɪɚɬɢɩɨɫɬɭɩɚɤ ɪɟɲɚɜɚʃɚ ɡɚɞɚɬɤɚ ɢɞɨɩɭɧɢɲɬɚʁɟɩɨɬɪɟɛɧɨ

187

ɂɡɪɚɱɭɧɚɜɚɦɨ ɛɪɨʁ ɤɭɩʂɟɧɢɯ ɫɥɢɱɢɰɚ

ɂɡɪɚɱɭɧɚɜɚɦɨ ɭɤɭɩɚɧ ɛɪɨʁɫɥɢɱɢɰɚ.

187 + ___

187 + 120 = ___

TA

Ɍɨɦ ɛɪɨʁɭ ɞɨɞɚʁɟɦɨ ɛɪɨʁ ɤɭɩʂɟɧɢɯ ɫɥɢɱɢɰɚ 15 ɩɚɤɟɬɚɩɨ 8 ɫɥɢɱɢɰɚ ɭ ʁɟɞɧɨɦɩɚɤɟɬɭ. 187 + __ · 8

R

Ɂɚɩɢɫɭʁɟɦɨ ɛɪɨʁ ɫɥɢɱɢɰɚ ɤɨʁɟ ȳɨɜɚɧ ɢɦɚ.

L

1. ȳɨɜɚɧ ɢɦɚ 187 ɫɥɢɱɢɰɚ ɮɭɞɛɚɥɟɪɚ. ȳɭɬɪɨɫʁɟ ɤɭɩɢɨ 15ɧɨɜɢɯɩɚɤɨɜɚʃɚ.ɍɫɜɚɤɨɦ ɩɚɤɨɜɚʃɭɫɟɧɚɥɚɡɢ ɩɨ 8ɫɥɢɱɢɰɚ.Ʉɨɥɢɤɨɫɚɞɚ ɢɦɚȳɨɜɚɧɢɦɚɫɥɢɱɢɰɚ"

ȳɨɜɚɧ ɫɚɞɚ ɢɦɚ ___ɫɥɢɱɢɰɚ.

-P

O

Ɂɚ ɪɟɲɚɜɚʃɟ ɡɚɞɚɬɤɚ ɫɚɫɬɚɜɢɥɢ ɫɦɨ ɢɡɪɚɡ: 187 + 15  8.ɍ ɬɨɦ ɢɡɪɚɡɭ ɫɦɨ ɭɩɨɬɪɟɛɢɥɢ ɞɜɟ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ ɫɚɛɢɪɚʃɟ ɢ ɦɧɨɠɟʃɟ. Ȼɪɨʁ187ʁɟɩɪɜɢɫɚɛɢɪɚɤ, ɚɩɪɨɢɡɜɨɞ ɛɪɨʁɟɜɚ 15 ɢ 8ʁɟɞɪɭɝɢ ɫɚɛɢɪɚɤ. 2. Ɂɨɪɢɰɚ ʁɟ ɤɭɩɢɥɚ 3ɫɥɚɞɨɥɟɞɚɩɨ 125ɞɢɧɚɪɚ ɢʁɟɞɧɭ ɱɨɤɨɥɚɞɭ ɡɚ 119ɞɢɧɚɪɚ. Ʉɨɥɢɤɢ ʁɟɁɨɪɢɱɢɧɪɚɱɭɧ"

U KA

ɉɪɚɬɢɩɨɫɬɭɩɚɤ ɪɟɲɚɜɚʃɚ ɡɚɞɚɬɤɚ ɢɞɨɩɭɧɢɲɬɚʁɟɩɨɬɪɟɛɧɨ Ɂɚɩɢɫɭʁɟɦɨɪɚɱɭɧ ɡɚ ɫɥɚɞɨɥɟɞɟ: ɫɥɚɞɨɥɟɞɚ ɩɨ 125 ɞɢɧɚɪɚ 125 · 3

ɂɡɪɚɱɭɧɚɜɚɦɨ Ɋɚɱɭɧɭ ɡɚ ɤɭɩʂɟɧɟ ɂɡɪɚɱɭɧɚɜɚɦɨ ɢɡɧɨɫɁɨɪɢɱɢɧɨɝ ɫɥɚɞɨɥɟɞɟ ɞɨɞɚʁɟɦɨ ɤɨɥɢɤɨɢɡɧɨɫɢ ɪɚɱɭɧ ɡɚ ɤɭɩʂɟɧɟ ɪɚɱɭɧɚ ɰɟɧɭ ɱɨɤɨɥɚɞɟ ɫɥɚɞɨɥɟɞɟ. ___ + 119 375 + 119 = ___ 125 · 3 + 119

ED

Ɂɨɪɢɱɢɧɪɚɱɭɧʁɟ ___ɞɢɧɚɪɚ.

Ɂɚ ɪɟɲɚɜɚʃɟ ɡɚɞɚɬɤɚ ɫɚɫɬɚɜɢɥɢ ɫɦɨ ɢɡɪɚɡ: 125 3 + 119. ɍ ɬɨɦ ɢɡɪɚɡɭɫɦɨ ɭɩɨɬɪɟɛɢɥɢ ɞɜɟ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ, ɦɧɨɠɟʃɟ ɢ ɫɚɛɢɪɚʃɟ. ɉɪɨɢɡɜɨɞɛɪɨʁɟɜɚ 125 ɢ 3 ʁɟɩɪɜɢɫɚɛɢɪɚɤ ɚ ɛɪɨʁ119 ʁɟ ɞɪɭɝɢ ɫɚɛɢɪɚɤ.

Ɣ

Ɂɚɫɜɚɤɢɫɥɟɞɟʄɢ ɡɚɞɚɬɚɤ ɫɚɫɬɚɜɢ ɨɞɝɨɜɚɪɚʁɭʄɢ ɢɡɪɚɡ ɢ ɢɡɪɚɱɭɧɚʁ ɨɞɪɟɞɢ ʃɟɝɨɜɭɜɪɟɞɧɨɫɬ.

3. Ȼɪɨʁɭ 349 ɞɨɞɚʁɩɪɨɢɡɜɨɞɛɪɨʁɟɜɚ 155 ɢ 2. __________________________________

4. ɉɪɨɢɡɜɨɞ ɛɪɨʁɟɜɚ 176 ɢ 5 ɭɜɟʄɚʁɡɚ 120. __________________________________

5. Ʉɚɪɥɨ ʁɟ ɤɭɩɢɨ 4ɫɜɟɫɤɟɩɨ 58ɞɢɧɚɪɚ ɢ ɲɟɫɬɚɪ ɡɚ 758ɞɢɧɚɪɚ. Ʉɨɥɢɤɢ ʁɟ Ʉɚɪɥɨɜɪɚɱɭɧ" __________________________________ Ɉɞɝɨɜɨɪ : __________________________________ 6. ɇɚɲɤɨɥɫɤɨʁɩɪɢɪɟɞɛɢ ɭ 8 ɪɟɞɨɜɚɫɟɞɢ ɩɨ 25 ɪɨɞɢɬɟʂɚ. ɇɚ ɤɥɭɩɚɦɚ ɫɟɞɢ 56 ɭɱɟɧɢɤɚ ɢ ɧɚɫɬɚɜɧɢɤɚ. Ʉɨɥɢɤɨʁɟ ɭɤɭɩɧɨ ɝɥɟɞɚɥɚɰɚ ɧɚɬɨʁɩɪɢɪɟɞɛɢ" ______________________________ Ɉɞɝɨɜɨɪ: _______________________________________

102


ɁȺȾȺɐɂ ɋȺ Ⱦȼȿ ɈɉȿɊȺɐɂȳȿ ɆɇɈɀȿȵȿ ɂ ɋȺȻɂɊȺȵȿ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɨ 1000, ɡɚɞɚɰɢ ɫɚ ɞɜɟ ɨɩɟɪɚɰɢʁɟ, ɦɧɨɠɟʃɟ ɢ ɫɚɛɢɪɚʃɟ

1 ɍɞɚɬɢɦ ɢɡɪɚɡɢɦɚɰɪɜɟɧɨɦ ɛɨʁɨɦ ɩɨɞɜɭɰɢ ɩɪɜɢ ɫɚɛɢɪɚɤ, ɚɩɥɚɜɨɦ ɞɪɭɝɢ ɫɚɛɢɪɚɤ Ɂɚɬɢɦ ɨɞɪeɞɢ ɜɪɟɞɧɨɫɬɢ ɢɡɪɚɡɚ Ɣ

212 + 112 · 5 = ___________________;

Ɣ

317 · 2 + 366 = ___________________;

Ɣ

7 · 109 + 137 = ___________________;

Ɣ

444 + 89 · 5 = ____________________

155 ɞɢɧ

99 ɞɢɧ 699 ɞɢɧ

500 ɞɢɧ

109 ɞɢɧ

35 ɞɢɧ

-P

O

699 + 99 · __ = _______

3 ɉɪɨɢɡɜɨɞɛɪɨʁɟɜɚ 128 ɢ 6 ɭɜɟʄɚʁ ɡɚ 168

4 Ȼɪɨʁ 327 ɭɜɟʄɚʁ ɡɚɩɪɨɢɡɜɨɞɛɪɨʁɟɜɚ 99 ɢ 6

U KA

________________________________ 5 Ⱥɰɢɧɚɫɟɫɬɪɚʁɟɧɚɩɭɧɢɥɚ ɞɟɫɟɬ ɢ ɩɨ Ʉ ɝɨɞɢɧɚɄɨɥɢɤɨʁɟ ɬɨ ɦɟɫɟɰɢ?

________________________________

6 Ɉɥɝɚ ɬɪɟɛɚɞɚɜɪɚɬɢ ɤɪɟɞɢɬ ɡɚ 6 ɝɨɞɢɧɚ ɢ 11 ɦɟɫɟɰɢɄɨɥɢɤɨʁɟ ɬɨ ɦɟɫɟɰɢ"

________________________________ Ⱦɟɫɟɬ ɢ ɩɨ ɝɨɞɢɧɚʁɟ _______________

________________________________ 6 ɝɨɞɢɧɚ ɢ 11 ɦɟɫɟɰɢ ʁɟ ______________

ED

7 ɇɨɜɚɤ ȭɨɤɨɜɢʄʁɟ 14ʁɭɥɚ 2019ɝɨɞɢɧɟɩɨɛɟɞɢɨ ɊɨʇɟɪɚɎɟɞɟɪɟɪɚ Ɍɚɤɨʁɟ ɩɟɬɢ ɩɭɬ ɨɫɜɨʁɢɨɮɢɧɚɥɟ ɩɪɟɫɬɢɠɧɨɝ ɬɭɪɧɢɪɚ ɭ ȼɢɦɛɥɞɨɧɭ Ɇɟɱʁɟ ɬɪɚʁɚɨ 5 ɱɚɫɨɜɚ ɢ ʁɟɞɚɧɦɢɧɭɬɄɨɥɢɤɨʁɟ ɦɢɧɭɬɚ ɬɪɚʁɚɨ ɦɟɱ" Ɂɚɞɚɬɚɤ ɪɟɲɢɫɚɫɬɚɜʂɚʃɟɦ ɢɡɪɚɡɚɫɚ ɦɧɨɠɟʃɟɦ ɢ ɫɚɛɢɪɚʃɟɦ ____________________________ ɉɪɟɰɪɬɚʁ ɥɨɩɬɢɰɟɫɚɧɟɬɚɱɧɢɦ ɪɟɲɟʃɟɦ

8 ɇɚɲɚ ɚɬɥɟɬɢɱɚɪɤɚ ɂɜɚɧɚ ɒɩɚɧɨɜɢʄʁɟ ɭ ɦɚɪɬɭ 2019 ɝɨɞɢɧɟ ɩɨɫɬɚɥɚ ɲɚɦɩɢɨɧɤɚ ȿɜɪɨɩɟ ɭɫɤɨɤɭ ɭɞɚʂ ɭ ɞɜɨɪɚɧɢ ɂɜɚɧɚʁɟ ɬɪɢʁɭɦɮɨɜɚɥɚ ɡɚɯɜɚʂɭʁɭʄɢ ɫɤɨɤɭ ɞɭɠɢɧɟ 6 m 99 cm Ʉɨɥɢɤɚ ʁɟ ɞɭɠɢɧɚ ɂɜɚɧɨɝɫɤɨɤɚ ɭɰɟɧɬɢɦɟɬɪɢɦɚ? Ɂɚɞɚɬɚɤ ɪɟɲɢɫɚɫɬɚɜʂɚʃɟɦ ɢɡɪɚɡɚ ɫɚ ɦɧɨɠɟʃɟɦ ɢ ɫɚɛɢɪɚʃɟɦ _________________________________ Ɉɛɨʁɩɚɬɢɤɭ ɫɚɬɚɱɧɢɦ ɪɟɲɟʃɟɦ

188 ɞɢɧ

R

657 ɞɢɧ

TA

L

2 ɉɪɟɦɚ ɞɚɬɢɦ ɩɨɞɚɰɢɦɚ, ɫɚɫɬɚɜɢɢɡɪɚɡɟ ɢɨɞɪɟɞɢ ɪɚɱɭɧɟ ɡɚ ɨɛɚɜʂɟɧɭ ɤɭɩɨɜɢɧɭ

ɚ)

ɛ)

103

ɜ


ɁȺȾȺɐɂ ɋȺ Ⱦȼȿ ɈɉȿɊȺɐɂȳȿ – ɆɇɈɀȿȵȿ ɂ ɈȾɍɁɂɆȺȵȿ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɨ 1000, ɡɚɞɚɰɢ ɫɚ ɞɜɟ ɨɩɟɪɚɰɢʁɟ, ɦɧɨɠɟʃɟ ɢ ɨɞɭɡɢɦɚʃɟ

1 ɐɟɧɚʁɟɞɧɨɝɩɚɤɨɜɚʃɚ ɦɚɥɢɧɚ ɢɡɧɨɫɢ 135ɞɢɧɚɪɚ ɇɢɧɚ ʁɟ ɤɭɩɢɥɚ 3 ɬɚɤɜɚɩɚɤɨɜɚʃɚ ɢ ɩɥɚɬɢɥɚ ɢɯɧɨɜɱɚɧɢɰɨɦ ɨɞ 500ɞɢɧɚɪɚ Ʉɨɥɢɤɢʁɟɇɢɧɢɧɤɭɫɭɪ? ɉɪɚɬɢ ɩɨɫɬɭɩɚɤ ɪɟɲɚɜɚʃɚ ɡɚɞɚɬɤɚ ɢɞɨɩɭɧɢɲɬɚʁɟɩɨɬɪɟɛɧɨ ɂɡɪɚɱɭɧɚɜɚɦɨ ɢɡɧɨɫ ɂɡɪɚɱɭɧɚɜɚɦɨ ɇɢɧɢɧ ɪɚɱɭɧɚ ɡɚ ɤɭɩʂɟɧɟ ɤɭɫɭɪ ɦɚɥɢɧɟ 500 – ___ 500 – 405 = ___

L

Ɉɞ ɬɨɝ ɛɪɨʁɚ ɨɞɭɡɢɦɚɦɨ Ɂɚɩɢɫɭʁɟɦɨ ɤɨɥɢɤɨɇɢɧɚ ɢɦɚ ɪɚɱɭɧ ɡɚ ɤɭɩʂɟɧɟ ɦɚɥɢɧɟ 3 ɩɚɤɨɜɚʃɚ ɩɨ 135 ɞɢɧɚɪɚ ɞɢɧɚɪɚ 500 500 – 135 · __

ɇɢɧɢɧɤɭɫɭɪʁɟ ___ɞɢɧɚɪɚ

Ɂɧɚɦɨɞɚ ɭ ɦɚɬɟɦɚɬɢɱɤɢɦ ɢɡɪɚɡɢɦɚ ɫɚ ɦɧɨɠɟʃɟɦ ɢɨɞɭɡɢɦɚʃɟɦɨɩɟɪɚɰɢʁɚ ɦɧɨɠɟʃɚ ɢɦɚ ɩɪɟɞɧɨɫɬ ɭ ɨɞɧɨɫɭɧɚ ɨɞɭɡɢɦɚʃɟ Ɂɚɬɨɫɦɨɩɪɜɨ ___________,ɩɚ ɬɟɤ ɨɧɞɚ ɨɞɭɡɢɦɚɥɢ

R

Ɣ

TA

Ɂɚ ɪɟɲɚɜɚʃɟ ɡɚɞɚɬɤɚɫɚɫɬɚɜɢɥɢ ɫɦɨ ɢɡɪɚɡ: 500 – 135 · 3 ɍ ɬɨɦ ɢɡɪɚɡɭɫɦɨ ɭɩɨɬɪɟɛɢɥɢ ɞɜɟ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ, ɨɞɭɡɢɦɚʃɟ ɢ ɦɧɨɠɟʃɟ Ȼɪɨʁ500 ʁɟ ɭɦɚʃɟɧɢɤ, ɚ ɩɪɨɢɡɜɨɞ ɛɪɨʁɟɜɚ 135 ɢ 3 ʁɟ ɭɦɚʃɢɥɚɰ

105 ɞɢɧ

25 ɞɢɧ

U KA

199 ɞɢɧ

-P

O

2 ɉɪɟɦɚ ɞɚɬɢɦ ɩɨɞɚɰɢɦɚ,ɫɚɫɬɚɜɢ ɢɡɪɚɡɟ ɢ ɨɞɪɟɞɢ ɤɭɫɭɪɟ ɡɚ ɨɛɚɜʂɟɧɭ ɤɭɩɨɜɢɧɭ

ED

3 Ȼɚɤɚ ʁɟɧɚɩɢʁɚɰɭɞɨɧɟɥɚ 25 ɤɭɬɢʁɚ ɭ ɤɨʁɢɦɚɫɟ ɧɚɥɚɡɢɥɨɩɨ 10ʁɚʁɚ ɉɪɨɞɚɥɚʁɟ 180ʁɚʁɚ Ʉɨɥɢɤɨʁɚʁɚ ʁɟ ɜɪɚɬɢɥɚ ɤɭʄɢ" ɉɪɚɬɢ ɩɨɫɬɭɩɚɤ ɪɟɲɚɜɚʃɚ ɡɚɞɚɬɤɚ ɢɞɨɩɭɧɢɲɬɚʁɟɩɨɬɪɟɛɧɨ Ɂɚɩɢɫɭʁɟɦɨ ɛɪɨʁ Ɉɞ ɬɨɝ ɩɪɨɢɡɜɨɞɚ ɂɡɪɚɱɭɧɚɜɚɦɨ ɞɨɧɟɬɢɯʁɚʁɚ: 25 ɤɭɬɢʁɚ, ɨɞɭɡɢɦɚɦɨɛɪɨʁ ɛɪɨʁ ɞɨɧɟɬɢɯ ɩɨ 10 ʁɚʁɚɭ ʁɟɞɧɨʁ ɤɭɬɢʁɢ ɩɪɨɞɚɬɢɯʁɚʁɚ ʁɚʁɚ 25 · 10 25 · 10 – ___ ___ – 180

ɂɡɪɚɱɭɧɚɜɚɦɨ ɛɪɨʁ ɩɪɟɨɫɬɚɥɢɯ ʁɚʁɚ 250 – 180 = __

Ȼɚɤɚʁɟ ɤɭʄɢ ɜɪɚɬɢɥɚ __ ʁɚʁɚ Ɂɚ ɪɟɲɚɜɚʃɟ ɡɚɞɚɬɤɚɫɚɫɬɚɜɢɥɢ ɫɦɨ ɢɡɪɚɡ: 25 · 10 – 180 ɍ ɬɨɦ ɢɡɪɚɡɭɫɦɨ ɭɩɨɬɪɟɛɢɥɢ ɞɜɟ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ, ɦɧɨɠɟʃɟ ɢ ɨɞɭɡɢɦɚʃɟ ɉɪɨɢɡɜɨɞɛɪɨʁɟɜɚ 25 ɢ 10 ɭɦɚʃɟɧɢɤ ɚɛɪɨʁ180 ʁɟ ɭɦɚʃɢɥɚɰ 4 ɍɦɚʃɟɧɢɤʁɟ ɩɪɨɢɡɜɨɞɛɪɨʁɟɜɚ 225ɢ 3, ɚ ɭɦɚʃɢɥɚɰʁɟɧɚʁɜɟʄɢ ɛɪɨʁɩɟɬɟɫɬɨɬɢɧɟ ɂɡɪɚɱɭɧɚʁ ɪɚɡɥɢɤɭ __________________________________________ Ɋɚɡɥɢɤɚ ʁɟ ___

104


ɁȺȾȺɐɂ ɋȺ Ⱦȼȿ ɈɉȿɊȺɐɂȳȿ – ɆɇɈɀȿȵȿɂ ɈȾɍɁɂɆȺȵȿ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɨ 1000 ɡɚɞɚɰɢ ɫɚ ɞɜɟ ɨɩɟɪɚɰɢʁɟ ɦɧɨɠɟʃɟ ɢ ɨɞɭɡɢɦɚʃɟ

1. ɍɞɚɬɢɦ ɢɡɪɚɡɢɦɚɩɥɚɜɨɦɛɨʁɨɦ ɩɨɞɜɭɰɢ ɭɦɚʃɟɧɢɤ ɚ ɠɭɬɨɦ ɭɦɚʃɢɥɚɰ Ɂɚɬɢɦ ɨɞɪeɞɢ ɜɪɟɞɧɨɫɬɢ ɢɡɪɚɡɚ. Ɣ

869 – 148 · 4 = ___________________;

Ɣ

325 · 3 – 806 = ___________________;

Ɣ

9 · 103 – 908 = ___________________;

Ɣ

900 – 136 · 6 = ___________________ .

Ɋɚɡɥɢɤɚʁɟ ___.

3

TA

__________________________________________

L

2. ɍɦɚʃɟɧɢɤ ʁɟ ɛɪɨʁ778 ɚ ɭɦɚʃɢɥɚɰʁɟɩɪɨɢɡɜɨɞɛɪɨʁɟɜɚ 169ʁɟ 4. ɂɡɪɚɱɭɧɚʁ ɪɚɡɥɢɤɭ.

ɍɦɚʃɟɧɢɤʁɟ ɩɪɨɢɡɜɨɞɛɪɨʁɟɜɚ 149 ʁɟ 6 ɚ ɭɦɚʃɢɥɚɰ ʁɟ ɛɪɨʁ357. ɂɡɪɚɱɭɧɚʁ ɪɚɡɥɢɤɭ.

Ɋɚɡɥɢɤɚ ʁɟ ___.

R

__________________________________________

O

4. ɍɮɥɚɲɢʁɟɛɢɥɚʁɟɞɧɚ ɥɢɬɪɚʁɨɝɭɪɬɚ. Ⱦɭʃɚʁɟ ɢɡ ɬɟ ɮɥɚɲɟ ɩɪɟɫɭɥɚʁɨɝɭɪɬ ɭ 3ɲɨʂɟ. ɍɫɜɚɤɭɲɨʂɭ ʁɟɭɫɭɥɚ ɬɚɱɧɨ 250 ml ʁɨɝɭɪɬɚ. Ʉɨɥɢɤɨ ʁɟ ɦɢɥɢɥɢɬɚɪɚʁɨɝɭɪɬɚ ɨɫɬɚɥɨ ɭ ɮɥɚɲɢ" Ɉɫɬɚɬɚɤʁɨɝɭɪɬɚ ɢɡɪɚɡɢ ɭɰɟɧɬɢɥɢɬɪɢɦɚ.

-P

________________________________ Ɉɞɝɨɜɨɪ: __________________________________

U KA

5. ɀɟʂɤɨ ʁɟ ɭɲɤɨɥɭɞɨɧɟɨ 10ɩɚɤɨɜɚʃɚɩɨ 12 ɛɚɥɨɧɚ. Ⱦɪɭɝɚɪɢɦɚ ʁɟɩɨɤɥɨɧɢɨ 108ɛɚɥɨɧɚ.Ʉɨɥɢɤɨ ɛɚɥɨɧɚ ɦɭʁɟɩɪɟɨɫɬɚɥɨ" ________________________________ Ɉɛɨʁɛɚɥɨɧ ɫɚ ɬɚɱɧɢɦ ɨɞɝɨɜɨɪɨɦ.

ED

6. Ɇɚʁɚ ʁɟ ɡɚ ɫɜɨʁɪɨɻɟɧɞɚɧɭɲɤɨɥɭɞɨɧɟɥɚ 135 ɱɨɤɨɥɚɞɢɰɚ ɋɜɚɤɨɦ ɨɞ 26 ɭɱɟɧɢɤɚɞɚɥɚʁɟ ɩɨ 5ɱɨɤɨɥɚɞɢɰɚ. ɉɪɟɨɫɬɚɥɢɛɪɨʁɱɨɤɨɥɚɞɢɰɚɧɚɦɟɧɢɥɚʁɟ ɭɱɢɬɟʂɢɰɢ

ɚ)

ɚ ɉɨɩɭɧɢɰɪɬɟɠ ɡɚ ɪɟɲɚɜɚʃɟ ɡɚɞɚɬɤɚ ɨɞɝɨɜɚɪɚʁɭʄɢɦ ɛɪɨʁɟɜɢɦɚ. ɛ) Ʉɨɥɢɤɨ ʁɟɱɨɤɨɥɚɞɢɰɚ ɞɨɛɢɥɚ ɭɱɢɬɟʂɢɰɚ" ______________________________

Ɉɞɝɨɜɨɪ: _____________________________________

7. ɉɪɟɦɚ ɢɡɪɚɡɭ 119 · 6 – 527 ɫɚɫɬɚɜɢɬɟɤɫɬ ɡɚɞɚɬɤɚ. Ɋɟɲɢɡɚɞɚɬɚɤ ɢɧɚɩɢɲɢ ɨɞɝɨɜɨɪ. Ɂɚɞɚɬɚɤ: ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ Ɋɟɲɟʃɟ: ____________________________________ Ɉɞɝɨɜɨɪ: _______________________________________________________________________

105


ɉɂɋɆȿɇɈ ȾȿȴȿȵȿɌɊɈɐɂɎɊȿɇɈȽ ȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ: 693 : 3; 456 : 3 Ʉʂɭɱɧɟɪɟɱɢ: ɞɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

 ɇɚɭɱɢɥɢ ɫɦɨ ɤɚɤɨɞɚ ɪɚɱɭɧɚɦɨ ɤɨɥɢɱɧɢɤɛɪɨʁɟɜɚ ɭɫɦɟɧɢɦɩɨɫɬɭɩɤɨɦ.

ɉɪɢɦɟʃɭʁɟɦɫɜɨʁɫɬɜɨ ɞɟʂɟʃɚ ɡɛɢɪɚɛɪɨʁɟɦ

693 : 3 = (600 + 90 + 3) : 3 = (600 : 3) + (90 : 3) + (3 : 3) = 200 + 30 + 1 = 231 ɉɪɜɨ ɞɟɥɢɦɨ ɫɬɨɬɢɧɟ, ɡɚɬɢɦɞɟɫɟɬɢɰɟ ɢ ɧɚ ɤɪɚʁɭʁɟɞɢɧɢɰɟ.

ɋ 2

Ⱦ 3

ȳ 1

ɋ 3 = ɋ. ɐɢɮɪɭ 2 ɡɚɩɢɫɭʁɟɦɨɢɡɚɡɧɚɤɚ ʁɟɞɧɚɤɨɫɬɢ. Ⱦɟʂɟʃɟɩɪɨɜɟɪɚɜɚɦɨ ɦɧɨɠɟʃɟɦ: ɋ· 3 =ɋ ɐɢɮɪɭ ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞ ɫɬɨɬɢɧɚ ɢ ɨɞɭɡɢɦɚɦɨ: ɋ ɋ = 0ɋ

TA

9 9 0 –

=

ɋɩɭɲɬɚɦɨ 9 ɞɟɫɟɬɢɰɚ ɢ ɞɟɥɢɦɨ ɢɯ ɫɚ3: 9Ⱦ : 3 = 3Ⱦ. ɐɢɮɪɭ 3 ɡɚɩɢɫɭʁɟɦɨɧɚ ɦɟɫɬɨ ɞɟɫɟɬɢɰɚ Ⱦɟʂɟʃɟɩɪɨɜɟɪɚɜɚɦɨ ɦɧɨɠɟʃɟɦ 3Ⱦ  3 = 9Ⱦ ɐɢɮɪɭ 9 ɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞ ɞɟɫɟɬɢɰɚ ɢɨɞɭɡɢɦɚɦɨ: 3Ⱦ – 3Ⱦ = 0Ⱦ.

3 3 0

ɉɪɨɜɟɪɚɜɚɦɨ:

R

Ⱦ ȳ 9 3 : 3

ɋɩɭɲɬɚɦɨ 3 ʁɟɞɢɧɢɰɟ ɢ ɞɟɥɢɦɨ ɢɯ ɫɚ3: 3ȳ : 3 =ȳ. ɐɢɮɪɭ 1 ɡɚɩɢɫɭʁɟɦɨɧɚ ɦɟɫɬɨʁɟɞɢɧɢɰɚ Ⱦɟʂɟʃɟ ɩɪɨɜɟɪɚɜɚɦɨɦɧɨɠɟʃɟɦ: 1ȳ · 3 = 3ȳ. ɐɢɮɪɭ 3 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ʁɟɞɢɧɢɰɚ ɢ ɨɞɭɡɢɦɚɦɨ: 3ȳ – 3 = 0ȳ.

231 · 3 693

O

ɋ 6 6 0 –

L

‡ Ɍɪɨɰɢɮɪɟɧɟɛɪɨʁɟɜɟɥɚɤɲɟ ɢɛɪɠɟɞɟɥɢɦɨ ʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɜɢɦɚɩɢɫɦɟɧɢɦɩɨɫɬɭɩɤɨɦ ɉɪɜɨɞɟɥɢɦɨɫɬɨɬɢɧɟ, ɡɚɬɢɦɞɟɫɟɬɢɰɟ ɢ ɧɚ ɤɪɚʁɭʁɟɞɢɧɢɰɟ.

5 5 0 

4 0 4

=

ɋ 1

Ⱦ 1

ȳ 0

Ɣ Ɂɧɚɲɞɚ ɫɟɩɪɢ ɞɟʂɟʃɭɧɟɤɢɯɛɪɨʁɟɜɚʁɚɜʂɚ ɨɫɬɚɬɚɤ Ɍɚɱɧɨɫɬɞɟʂɟʃɚ ɫɚ ɨɫɬɚɬɤɨɦ ɩɪɨɜɟɪɚɜɚɦɨɧɚɩɨɡɧɚɬɢ ɧɚɱɢɧ ɩɨɦɧɨɠɢɦɨ ɤɨɥɢɱɧɢɤɢɞɟɥɢɥɚɰɢɞɨɛɢʁɟɧɨɦ ɩɪɨɢɡɜɨɞɭɞɨɞɚɦɨ ɨɫɬɚɬɚɤ. Ⱥɤɨ ɫɟɞɨɛɢʁɟɞɟʂɟɧɢɤ ɡɧɚɱɢɞɚɫɦɨ ɬɚɱɧɨ ɨɞɪɟɞɢɥɢɤɨɥɢɱɧɢɤ ɢ ɨɫɬɚɬɚɤ.

U KA

Ⱦ ȳ 5 4 : 5

ɨɫɬɚɬɚɤ

ED



ɋ 5 5 0 

-P

1. ɉɢɫɦɟɧɢɦɩɨɫɬɭɩɤɨɦ ɩɨɞɟɥɢ ɫɥɟɞɟʄɟɛɪɨʁɟɜɟ: Ɣ 555 ɢ 5; Ɣ 488 ɢ 4; Ɣ 284 ɢ 2; Ɣ 393 ɢ 3; Ɣ 524 ɢ 2; Ɣ 963 ɢ 3; Ɣ 668 ɢ 2; Ɣ 848 ɢ 4.

Ɂɚɩɢɫɭʁɟɦɨ: 554 : 4 = 110 (ɨɫɬɚɬɚɤ 4 ɢɥɢ 554 : 4 = 110 (4) ɉɪɨɜɟɪɚɜɚɦɨ: (110 · 5) + 4 = 550 + 4 = 554

2. Ɉɞɪɟɞɢ ɤɨɥɢɱɧɢɤɢ ɨɫɬɚɬɚɤ, ɚ ɡɚɬɢɦ ɢɡɜɪɲɢɩɪɨɜɟɪɭ: ɚ) 429 : 2; ɛ) 482 : 4; ɜ 365 : 3. ɋ 4 – 3 1 – 1

Ⱦ ȳ ɋ Ⱦ ȳ 5 6 : 3 = 1 5 2

4ɋ3 = ɋ (ɨɫɬɚɬɚɤ). ɐɢɮɪɭ 1 ɡɚɩɢɫɭʁɟɦɨɢɡɚɡɧɚɤɚ ʁɟɞɧɚɤɨɫɬɢ. Ⱦɟʂɟʃɟɩɪɨɜɟɪɚɜɚɦɨ ɦɧɨɠɟʃɟɦ: 1ɋ· 3 = 3ɋ ɐɢɮɪɭ 3 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɫɬɨɬɢɧɚ ɢ ɨɞɭɡɢɦɚɦɨ4ɋ– 3ɋ = ɋ

5 5 0 6 – 6 0

ɉɨɪɟɞɋ(10 Ⱦ) ɫɩɭɲɬɚɦɨ5 ɞɟɫɟɬɢɰɚ 1ɋɢ 5Ⱦ ʁɟ 15Ⱦ. 15Ⱦ : 3 =Ⱦ. ɐɢɮɪɭ 5 ɡɚɩɢɫɭʁɟɦɨɧɚɦɟɫɬɨ ɞɟɫɟɬɢɰɚ. Ⱦɟʂɟʃɟɩɪɨɜɟɪɚɜɚɦɨ ɦɧɨɠɟʃɟɦ: 5Ⱦ · 3 = 15Ⱦ. 15 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɞɟɫɟɬɢɰɚɢ ɨɞɭɡɢɦɚɦɨ: 15Ⱦ – 15Ⱦ = 0Ⱦ.

ɉɪɨɜɟɪɚɜɚɦɨ:

152 · 3 456

ɋɩɭɲɬɚɦɨ 6 ʁɟɞɢɧɢɰɚ ɢ ɞɟɥɢɦɨ ɢɯ ɫɚ3: 6ȳ : 3 = ȳ. ɐɢɮɪɭ 2 ɡɚɩɢɫɭʁɟɦɨɧɚɦɟɫɬɨʁɟɞɢɧɢɰɚ. Ⱦɟʂɟʃɟɩɪɨɜɟɪɚɜɚɦɨ ɦɧɨɠɟʃɟɦ: 2ȳ · 3 = 6ȳ. ɐɢɮɪɭ 6 ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ʁɟɞɢɧɢɰɚ ɢ ɨɞɭɡɢɦɚɦɨ: 6 – 6 = 0ȳ.

3. ɉɢɫɦɟɧɢɦ ɩɨɫɬɭɩɤɨɦ ɩɨɞɟɥɢ ɫɥɟɞɟʄɟɛɪɨʁɟɜɟ: Ɣ 684 ɢ 4; Ɣ 584 ɢ 2; Ɣ 759 ɢ 3; Ɣ 917 ɢ 7.

106


ɉɂɋɆȿɇɈȾȿȴȿȵȿɌɊɈɐɂɎɊȿɇɈȽȻɊɈȳȺ

ȳȿȾɇɈɐɂɎɊȿɇɂɆȻɊɈȳȿɆ:693:34563 Ʉʂɭɱɧɟɪɟɱɢ:ɞɟʂɟʃɟɬɪɨɰɢɮɪɟɧɨɝɛɪɨʁɚʁɟɞɧɨɰɢɮɪɟɧɢɦɛɪɨʁɟɦ

1. ɂɡɪɚɱɭɧɚʁɤɨɥɢɱɧɢɤɢɩɪɨɜɟɪɢɬɚɱɧɨɫɬɞɟʂɟʃɚ.

      

3      

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9      

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8      

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L



9      

TA



      

R



-P

O

2.Ⱦɟʂɟɧɢɤʁɟ724,ɚɞɟɥɢɥɚɰʁɟɛɪɨʁ4.3.Ɋɚɱɭɧɡɚ3ɱɨɤɨɥɚɞɟɩɨɢɫɬɨʁɰɟɧɢɢɡɧɨɫɢ Ɉɞɪɟɞɢɤɨɥɢɱɧɢɤ489ɞɢɧɚɪɚ.Ɉɞɪɟɞɢɰɟɧɭʁɟɞɧɟɱɨɤɨɥɚɞɟ.      :  =        :  =                                                                                       ɐɟɧɚʁɟɞɧɟ                      ɱɨɤɨɥɚɞɟʁɟ___ Ʉɨɥɢɱɧɢɤʁɟ___.                     ɞɢɧɚɪɚ.

U KA



 3.ɂɡɪɚɱɭɧɚʁɤɨɥɢɱɧɢɤɢɩɪɨɜɟɪɢɬɚɱɧɨɫɬɞɟʂɟʃɚ.        

7      

0      

5      

:      

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ED

   

      

      

      

4      

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6      

:      

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 4.Ɉɞɪɟɞɢ: ɚ)ɩɨɥɨɜɢɧɭɛɪɨʁɚ968;ɛ)ɱɟɬɜɪɬɢɧɭɛɪɨʁɚ508.ɜ)ɬɪɟʄɢɧɭɛɪɨʁɚ513.     

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

      

Ɍɨʁɟɛɪɨʁ___.Ɍɨʁɟɛɪɨʁ___.Ɍɨʁɟɛɪɨʁ___. 

107


ɉɂɋɆȿɇɈ ȾȿȴȿȵȿɌɊɈɐɂɎɊȿɇɈȽ ȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ: 850 : 2; 672 : 4 Ʉʂɭɱɧɟɪɟɱɢ: ɞɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

‡ ɇɟɦɚʃɚʁɟ ɞɜɚ ɡɟɰɚɩɥɚɬɢɨ 850 ɞɢɧɚɪɚ. Ʉɨɥɢɤɚʁɟɰɟɧɚʁɟɞɧɨɝ ɡɟɰɚ? ɉɪɨɭɱɢɩɪɢɤɚɡɚɧɩɨɫɬɭɩɚɤ ɢ ɨɛʁɚɫɧɢɞɟʂɟʃɟ. Ⱦ ȳ ɋ Ⱦ ȳ 5 0 : 2 = 4 2 5

5Ⱦ : 2 = 2Ⱦ, 2Ⱦ · 2 = 4Ⱦ,

5Ⱦ – 4Ⱦ = 1Ⱦ

10ȳ: 2 = 5ȳ 5ȳ· 2 = 10ȳ 10ȳ– 10ȳ ȳ. ɉɪɨɜɟɪɚɜɚɦɨ:

L

5 4 1 0 – 1 0 0

8ɋ: 2 = 4ɋ, 4ɋ · 2 = 8ɋ 8ɋ– 8ɋ= 0ɋ.

 ɐɟɧɚ ʁɟɞɧɨɝ ɡɟɰɚʁɟ ___ ɞɢɧɚɪɚ.

425 · 2 850

TA

ɋ 8 – 8 0 –

Ȼɟɡ ɬɚɛɥɢɰɟ:

 550 ɢ 5;

O

 492 ɢ 4;

R

1. ɉɢɫɦɟɧɢɦɩɨɫɬɭɩɤɨɦ ɩɨɞɟɥɢ ɫɥɟɞɟʄɟ ɛɪɨʁɟɜɟ:

 692 ɢ 2;

 650 ɢ 3;

 651 ɢ 3;

 894 ɢ 4;

 677 ɢ 2;

 784 ɢ 7.

-P

850:2=425 – 8 05 – 4 10 –10 0

ɋ 6 4 – 2 – 2

U KA

‡ ȳɟɞɧɚ ɤʃɢɠɚɪɚ ʁɟɩɨɪɭɱɢɥɚ 672 ɫɜɟɫɤɟ ɦɚɥɨɝɮɨɪɦɚɬɚ ɢ 4ɩɭɬɚ ɦɚʃɟɫɜɟɡɚɤɚɜɟɥɢɤɨɝ ɮɨɪɦɚɬɚ. Ʉɨɥɢɤɨʁɟɩɨɪɭɱɟɧɨɫɜɟɡɚɤɚɜɟɥɢɤɨɝɮɨɪɦɚɬɚ? Ⱦ ȳ ɋ Ⱦ ȳ 7 2 : 4 = 1 6 8

ED

7 4 3 2 – 3 2 0

ɉɪɨɜɟɪɚɜɚɦɨ: 168 · 4 672 Ȼɟɡ ɬɚɛɥɢɰɟ: 672:4=168 – 4 27 – 24 32 –32 0

6ɋ4 =ɋ. ɐɢɮɪɭ 1 ɡɚɩɢɫɭʁɟɦɨ ɢɡɚɡɧɚɤɚʁɟɞɧɚɤɨɫɬɢ. Ⱦɟʂɟʃɟ ɩɪɨɜɟɪɚɜɚɦɨ ɦɧɨɠɟʃɟɦ: ɋ4 = ɋ ɐɢɮɪɭ 4ɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ɫɬɨɬɢɧɚ ɢ ɨɞɭɡɢɦɚɦɨ ɋ– 4ɋ = 2ɋ. Ɉɫɬɚɬɚɤɩɪɢ ɞɟʂɟʃɭ ɫɭ 2 ɫɬɨɬɢɧɟ. ɉɨɪɟɞ 2ɋ (20Ⱦ ɫɩɭɲɬɚɦɨ7 ɞɟɫɟɬɢɰɚ 2ɋɢ 7Ⱦ ʁɟ 27Ⱦ. 27Ⱦ : 4 = 6Ⱦ. ɐɢɮɪɭ 6 ɡɚɩɢɫɭʁɟɦɨɧɚɦɟɫɬɨ ɞɟɫɟɬɢɰɚ Ⱦɟʂɟʃɟɩɪɨɜɟɪɚɜɚɦɨ ɦɧɨɠɟʃɟɦ: 6Ⱦ  4 = 24Ⱦ. 24 ɞɟɫɟɬɢɰɟɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞ ɞɟɫɟɬɢɰɚɢ ɨɞɭɡɢɦɚɦɨ: 27Ⱦ – 24Ⱦ = 3Ⱦ. Ɉɫɬɚɬɚɤ ɩɪɢ ɞɟʂɟʃɭ ɫɭ 3 ɞɟɫɟɬɢɰɟ.

ɉɨɪɟɞ 3Ⱦ (30ȳ ɫɩɭɲɬɚɦɨ 2 ʁɟɞɢɧɢɰɟ. 3Ⱦ ɂ 2ȳ ɫɭ 32ȳ. 32ȳ : 4 = 8ȳ. ɐɢɮɪɭ 8 ɡɚɩɢɫɭʁɟɦɨɧɚɦɟɫɬɨʁɟɞɢɧɢɰɚ Ⱦɟʂɟʃɟ ɩɪɨɜɟɪɚɜɚɦɨ ɦɧɨɠɟʃɟɦ: 8ȳ  4 = 32ȳ. 32 ʁɟɞɢɧɢɰɟɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞ ʁɟɞɢɧɢɰɚ ɢ ɨɞɭɡɢɦɚɦɨ: 32ȳ – 32ȳ = 0ȳ.



ɉɨɪɭɱɟɧɨʁɟ ___ ɫɜɟɡɚɤɚɜɟɥɢɤɨɝɮɨɪɦɚɬɚ.

2. ɉɢɫɦɟɧɢɦɩɨɫɬɭɩɤɨɦ ɩɨɞɟɥɢ ɫɥɟɞɟʄɟɛɪɨʁɟɜɟ:  568 ɢ 4;

 732 ɢ 5;

 855 ɢ 3;

 942 ɢ 6;

 992 ɢ 8;

 734 ɢ 2;

 964 ɢ 7;

 561 ɢ 3.

108


ɉɂɋɆȿɇɈ Ⱦȿȴȿȵȿ ɌɊɈɐɂɎɊȿɇɈȽ ȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ: 850 : 2; 672 : 4 Ʉʂɭɱɧɟɪɟɱɢ: ɞɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

1. ɇɚɫɥɢɰɢ ɫɟ ɧɚɥɚɡɟɧɟɤɢɩɪɨɢɡɜɨɞɢ ɢ ʃɢɯɨɜɟ ɰɟɧɟ ɡɚ ɦɚɫɭ ɨɞʁɟɞɧɨɝ ɤɢɥɨɝɪɚɦɚ. Ʉɨɥɢɤɢ ɛɢ ɛɢɨ ɪɚɱɭɧɚɤɨɫɟ ɤɭɩɢɩɨɥɚ ɤɢɥɨɝɪɚɦɚɫɜɚɤɨɝɩɪɨɢɡɜɨɞɚ? 468ɞɢɧ :

=

654ɞɢɧ

=

:

=

___ɞɢɧɚɪɚ

TA

L

:

876ɞɢɧ

___ɞɢɧɚɪɚ

3. ɍ ʁɟɞɧɭ ɤɭɬɢʁɭɫɟɩɚɤɭʁɟ ɩɨ 6ɱɚɲɚ. Ʉɨɥɢɤɨʁɟ ɩɨɬɪɟɛɧɨ ɤɭɬɢʁɚ ɞɚɫɟ ɫɩɚɤɭʁɟ 684ɱɚɲɚ?

-P

O

R

2. ɍ ɩɟɤɚɪɢ ʁɟ ɡɚʁɟɞɧɨ ɩɪɟɩɨɞɧɟ ɩɪɨɞɚɬɨ 357 ɤɢɮɥɢ ɢ 3ɩɭɬɚ ɦɚʃɟ ɩɟɪɟɰɚ. Ʉɨɥɢɤɨ ʁɟ ɩɪɨɞɚɬɨɩɟɪɟɰɚ?

___ɞɢɧɚɪɚ

U KA

ɉɪɨɞɚɬɨʁɟ ___ ɩɟɪɟɰɚ.

ɉɨɬɪɟɛɧɨ ʁɟ ___ ɤɭɬɢʁɚ

4. ɂɡɪɚɱɭɧɚʁɤɨɥɢɱɧɢɤɢɩɪɨɜɟɪɢ ɬɚɱɧɨɫɬ ɞɟʂɟʃɚ. 7 1 5 : 3 =

8 9 2 : 5 =

ED

3 7 3 : 2 =

5. ɋɬɟɮɚɧʁɟ ɧɚ ʁɟɞɧɨɦ ɬɪɟɧɢɧɝɭ ɩɪɟɩɥɢɜɚɨ 156 m ɚ ɍɪɨɲ 3ɩɭɬɚ ɦɚʃɟ ɨɞʃɟɝɚ. Ʉɨɥɢɤɨ ɦɟɬɚɪɚʁɟ ɩɪɟɩɥɢɜɚɨ ɍɪɨɲ?

6. Ɉɞ375ɱɥɚɧɨɜɚ ʁɟɞɧɨɝ ɟɤɨɥɨɲɤɨɝ ɭɞɪɭɠɟʃɚ ɫɜɚɤɢ ɩɟɬɢ ɱɥɚɧʁɟ ɞɟɬɟ. Ʉɨɥɢɤɨ ɢɦɚɞɟɰɟ ɭ ɬɨɦ ɭɞɪɭɠɟʃɭ?

ɫɥɢɤɚɞɟɱɚɤɚ ɭ ɛɚɡɟɧɭ

ɍɪɨɲʁɟɩɪɟɩɥɢɜɚɨ ___ m.

109

ɍ ɭɞɪɭɠɟʃɭ ɢɦɚ ___ɞɟɰɟ.


ɉɂɋɆȿɇɈ Ⱦȿȴȿȵȿ ɌɊɈɐɂɎɊȿɇɈȽ ȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ 415  5; 459 9 Ʉʂɭɱɧɟɪɟɱɢ ɞɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

‡ Ʉɨʁɢɛɪɨʁʁɟ 5ɩɭɬɚ ɦɚʃɢɨɞɛɪɨʁɚ 415? ɋ Ⱦ ȳ Ⱦ ȳ 4 1 5  5 = 8 3 – 4 0 1 5 – 1 5 0

L

41Ⱦ 5 = 8Ⱦ. ɐɢɮɪɭ 8 ɡɚɩɢɫɭʁɟɦɨɢɡɚɡɧɚɤɚ ʁɟɞɧɚɤɨɫɬɢ. Ⱦɟʂɟʃɟɩɪɨɜɟɪɚɜɚɦɨ ɦɧɨɠɟʃɟɦ 8Ⱦ · 5 = 40Ⱦ. 40 ɞɟɫɟɬɢɰɚɡɚɩɢɫɭʁɟɦɨ ɢɫɩɨɞ ɞɟɫɟɬɢɰɚ ɢ ɨɞɭɡɢɦɚɦɨ 41Ⱦ– 40Ⱦ = 1Ⱦ. Ɉɫɬɚɬɚɤɩɪɢ ɞɟʂɟʃɭ ʁɟ 1 ɞɟɫɟɬɢɰɚ.

TA

ɉɨɪɟɞ 1Ⱦ (10 ȳ) ɫɩɭɲɬɚɦɨ5 ʁɟɞɢɧɢɰɚ. 1Ⱦ ɢ 5ȳ ɫɭ 15ȳ. 15ȳ 5 = 3ȳ. ɐɢɮɪɭ 3 ɡɚɩɢɫɭʁɟɦɨɧɚ ɦɟɫɬɨʁɟɞɢɧɢɰɚ Ⱦɟʂɟʃɟɩɪɨɜɟɪɚɜɚɦɨ ɦɧɨɠɟʃɟɦ 3ȳ · 5 = 15ȳ. 15 ʁɟɞɢɧɢɰɚɡɚɩɢɫɭʁɟɦɨɢɫɩɨɞ ʁɟɞɢɧɢɰɚɢ ɨɞɭɡɢɦɚɦɨ 15ȳ – 15ȳ = 0ȳ.

83 · 5 415

ɉɪɨɜɟɪɚɜɚɦɨ

Ȼɪɨʁ 83ʁɟ 5ɩɭɬɚ ɦɚʃɢɨɞɛɪɨʁɚ 415.

R



ɇɟɦɨɠɟɦɨ ɞɚɩɨɞɟɥɢɦɨ 4 ɫɬɨɬɢɧɟɫɚ5.Ɂɚɬɨɫɬɨɬɢɧɟ ɢɡɪɚɠɚɜɚɦɨ ɞɟɫɟɬɢɰɚɦɚ ɋ = 40Ⱦ, 40Ⱦ + 1Ⱦ = 41Ⱦ.

O

1. ɂɡɪɚɱɭɧɚʁɤɨɥɢɱɧɢɤɛɪɨʁɟɜɚ Ɣ 134 ɢ 2; Ɣ 270 ɢ 4; Ɣ 385 ɢ 5; Ɣ 351 ɢ 6; Ɣ 255 ɢ 3; Ɣ 520 ɢ 8. Ɣ 255 ɢ 7; Ɣ 621 ɢ 9; Ɣ 406 ɢ 7; Ɣ 294 ɢ 5; Ɣ520 ɢ 6; Ɣ495 ɢ 9.

-P

2. ɇɚɫɥɢɰɢ ɫɭɞɜɚ ɞɟɥɚɫɥɚɝɚɥɢɰɟ. Ʉɨʁɢɞɟɨɫɥɚɝɚɥɢɰɟ ɬɪɟɛɚɞɚɫɬɚɜɢɲɢɡɦɟɻɭʃɢɯ, ɞɚɛɢ ɞɟʂɚʃɚɛɢɥɚ ɬɚɱɧɚ" Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞɬɚɱɧɨɝ ɪɟɲɟʃɚ.

U KA

ɚ)

ɛ)

‡ ɉɪɨɭɱɢɩɪɢɤɚɡɚɧɩɨɫɬɭɩɚɤ ɢɨɛʁɚɫɧɢ ɞɟʂɟʃɟ.

3.

455  9=5 –45 0

ED

455  9=

ɉɪɨɜɟɪɚɜɚɦɨ (50 · 9) + 5 = 450 + 5 = 455

ɂɡɪɚɱɭɧɚʁɤɨɥɢɱɧɢɤɛɪɨʁɟɜɚɧɚ ɝɨɪɟɩɪɢɤɚɡɚɧɧɚɱɢɧ 6 3 6  9 =

4 8 3  6 =

4.

455  9=50 –45 05 –0 5

ɋɜɚɤɢɞɚɬɢɛɪɨʁɭɦɚʃɢ 5ɩɭɬɚ. 345

290

435

Ⱦɟʂɟɧɢɤ ʁɟ ɛɪɨʁ 624, ɚ ɞɟɥɢɥɚɰʁɟ ɛɪɨʁ 8.

5.

Ɉɞɪɟɞɢ ɤɨɥɢɱɧɢɤ

190

6. Ʉɨʁɢʁɟ ɛɪɨʁ ɚ) 3ɩɭɬɚ ɦɚʃɢ ɨɞɛɪɨʁɚ 276? Ɍɨʁɟɛɪɨʁ___.

3 6 2  6 =

ɛ) 7ɩɭɬɚ ɦɚʃɢɨɞɛɪɨʁɚ 567? Ɍɨʁɟ ɛɪɨʁ___.

110


ɉɂɋɆȿɇɈ Ⱦȿȴȿȵȿ ɌɊɈɐɂɎɊȿɇɈȽȻɊɈȳȺ ȳȿȾɇɈɐɂɎɊȿɇɂɆ ȻɊɈȳȿɆ: 415 : 5; 459 : 9 Ʉʂɭɱɧɟɪɟɱɢ: ɞɟʂɟʃɟ ɬɪɨɰɢɮɪɟɧɨɝ ɛɪɨʁɚ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ

1. ɉɚɤɨɜɚʃɟ ɨɞ 6 kg ɯɪɚɧɟ ɡɚɩɫɟ ɤɨɲɬɚ 588ɞɢɧɚɪɚ.Ʉɨɥɢɤɚʁɟɰɟɧɚ 1 kg ɯɪɚɧɟ" :

2. ɋɚɪɢɧɚɛɚɤɚʁɟ 3 kg ɤɚʁɫɢʁɚ ɩɥɚɬɢɥɚ 285 ɞɢɧɚɪɚ. Ʉɨɥɢɤɨ ɤɨɲɬɚ 1 kg ɤɚʁɫɢʁɚ" :

=

Ɉɞɝɨɜɨɪ: _____________________________

L

Ɉɞɝɨɜɨɪ: _____________________________

=

ɚ) 255 : 3;

7 2 5 9 2 4 0 9

ɛ) 468 : 6;

3 5 1 3 7 9 1 5 4 8 4 0 3 1 3 6 0 1 0 8 0 7 3 2

ɻ) 477 : 9;

R

2 0 1 3 0 5 8 1

O

2 7 8 9 4 9 5 8

TA

3. Ɋɟɲɟʃɚ ɡɚɞɚɬɚɤɚɫɭɫɤɪɢɜɟɧɚ ɭ ɬɚɛɥɢɰɢɫɚɛɪɨʁɟɜɢɦɚ. Ɇɨɝɭɛɢɬɢɧɚɩɢɫɚɧɚ ɭɛɢɥɨ ɤɨɦ ɩɪɚɜɰɭ. ɉɪɨɧɚɻɢ ɢɯ ɢ ɭɨɤɜɢɪɢ ɤɚɨɲɬɨ ʁɟ ɩɨɤɚɡɚɧɨ ɭɩɪɢɦɟɪɭ. Ⱦɨɛɢʁɟɧɚ ɪɟɲɟʃɚ ɭɩɨɪɟɞɢ ɫɚɫɜɨʁɢɦɩɚɪɨɦ

ɜ) 296 : 4;

ɝ) 192 : 2;

-P

ɞ) 616 : 7;

1 9 4 0 5 3 0 7

ɟ) 776 : 8;

U KA

3 6 1 2 4 0 5 4

ɠ 325 : 5.

435

5

590

5

675

5

ED

4. Ɉɞɤɨɫɦɨɧɚɭɬɚ ɞɨ ɫɜɟɦɢɪɫɤɨɝɛɪɨɞɚ ɜɨɞɢɜɢɲɟɩɭɬɟɜɚ. Ɇɟɻɭɬɢɦ, ɫɚɦɨ ʁɟɞɚɧɩɭɬ ɜɨɞɢ ɩɪɟɤɨ ɛɪɨʁɟɜɚ ɱɢʁɢʁɟ ɤɨɥɢɱɧɢɤɛɪɨʁɤɨɝɚ ɱɢɧɟ ɫɚɦɨɧɟɩɚɪɧɟɰɢɮɪɟ. ɉɪɨɧɚɻɢ ɬɚʁɩɭɬ ɢɨɛɨʁ ɝɚ.

5

625

5. Ⱦɭɲɚɧʁɟ ɭɩɢɫɢɜɚɨɛɪɨʁɟɜɟ ɭ „ɩɢɪɚɦɢɞɭ“ ɧɚ ɫɥɢɰɢ ɋɜɚɤɢɛɪɨʁʁɟɞɧɚɤ ʁɟɩɪɨɢɡɜɨɞɭɞɜɚ ɛɪɨʁɚ ɢɫɩɨɞ ʃɟɝɚ.ɄɨʁɢɛɪɨʁȾɭɲɚɧɬɪɟɛɚɞɚ ɭɩɢɲɟ ɭɩɥɚɜɨɩɨʂɟ" Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ ɚ)

304

ɚ) 86

ɛ)

504

ɛ) 96 1

4

ɜ) 76

ɚ) 84 ɛ) 94

1 111111

6

ɜ) 74


ɁȺȾȺɐɂ ɋȺ Ⱦȼȿ ɈɉȿɊȺɐɂȳȿ – Ⱦȿȴȿȵȿ ɂ ɋȺȻɂɊȺȵȿ Ʉʂɭɱɧɟɪɟɱɢ: ɡɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ, ɞɟʂɟʃɟ ɢ ɫɚɛɢɪɚʃɟ

Ɍɜɨʁɟɩɪɟɬɯɨɞɧɨ ɡɧɚʃɟ... ɍ ɦɚɬɟɦɚɬɢɱɤɢɦ ɢɡɪɚɡɢɦɚ ɨɩɟɪɚɰɢʁɚ ɞɟʂɟʃɚ ɢɦɚ ɩɪɟɞɧɨɫɬ ɭ ɨɞɧɨɫɭɧɚɫɚɛɢɪɚʃɟ ɢɨɞɭɡɢɦɚʃɟ. ɉɪɜɨɫɟɞɟɥɢ, ɚ ɡɚɬɢɦ ɫɚɛɢɪɚ ɢɨɞɭɡɢɦɚ. 48 + 48 : 6 = 48 + 8 = 56. Ɉɜɨ ɩɪɚɜɢɥɨɩɪɢɦɟʃɭʁɟɦɨ ɢ ɭ ɦɚɬɟɦɚɬɢɱɤɢɦ ɢɡɪɚɡɢɦɚɱɢʁɚʁɟ ɜɪɟɞɧɨɫɬɜɟʄɚ ɨɞ 100.

ɉɪɚɬɢɩɨɫɬɭɩɚɤ ɪɟɲɚɜɚʃɚ ɡɚɞɚɬɤɚ ɢɞɨɩɭɧɢɲɬɚʁɟɩɨɬɪɟɛɧɨ

204

ɂɡɪɚɱɭɧɚɜɚɦɨ ɛɪɨʁ ɩɪɢʁɚɜʂɟɧɢɯ ɞɟɱɚɤɚ

ɂɡɪɚɱɭɧɚɜɚɦɨ ɭɤɭɩɚɧ ɛɪɨʁ ɩɪɢʁɚɜʂɟɧɢɯ ɭɱɟɫɧɢɤɚ

TA

Ɍɨɦ ɛɪɨʁɭ ɞɨɞɚʁɟɦɨ ɛɪɨʁ ɩɪɢʁɚɜʂɟɧɢɯ ɞɟɱɚɤɚ: ɤɨɥɢɱɧɢɤ ɛɪɨʁɟɜɚ 204 ɢ 6. 204 + 204 : __

204 + ___

204 + 34 = ___

R

Ɂɚɩɢɫɭʁɟɦɨ ɛɪɨʁ ɩɪɢʁɚɜʂɟɧɢɯ ɞɟɜɨʁɱɢɰɚ.

L

1. ɇɚ ɬɚɤɦɢɱɟʃɟ ɭ ɝɢɦɧɚɫɬɢɰɢɩɪɢʁɚɜʂɟɧɨʁɟ 204ɞɟɜɨʁɱɢɰɟ ɢ 6ɩɭɬɚ ɦɚʃɟɞɟɱɚɤɚ. Ʉɨɥɢɤɨʁɟ ɭɤɭɩɧɨ ɭɱɟɫɧɢɤɚɩɪɢʁɚɜʂɟɧɨ ɡɚ ɨɜɨ ɬɚɤɦɢɱɟʃɟ?

ɇɚ ɬɚɤɦɢɱɟʃɟʁɟɩɪɢʁɚɜʂɟɧɨ ___ ɬɚɤɦɢɱɚɪɚ.

-P

O

Ɂɚ ɪɟɲɚɜɚʃɟ ɡɚɞɚɬɤɚɫɚɫɬɚɜɢɥɢ ɫɦɨ ɢɡɪɚɡ: 204 + 204 : 6. ɍ ɬɨɦ ɢɡɪɚɡɭɫɦɨ ɭɩɨɬɪɟɛɢɥɢ ɞɜɟ ɪɚɱɭɧɫɤɟɨɩɟɪɚɰɢʁɟ,ɫɚɛɢɪɚʃɟɢ ɞɟʂɟʃɟ. Ȼɪɨʁ 204 ʁɟ ɩɪɜɢɫɚɛɢɪɚɤ, ɚ ɤɨɥɢɱɧɢɤ ɛɪɨʁɟɜɚ 204 ɢ 6 ʁɟɞɪɭɝɢ ɫɚɛɢɪɚɤ. 2. ɂɡɪɚɱɭɧɚʁɜɪɟɞɧɨɫɬ ɢɡɪɚɡɚ. ɐɪɜɟɧɨɦɛɨʁɨɦ ɩɨɞɜɭɰɢ ɩɪɜɢɫɚɛɢɪɚɤ, ɚ ɡɟɥɟɧɨɦ ɞɪɭɝɢ ɫɚɛɢɪɚɤ ɛ) 492 + 492 : 3 = _______________________

U KA

ɚ) 349 + 504 : 9 = _____________________

3. ɍ ɤʃɢɠɚɪɢ ʁɟ ɢɡɥɨɠɟɧɨ 150ɛɨʁɚɧɤɢ, ɨɞ ɤɨʁɢʁɟ ɫɜɚɤɚ ɬɪɟʄɚ ɫɚ ɫɥɢɤɚɦɚ ɠɢɜɨɬɢʃɚ. ɂɡɥɨɠɟɧɨ ʁɟ ɢ 120 ɫɥɢɤɨɜɧɢɰɚ ɨ ɠɢɜɨɬɢʃɚɦɚ. Ʉɨɥɢɤɨɫɟ ɭ ɬɨʁɤʃɢɠɚɪɢ ɧɚɥɚɡɢɛɨʁɚɧɤɢ ɢɫɥɢɤɨɜɧɢɰɚ ɨ ɠɢɜɨɬɢʃɚɦɚ? ɉɪɚɬɢɩɨɫɬɭɩɚɤ ɪɟɲɚɜɚʃɚ ɡɚɞɚɬɤɚ ɢɞɨɩɭɧɢɲɬɚʁɟɩɨɬɪɟɛɧɨ

ED

Ɂɚɩɢɫɭʁɟɦɨ ɛɪɨʁ ɛɨʁɚɧɤɢ ɨ Ɍɨɦ ɤɨɥɢɱɧɢɤɭ ɞɨɞɚʁɟɦɨ ɂɡɪɚɱɭɧɚɜɚɦɨ ɛɪɨʁ ɫɥɢɤɨɜɧɢɰɚ ɨ ɛɪɨʁ ɛɨʁɚɧɤɢ ɨ ɠɢɜɨɬɢʃɚɦɚ: ɠɢɜɨɬɢʃɚɦɚ. ɤɨɥɢɱɧɢɤ ɛɪɨʁɟɜɚ 150 ɢ 3. ɠɢɜɨɬɢʃɚɦɚ. 150 : 3

150 : 3 + ___

__ + 120

ɂɡɪɚɱɭɧɚɜɚɦɨ ɭɤɭɩɚɧ ɛɪɨʁ ɛɨʁɚɧɤɢ ɢ ɫɥɢɤɨɜɧɢɰɚ ɨ ɠɢɜɨɬɢʃɚɦɚ. 50 + 120 = ___

ɍ ɤʃɢɠɚɪɢ ɫɟɧɚɥɚɡɢ ___ɛɨʁɚɧɤɢ ɢ ɫɥɢɤɨɜɧɢɰɚ ɨ ɠɢɜɨɬɢʃɚɦɚ. Ɂɚ ɪɟɲɚɜɚʃɟ ɡɚɞɚɬɤɚɫɚɫɬɚɜɢɥɢ ɫɦɨ ɢɡɪɚɡ:150 : 3 + 120. ɍ ɬɨɦ ɢɡɪɚɡɭɫɦɨ ɭɩɨɬɪɟɛɢɥɢ ɞɜɟ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ,ɞɟʂɟʃɟ ɢ ɫɚɛɢɪɚʃɟ. Ʉɨɥɢɱɧɢɤɛɪɨʁɟɜɚ 150 ɢ 5ʁɟɩɪɜɢɫɚɛɢɪɚɤ, ɚ ɛɪɨʁ120 ʁɟ ɞɪɭɝɢ ɫɚɛɢɪɚɤ. 4. Ʉɨɥɢɱɧɢɤɛɪɨʁɟɜɚ 964 ɢ 2 ɭɜɟʄɚʁɡɚ 318. _________________________________ 5. Ɉɞɪɟɞɢ ɛɪɨʁɤɨʁɢʁɟ ɡɚ 559ɜɟʄɢɨɞ ɤɨɥɢɱɧɢɤɚɛɪɨʁɟɜɚ 395 ɢ 5. __________________________________

112


ɁȺȾȺɐɂ ɋȺ Ⱦȼȿ ɈɉȿɊȺɐɂȳȿ – Ⱦȿȴȿȵȿ ɂ ɋȺȻɂɊȺȵȿ Ʉʂɭɱɧɟɪɟɱɢ: ɡɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ, ɞɟʂɟʃɟ ɢ ɫɚɛɢɪɚʃɟ

1. Ʉɨɥɢɤɨ ɢɡɧɨɫɢɡɛɢɪɛɪɨʁɚ 576 ɢ ʃɟɝɨɜɟ ɲɟɫɬɢɧɟ? Ɣ Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞ ɢɡɪɚɡɚ ɩɨɦɨʄɭ ɤɨɝɚ ʄɟɲɞɨʄɢ ɞɨ ɪɟɲɟʃɚ. ɚ) 576 + 6 : 6 ɛ) 576 + 576 : 6 ɜ) 576 – 576 : 6 Ɣ ɂɡɪɚɱɭɧɚʁɜɪɟɞɧɨɫɬ ɬɨɝ ɢɡɪɚɡɚ.

ɝ) 576 + 6 : 6

___________________________________________

L

2. ɂɡɪɚɱɭɧɚʁɜɪɟɞɧɨɫɬ ɢɡɪɚɡɚ. 326 + 326 : 2 = ___________________;

Ɣ

840 : 5 + 169 = ___________________;

Ɣ

819 : 7 + 873 = ___________________;

Ɣ

628 + 628 : 4 = ___________________ .

TA

Ɣ

3. ɉɪɜɢɫɚɛɢɪɚɤ ʁɟɛɪɨʁ266,ɚ ɞɪɭɝɢ ɫɚɛɢɪɚɤ ʁɟ ɤɨɥɢɱɧɢɤɛɪɨʁɟɜɚ 928 ɢ 8. ɂɡɪɚɱɭɧɚʁʃɢɯɨɜɡɛɢɪ. Ɂɛɢɪ ʁɟ ___.

R

__________________________________________

O

4. ɉɪɜɢɫɚɛɢɪɚɤ ʁɟ ɤɨɥɢɱɧɢɤɛɪɨʁɟɜɚ 504 ɢ 3, ɚɞɪɭɝɢ ɫɚɛɢɪɚɤ ʁɟ ɧɚʁɦɚʃɢ ɛɪɨʁɩɟɬɟɫɬɨɬɢɧɟ. ɂɡɪɚɱɭɧɚʁʃɢɯɨɜɡɛɢɪ. Ɂɛɢɪʁɟ ___.

-P

__________________________________________

5. ɍʁɟɞɧɨɦ ɤɚɦɢɨɧɭɫɟɧɚɥɚɡɢ 280 kg ɤɪɨɦɩɢɪɚ, ɚ ɭɞɪɭɝɨɦ 4ɩɭɬɚ ɦɚʃɟ. Ʉɨɥɢɤɨ ɤɢɥɨɝɪɚɦɚ ɤɪɨɦɩɢɪɚ ɢɦɚ ɭ ɨɛɚ ɤɚɦɢɨɧɚ?

ɚ)

U KA

ɚ ɉɨɩɭɧɢɰɪɬɟɠ ɡɚ ɪɟɲɚɜɚʃɟ ɡɚɞɚɬɤɚ ɨɞɝɨɜɚɪɚʁɭʄɢɦ ɛɪɨʁɟɜɢɦɚ. ɛ) ɋɚɫɬɚɜɢ ɢɡɪɚɡ ɢ ɪɟɲɢɡɚɞɚɬɚɤ.

________________________________

Ɉɞɝɨɜɨɪ: __________________________________

6. ɍʁɟɞɧɨɦɩɪɟɞɭɡɟʄɭʁɟ ɡɚɩɨɫɥɟɧɨ 465 ɠɟɧɚ ɢ 5ɩɭɬɚ ɦɚʃɟ ɦɭɲɤɚɪɚɰɚ. Ʉɨɥɢɤɨ ɭ ɨɜɨɦ ɩɪɟɞɭɡɟʄɭ ɢɦɚ ɪɚɞɧɢɤɚ? Ɉɞɝɨɜɨɪ: ____________________________________

ED

_________________________________

7. Ɉɝʃɟɧʁɟ ʁɟɞɧɭ ɤʃɢɝɭ ɩɪɨɱɢɬɚɨ ɡɚ ɞɜɚ ɞɚɧɚ. ɉɪɜɨɝɞɚɧɚʁɟɩɪɨɱɢɬɚɨ 112ɫɬɪɚɧɚ, ɚɞɪɭɝɨɝɞɚɧɚ 4ɩɭɬɚ ɦɚʃɟ. Ʉɨɥɢɤɨɫɬɪɚɧɚ ɢɦɚ ɬɚ ɤʃɢɝɚ" __________________________________ Ɉɞɝɨɜɨɪ: ____________________________________________________ 8. ɇɚɩɢɲɢɬɟɤɫɬ ɡɚɞɚɬɤɚ ɤɨʁɢʄɟɲɪɟɲɢɬɢ ɩɨɦɨʄɭ ɢɡɪɚɡɚɫɚɫɚɛɢɪɚʃɟɦ ɢ ɞɟʂɟʃɟɦ ɋɚɫɬɚɜɢ ɢɡɪɚɡ ɢ ɨɞɪɟɞɢ ʃɟɝɨɜɭɜɪɟɞɧɨɫɬ. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ɂɡɪɚɡ: _____________________________ Ɉɞɝɨɜɨɪ: ___________________________________________________________

113


ɁȺȾȺɐɂ ɋȺ Ⱦȼȿ ɈɉȿɊȺɐɂȳȿ – Ⱦȿȴȿȵȿ ɂ ɈȾɍɁɂɆȺȵȿ Ʉʂɭɱɧɟɪɟɱɢ: ɡɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ, ɞɟʂɟʃɟ ɢ ɨɞɭɡɢɦɚʃɟ

1 ɇɚ ɲɤɨɥɫɤɢ ɤɜɢɡɭ „ȼɨɥɢɦɋɪɛɢʁɭ”, ɭɱɟɫɬɜɨɜɚɥɨʁɟ 224 ɬɚɤɦɢɱɚɪɚ Ɉɞɬɨɝɛɪɨʁɚ,Ƚɨɰɢɧɬɢɦ ʁɟ ɢɦɚɨ 8ɩɭɬɚ ɦɚʃɟ ɬɚɤɦɢɱɚɪɚ Ɉɞɪɟɞɢ ɛɪɨʁ ɨɫɬɚɥɢɯ ɬɚɤɦɢɱɚɪɚɧɚ ɤɜɢɡɭ ɉɪɚɬɢɩɨɫɬɭɩɚɤ ɪɟɲɚɜɚʃɚ ɡɚɞɚɬɤɚ ɢɞɨɩɭɧɢɲɬɚʁɟɩɨɬɪɟɛɧɨ ɂɡɪɚɱɭɧɚɜɚɦɨ ɛɪɨʁ ɬɚɤɦɢɱɚɪɚ Ƚɨɰɢɧɨɝ ɬɢɦɚ

224 – 224 : __

224

224 – ___

ɂɡɪɚɱɭɧɚɜɚɦɨ ɛɪɨʁ ɨɫɬɚɥɢɯ ɩɪɢʁɚɜʂɟɧɢɯ ɬɚɤɦɢɱɚɪɚ

L

Ɉɞ ɬɨɝ ɛɪɨʁɚ ɨɞɭɡɢɦɚɦɨɛɪɨʁ ɬɚɤɦɢɱɚɪɚ Ƚɨɰɢɧɨɝ ɬɢɦɚ ɤɨɥɢɱɧɢɤ ɛɪɨʁɟɜɚ 224 ɢ 

224 – 28 = ___

TA

Ɂɚɩɢɫɭʁɟɦɨ ɭɤɭɩɚɧ ɛɪɨʁ ɬɚɤɦɢɱɚɪɚ

ɇɚ ɲɤɨɥɫɤɨɦ ɤɜɢɡɭ, ɩɪɟɞ ɬɚɤɦɢɱɚɪɚ Ƚɨɰɢɧɨɝ ɬɢɦɚ, ɭɱɟɫɬɜɨɜɚɥɨʁɟʁɨɲ___ ɬɚɤɦɢɱɚɪɚ

Ɂɧɚɦɨɞɚ ɭ ɦɚɬɟɦɚɬɢɱɤɢɦ ɢɡɪɚɡɢɦɚ ɫɚɞɟʂɟʃɟɦ ɢɨɞɭɡɢɦɚʃɟɦɨɩɟɪɚɰɢʁɚ ɞɟʂɟʃɚ ɢɦɚ ɩɪɟɞɧɨɫɬ ɭ ɨɞɧɨɫɭɧɚɨɞɭɡɢɦɚʃɟ Ɂɚɬɨɫɦɨ ɩɪɜɨ ____________, ɩɚ ɬɟɤ ɨɧɞɚ ɨɞɭɡɢɦɚɥɢ

-P

Ɣ

O

R

Ɂɚ ɪɟɲɚɜɚʃɟ ɡɚɞɚɬɤɚɫɚɫɬɚɜɢɥɢ ɫɦɨ ɢɡɪɚɡ: 224 – 224 : 8 ɍ ɬɨɦ ɢɡɪɚɡɭɫɦɨ ɭɩɨɬɪɟɛɢɥɢ ɞɜɟ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ, ɨɞɭɡɢɦɚʃɟ ɢ ɞɟʂɟʃɟ Ȼɪɨʁ224 ʁɟ ɭɦɚʃɟɧɢɤ, ɚ ɤɨɥɢɱɧɢɤ ɛɪɨʁɟɜɚ 224 ɢ 8 ʁɟ ɭɦɚʃɢɥɚɰ

2 ɂɡɪɚɱɭɧɚʁɜɪɟɞɧɨɫɬ ɢɡɪɚɡɚ ɐɪɜɟɧɨɦɛɨʁɨɦ ɩɨɞɜɭɰɢ ɭɦɚʃɟɧɢɤ, ɚ ɩɥɚɜɨɦ ɭɦɚʃɢɥɚɰ ɛ) 1000 – 1000 : 4 = _______________________

U KA

ɚ) 602 – 680 : 8 = _____________________

3 ɇɚ ʁɟɞɧɨɦɫɚʁɦɭɰɜɟʄɚ ɢɡɥɨɠɟɧɨ ʁɟ 360ɫɚɞɧɢɰɚɫɨɛɧɨɝɰɜɟʄɚ ɢ ɬɪɢ ɩɭɬɚ ɦɚʃɟɫɚɞɧɢɰɚɜɨʄɚ ɂɡɥɨɠɟɧɨ ʁɟ ɢ 115ɫɚɞɧɢɰɚɱɟɬɢɧɚɪɚ Ɂɚ ɤɨɥɢɤɨ ɢɦɚɜɢɲɟɫɚɞɧɢɰɚ ɜɨʄɚ ɨɞ ɫɚɞɧɢɰɚɱɟɬɢɧɚɪɚ? ɉɪɚɬɢɩɨɫɬɭɩɚɤ ɪɟɲɚɜɚʃɚ ɡɚɞɚɬɤɚ ɢɞɨɩɭɧɢɲɬɚʁɟɩɨɬɪɟɛɧɨ

ED

Ɂɚɩɢɫɭʁɟɦɨɤɨɥɢɤɨ ʁɟ ɢɡɥɨɠɟɧɨ ɫɚɞɧɢɰɚ ɜɨʄɚ: ɤɨɥɢɱɧɢɤ ɛɪɨʁɟɜɚ 360 ɢ  360 : 3

Ɉɞ ɬɨɝ ɤɨɥɢɱɧɢɤɚ ɂɡɪɚɱɭɧɚɜɚɦɨ ɨɞɭɡɢɦɚɦɨɛɪɨʁ ɫɚɞɧɢɰɚ ɛɪɨʁ ɫɚɞɧɢɰɚ ɱɟɬɢɧɚɪɚ ɜɨʄɚ 360 : 3 – ___

___ – 115

ɂɡɪɚɱɭɧɚɜɚɦɨ ɡɚ ɤɨɥɢɤɨ ɢɦɚɜɢɲɟ ɫɚɞɧɢɰɚ ɜɨʄɚ ɨɞ ɫɚɞɧɢɰɚ ɱɟɬɢɧɚɪɚ 120 – 115 = ___

ɋɚɞɧɢɰɚ ɜɨʄɚ ɢɦɚ ɡɚ __ ɜɢɲɟ ɨɞɫɚɞɧɢɰɚɱɟɬɢɧɚɪɚ Ɂɚ ɪɟɲɚɜɚʃɟ ɡɚɞɚɬɤɚɫɚɫɬɚɜɢɥɢ ɫɦɨ ɢɡɪɚɡ: 360 : 3 – 115 ɍ ɬɨɦ ɢɡɪɚɡɭɫɦɨ ɭɩɨɬɪɟɛɢɥɢ ɞɜɟ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ,ɞɟʂɟʃɟ ɢɨɞɭɡɢɦɚʃɟ Ʉɨɥɢɱɧɢɤɛɪɨʁɟɜɚ 360 ɢ 3 ʁɟɭɦɚʃɟɧɢɤ ɚɛɪɨʁ115 ʁɟ ɭɦɚʃɢɥɚɰ 4 Ʉɨɥɢɱɧɢɤɛɪɨʁɟɜɚ 750 ɢ 6 ɭɦɚʃɢ ɡɚ 105 ɋɚɫɬɚɜɢɢɡɪɚɡ ɢɨɞɪɟɞɢ ʃɟɝɨɜɭɜɪɟɞɧɨɫɬ _________________________________ 5 Ɉɞɪɟɞɢ ɛɪɨʁɤɨʁɢʁɟ ɡɚ 199 ɦɚʃɢɨɞ ɤɨɥɢɱɧɢɤɚɛɪɨʁɟɜɚ 1000 ɢ 4 __________________________________

114


ɁȺȾȺɐɂ ɋȺ Ⱦȼȿ ɈɉȿɊȺɐɂȳȿ – Ⱦȿȴȿȵȿ ɂ ɈȾɍɁɂɆȺȵȿ Ʉʂɭɱɧɟɪɟɱɢ: ɡɚɞɚɰɢ ɫɚɞɜɟ ɨɩɟɪɚɰɢʁɟ ɞɟʂɟʃɟ ɢ ɨɞɭɡɢɦɚʃɟ

1. ɍɲɤɨɥɫɤɨʁ ɛɢɛɥɢɨɬɟɰɢ ɢɦɚ 870 ɱɚɫɨɩɢɫɚ ɢ 5ɩɭɬɚ ɦɚʃɟ ɟɧɰɢɤɥɨɩɟɞɢʁɚ. Ʉɨʁɢɦɢɡɪɚɡɨɦ ʄɟɲ ɢɡɪɚɱɭɧɚɬɢ ɡɚ ɤɨɥɢɤɨ ʁɟ ɜɟʄɢ ɛɪɨʁ ɱɚɫɨɩɢɫɚ ɨɞ ɛɪɨʁɚ ɟɧɰɢɤɥɨɩɟɞɢʁɚ" Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ

ɚ) 870 : 5 Ɣ

ɛ) 870 – 870 – 5

ɜ) 870 – 870 : 5

ɞ) 870 – 5

Ɉɞɪɟɞɢ ɜɪɟɞɧɨɫɬ ɬɚɱɧɨ ɡɚɩɢɫɚɧɨɝ ɢɡɪɚɡɚ.

TA

L

___________________________________ Ȼɪɨʁɱɚɫɨɩɢɫɚʁɟ ɡɚ ___ɜɟʄɢɨɞ ɛɪɨʁɚ ɟɧɰɢɤɥɨɩɟɞɢʁɚ

2. ɂɡɪɚɱɭɧɚʁɞɚɬɟ ɢɡɪɚɡɟ. Ⱦɨɛɢʁɟɧɟɛɪɨʁɟɜɟɩɪɨɧɚɻɢ ɦɟɻɭɰɟɧɚɦɚɧɚɫɥɢɰɢ. Ɍɚɤɨ ʄɟɲ ɫɚɡɧɚɬɢɲɬɚʁɟ ɬɚɬɚ ɤɭɩɢɨȳɚɧɢ Ɏɢɥɢɩɭ ɢɆɚʁɢ. Ɏɢɥɢɩ

690 – 595 : 7 = _______________

700 – 900 : 4 = ________________

458 ɞɢɧ. 565 ɞɢɧ.

-P

O

992 : 2 – 38 = _______________

Ɇɚʁɚ

R

ȳɚɧɚ

799 ɞɢɧ.

389 ɞɢɧ. 605 ɞɢɧ.

U KA

475 ɞɢɧ.

ȳɚɧɚ ʁɟ ɞɨɛɢɥɚ _________________Ɏɢɥɢɩ___________________ ɚɆɚʁɚ ___________________. 3. ɍɦɚʃɟɧɢɤʁɟ ɤɨɥɢɱɧɢɤɛɪɨʁɟɜɚ 900 ɢ 2 ɚ ɭɦɚʃɢɥɚɰʁɟɧɚʁɜɟʄɢ ɛɪɨʁɱɟɬɜɪɬɟ ɫɬɨɬɢɧɟ Ʉɨɥɢɤɚ ʁɟ ɪɚɡɥɢɤɚ" Ɉɞɝɨɜɨɪ: _______________________________________

ED

____________________________ 4. ɂɡɪɚɱɭɧɚʁɜɪɟɞɧɨɫɬ ɢɡɪɚɡɚ.

ɚ) 350 – 750 : 6 = ________________________ ɛ) 952 : 4 – 109 = ________________________ ɜ) 830 – 830 : 2 = ________________________ ɝ) 812 : 7 – 115 = ________________________

5. Ʉɨɥɢɱɧɢɤɛɪɨʁɟɜɚ 950 ɢ 2 ɭɦɚʃɢ ɡɚ ɧɚʁɦɚʃɢ ɬɪɨɰɢɮɪɟɧɢɛɪɨʁɱɢʁɟ ɫɭɫɜɟ ɰɢɮɪɟ ɪɚɡɥɢɱɢɬɟ ɢ ɧɟɩɚɪɧɟ ________________________________ Ɉɛɨʁɩɨʂɚɫɚ ɬɚɱɧɨɦ ɪɚɡɥɢɤɨɦ. 350

340

330

360

6. ɇɚɩɢɲɢɬɟɤɫɬ ɡɚɞɚɬɤɚ ɤɨʁɢʄɟɲ ɪɟɲɢɬɢ ɩɨɦɨʄɭ ɢɡɪɚɡɚɫɚɞɟʂɟʃɟɦ ɢ ɨɞɭɡɢɦɚʃɟɦ ɋɚɫɬɚɜɢ ɢɡɪɚɡ ɢ ɨɞɪɟɞɢʃɟɝɨɜɭɜɪɟɞɧɨɫɬ. ___________________________________________________________________ ___________________________________________________________________ ɂɡɪɚɡ: ____________________________ Ɉɞɝɨɜɨɪ: ____________________________________________________________________

115


ɊȿȾɈɋɅȿȾ ɂɁȼɈȭȿȵȺ ɊȺɑɍɇɋɄɂɏ ɈɉȿɊȺɐɂȳȺ Ʉʂɭɱɧɟɪɟɱɢ: ɪɟɞɨɫɥɟɞ ɢɡɜɨɻɟʃɚ ɪɚɱɭɧɫɤɢɯ ɨɩɟɪɚɰɢʁɚ

Ƚɨɫɩɨɻɚ Ⱥɧɚʁɟɤɭɩɢɥɚ 3 kg ɩɚɩɪɢɤɟ ɢ 3 kg ɩɚɪɚɞɚʁɡɚ. ɐɟɧɚ ʁɟɞɧɨɝ ɤɢɥɨɝɪɚɦɚ ɩɚɩɪɢɤɟ ʁɟ 125ɞɢɧɚɪɚ, ɚ ɰɟɧɚ ʁɟɞɧɨɝ ɤɢɥɨɝɪɚɦɚ ɩɚɪɚɞɚʁɡɚ ʁɟ 115ɞɢɧɚɪɚ. Ʉɨɥɢɤɢ ʁɟɛɢɨ ɪɚɱɭɧɡɚ ɤɭɩʂɟɧɨ ɩɨɜɪʄɟ? Ɋɚɱɭɧɚɦɨ: 3 · (125 + 115) = 3 240 = 720 Ź Ɋɚɱɭɧɡɚ ɤɭɩʂɟɧɨ ɩɨɜɪʄɟ ʁɟ 720 ɞɢɧɚɪɚ. Ɣ Ɋɚɱɭɧɫɤɭ ɨɩɟɪɚɰɢʁɭɫɚɛɢɪɚʃɚ ɨɡɧɚɱɢɥɢ ɫɦɨ ɡɚɝɪɚɞɚɦɚ. ɉɪɜɨ ɫɦɨ ɢɡɪɚɱɭɧɚɥɢ ɡɛɢɪɛɪɨʁɟɜɚ 125 ɢ 115, ɚ ɡɚɬɢɦ ɫɦɨɞɨɛɢʁɟɧɢ ɡɛɢɪɩɨɦɧɨɠɢɥɢɛɪɨʁɟɦ 3.

L

Ɂɚɝɪɚɞɚɦɚɫɟ ɨɡɧɚɱɚɜɚ ɪɚɱɭɧɫɤɚ ɨɩɟɪɚɰɢʁɚ ɤɨʁɭ ɬɪɟɛɚ ɨɛɚɜɢɬɢ ɩɪɟɞɪɭɝɢɯ ɨɩɟɪɚɰɢʁɚ

TA

1. ɉɪɨɭɱɢɫɥɟɞɟʄɟ ɩɪɢɦɟɪɟ.Ⱦɨɩɭɧɢɲɬɚʁɟɩɨɬɪɟɛɧɨ

ɉɪɜɨ ɫɚɛɢɪɚɦɨ. Ⱦɨɛɢʁɟɧɢ ɡɛɢɪ ɦɧɨɠɢɦɨɛɪɨʁɟɦ 2.

R

Ɂɛɢɪɛɪɨʁɟɜɚ 327 ɢ 169 ɭɜɟʄɚʁ2ɩɭɬɚ. (327 + 169) · __ = 496 · 2 = ___

-P

Ɉɞɪɟɞɢ ɩɪɨɢɡɜɨɞɡɛɢɪɚ ɢ ɪɚɡɥɢɤɟ ɛɪɨʁɟɜɚ 83 ɢ 79. (83 + 79) · (83 – 79) = 162 · 4 = ___ 2. ɂɡɪɚɱɭɧɚʁ ɜɪɟɞɧɨɫɬ ɢɡɪɚɡɚ.

ɉɪɜɨ ɨɞɭɡɢɦɚɦɨ. Ⱦɨɛɢʁɟɧɭ ɪɚɡɥɢɤɭɞɟɥɢɦɨɛɪɨʁɟɦ 3.

O

Ɋɚɡɥɢɤɭɛɪɨʁɟɜɚ 725 ɢ 458 ɭɦɚʃɢ 3ɩɭɬɚ. (725 – ___) : 3 = 267 : __ = 89

ɛ) (896 – 597) · 3 = __________________;

U KA

ɚ) 5 · (107 + 87) = _____________________;

Ɂɚɝɪɚɞɚɦɚ ɢɫɬɢɱɟɦɨ ɞɚ ɩɪɜɨ ɫɚɛɢɪɚɦɨ ɢ ɨɞɭɡɢɦɚɦɨ, ɩɚ ɬɟɤ ɨɧɞɚ ɦɧɨɠɢɦɨ ɢ ɞɟɥɢɦɨ.

ɛ) Ɋɚɡɥɢɤɭɛɪɨʁɟɜɚ 800 ɢ 629 ɭɜɟʄɚʁ ɩɭɬɚ.

_______________________________

__________________________________

ɜ) (519 + 367) : 2 = ____________________; ɝ) (758 – 689) · (805 – 796) = ____________________________. 3. Ɂɚɩɢɲɢ ɢɡɪɚɡ ɢ ɢɡɪɚɱɭɧɚʁʃɟɝɨɜɭɜɪɟɞɧɨɫɬ.

ED

ɚ) Ɂɛɢɪ ɛɪɨʁɟɜɚ 472 ɢ 386 ɭɦɚʃɢ 2ɩɭɬɚ;

Ɇɢɥɚɧɚʁɟ ɤɭɩɢɥɚ 3 ɢɫɬɚɩɚɤɨɜɚʃɚɫɚɥɜɟɬɚ ɡɚ 225ɞɢɧɚɪɚ. Ʉɨɥɢɤɨ ɤɨɲɬɚ 5 ɩɚɤɨɜɚʃɚ ɬɚɤɜɢɯɫɚɥɜɟɬɚ? Ɋɚɱɭɧɚɦɨ: (225 : 3) · 5 = 75 · 5 = 375

Źɉɟɬ

ɩɚɤɨɜɚʃɚɫɚɥɜɟɬɚ ɤɨɲɬɚ 375 ɞɢɧɚɪɚ.

Ɇɧɨɠɟʃɟ ɢɞɟʂɟʃɟ ɫɭ ɪɚɜɧɨɩɪɚɜɧɟ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ Ɂɚɬɨɫɟ ɡɚɝɪɚɞɚɦɚ ɢɫɬɢɱɭ ɨɩɟɪɚɰɢʁɟ ɤɨʁɟ ɩɪɜɨ ɬɪɟɛɚ ɢɡɜɟɫɬɢ. 4. ɂɡɪɚɱɭɧɚʁ ɚ) 6 · (670 : 5) = __________________;

ɛ) (744 : 3) · 2 = ___________________ ;

ɜ) 10 · (144 : 2) = __________________; ɜ 3 · (406 : 7) · (45 : 9) = ______________________. 5. ɉɪɨɢɡɜɨɞ ɛɪɨʁɟɜɚ 348 ɢ 2 ɭɦɚʃɢ 6ɩɭɬɚ. _________________________________

6. Ʉɨɥɢɱɧɢɤɛɨʁɟɜɚ 392 ɢ 7 ɭɜɟʄɚʁ9ɩɭɬɚ. ________________________________

116


ɊȿȾɈɋɅȿȾ ɂɁȼɈȭȿȵȺ ɊȺɑɍɇɋɄɂɏ ɈɉȿɊȺɐɂȳȺ Ʉʂɭɱɧɟɪɟɱɢ: ɪɟɞɨɫɥɟɞ ɢɡɜɨɻɟʃɚ ɪɚɱɭɧɫɤɢɯ ɨɩɟɪɚɰɢʁɚ

ɍ ɢɡɪɚɡɭɛɟɡ ɡɚɝɪɚɞɚ ɩɪɜɨ ɫɟ ɦɧɨɠɢ ɢɞɟɥɢ, ɩɚ ɬɟɤ ɨɧɞɚ ɫɚɛɢɪɚ ɢ ɨɞɭɡɢɦɚ, ɨɧɢɦ ɪɟɞɨɦ ɤɚɤɨɫɭ ɨɩɟɪɚɰɢʁɟ ɡɚɩɢɫɚɧɟ Ɉɞɪɟɞɢɦɨɜɪɟɞɧɨɫɬ ɢɡɪɚɡɚ:



928 : 4 – 810 : 6 = 232 – 135 = 97





705 – 800 : 5 = 705 – 160 = 545

L

368 + 149 Â 2 = 368 + 298 = 666

154 Â 3 + 750 : 2 = 462 + 375 = 837

TA



7 ɂɡɪɚɱɭɧɚʁɜɪɟɞɧɨɫɬ ɢɡɪɚɡɚ:

ɛ) 568 : 4  100 = ______________________;

R

ɚ) 174 + 158 Â 3 = ___________________;

O

ɜ) 185 + 248 Â 3 – 791 = _________________; ɝ) 724 : 4 + 137 Â 5 = ______________________ 8 Ʉɨʁɢʁɟɛɪɨʁ4ɩɭɬɚ ɦɚʃɢɨɞɩɪɨɢɡɜɨɞɚɛɪɨʁɟɜɚ 128 ɢ 5?

-P

__________________________________________ Ɍɨʁɟɛɪɨʁ ___ 9 Ʉɨʁɢɛɪɨʁʁɟ 8ɩɭɬɚɜɟʄɢ ɨɞ ɤɨɥɢɱɧɢɤɚɛɪɨʁɟɜɚ 558 ɢ 6?

U KA

__________________________________________ Ɍɨʁɟɛɪɨʁ ___ 10 Ȼɪɨʁ728 ɭɦɚʃɢ ɡɚ ɤɨɥɢɱɧɢɤɛɪɨʁɟɜɚ 840 ɢ 3,ɩɚɞɨɛɢʁɟɧɭ ɪɚɡɥɢɤɭ ɭɜɟʄɚʁ2ɩɭɬɚ __________________________________________________________________

ED

11 ɍɱɟɧɢɰɢ ʁɟɞɧɟ ɲɤɨɥɟɫɭ ɨɬɢɲɥɢ ɧɚ ɟɤɫɤɭɪɡɢʁɭ ɍʁɟɞɚɧɚɭɬɨɛɭɫɫɦɟɲɬɟɧɨ ʁɟ 50 ɭɱɟɧɢɤɚ, ɚ ɭɞɜɚ ɚɭɬɨɛɭɫɚ ɫɦɟɲɬɟɧɨ ʁɟɩɨ 48 ɭɱɟɧɢɤɚ Ʉɨɥɢɤɨʁɟ ɭɱɟɧɢɤɚ ɬɟɲɤɨɥɟ ɨɬɢɲɥɨ ɧɚ ɟɤɫɤɭɪɡɢʁɭ? _________________________________________________ Ɉɞɝɨɜɨɪ: ________________________________________________________________ 12 Ʉɨʁɢɛɪɨʁɬɪɟɛɚɞɚɛɭɞɟ ɭɩɢɫɚɧ ɭ ɩɨʂɟ: ɚ ɫɚ

? ɛ ɫɚ

ɚ)

ɛ)

ɚ) 900 ɛ) 700 ɜ) 600 ɝ) 500

ɚ) 766 ɛ) 767 ɜ) 676 ɝ) 677

?

ɝ ɫɚ

?

117

ɚ) 867 ɛ) 678 ɜ) 768 ɝ) 876


ɊȿȾɈɋɅȿȾ ɂɁȼɈȭȿȵȺ ɊȺɑɍɇɋɄɂɏ ɈɉȿɊȺɐɂȳȺ Ʉʂɭɱɧɟɪɟɱɢ: ɪɟɞɨɫɥɟɞ ɢɡɜɨɻɟʃɚ ɪɚɱɭɧɫɤɢɯ ɨɩɟɪɚɰɢʁɚ

1. ɂɡɪɚɱɭɧɚʁ 

2 Â (137 + 218) = ________________;

 (1000 – 348) : 4 = ________________;

 (844 – 725) Â (506 – 498) = _____________________________________________;  (900 – 726) Â 5 = _________________;

 (95 + 87 Â5 = ___________________.

28 Â 6 : 3 = 56

124 Â 9 : 3 = 372

570 : 10 : 2 = 114

849 – 174 Â 3 = 327

147 Â 6 : 2 = 441

R

600 : 4 Â 5 = 750

100 : 4 Â 5 = 125

TA

635 + 245 : 5 = 176

L

2. Ɇɢɥɨɲʁɟ ɬɚɱɧɨ ɢɡɪɚɱɭɧɚɨɫɜɟ ɡɚɞɚɬɤɟ, ɚɥɢ ʁɟɩɪɢɥɢɤɨɦ ɩɪɟɩɢɫɢɜɚʃɚ ɡɚɛɨɪɚɜɢɨ ɞɚɩɪɟɩɢɲɟ ɢ ɡɚɝɪɚɞɟ. ɉɨɦɨɡɢɆɢɥɨɲɭ ɢɫɬɚɜɢɡɚɝɪɚɞɟɧɚ ʃɢɯɨɜɚ ɦɟɫɬɚ.

O

3. ɂɡɪɚɱɭɧɚʁɜɪɟɞɧɨɫɬ ɢɡɪɚɡɚ. ɉɪɢɦɟɧɢ ɩɪɚɜɢɥɚ ɨ ɪɟɞɨɫɥɟɞɭ ɨɛɚɜʂɚʃɚ ɪɚɱɭɧɫɤɢɯ ɨɩɟɪɚɰɢʁɚ M 1280 + 70 Â 7 – 418 = __________________________________________________

-P

N 189 : 3 + 9 Â 85 = ________________________________________________ O 115 + 295 Â 3 – 431 = _______________________________________________

U KA

P 555 – 55 : 5 + 256 = __________________________________________________ Q 136 Â 3 – 188 : 4 = _________________________________________ 4. Ʉɨʁɢɛɪɨʁɬɪɟɛɚɞɚɛɭɞɟ ɭɩɢɫɚɧɭɩɨʂɟ: ɚ ɫɚ

ɛ ɫɚ

?

ɛ)

ED

ɚ)

?

ɚ) 600 ɛ) 700 ɜ) 800 ɝ) 900

ɚ) 557 ɛ) 575 ɜ 757 ɝ) 577

5. ɇɚɩɢɲɢɛɪɨʁɟɜɧɢɢɡɪɚɡ ɱɢʁɚ ʁɟ ɜɪɟɞɧɨɫɬ 100, ɩɨɦɨʄɭ 5 ɩɟɬɢɰɚ ɢ ɡɧɚɤɨɜɚ ɪɚɱɭɧɫɤɢɯ ɨɩɟɪɚɰɢʁɚ ɦɧɨɠɟʃɚ ɢ ɨɞɭɡɢɦɚʃɚ 5 5 5 5 5 = 100

118

ɂɧɬɟɪɧɟɬ ɚɞɪɟɫɚ ɧɚ ɤɨʁɨʁ ɦɨɠɟɲ ɞɚɩɪɨɧɚɻɟɲ ɫɥɢɱɧɟɡɚɞɚɬɤɟ: https:// dms.rs/kengur/zadaci/


ɁȺȼɂɋɇɈɋɌ ɉɊɈɂɁȼɈȾȺ ɈȾɑɂɇɂɅȺɐȺ; ɋɌȺɅɇɈɋɌ ɉɊɈɂɁȼɈȾȺ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɨ 1000, ɡɚɜɢɫɧɨɫɬ ɩɪɨɢɡɜɨɞɚ ɨɞ ɱɢɧɢɥɚɰɚ, ɫɬɚɥɧɨɫɬ ɩɪɨɢɡɜɨɞɚ ɱɢɧɢɥɚɰ

6 · 100 = 600

ɩɪɨɢɡɜɨɞ

ɱɢɧɢɥɚɰ

ɍ ʁɟɞɧɨɦ ɪɚɫɚɞɧɢɤɭ ɫɭ ɧɚ ɝɪɚɮɢɤɨɧɭ ɩɪɟɞɫɬɚɜɢɥɢ ɛɪɨʁɡɚɫɚɻɟɧɢɯɫɚɞɧɢɰɚ ɭ ʁɟɞɧɨʁɧɟɞɟʂɢ Ɇɢɧɚ ʁɟɩɨɞɚɬɤɟɫɚ ɝɪɚɮɢɤɨɧɚɞɟɥɢɦɢɱɧɨ ɩɪɟɞɫɬɚɜɢɥɚ ɭ ɬɚɛɟɥɢ Ɍɢ ɞɨɩɭɧɢɲɬɚʁɟɩɨɬɪɟɛɧɨ 6 · 10 = 60

Ɣ ɒɬɚ

ɑɢɧɢɥɢɰ ʁɟɭɜɟʄɚɧ 2 ɩɭɬɚ ɢ ɩɪɨɢɡɜɨɞ ɫɟɭɜɟʄɚɨ ɩɭɬɚ

6 · (10 · 3 = 6 · __ = 180

ɑɢɧɢɥɢɰ ʁɟɭɜɟʄɚɧ __ ɩɭɬɚ ɢ ɩɪɨɢɡɜɨɞ ɫɟɭɜɟʄɚɨ 3 ɩɭɬɚ

(6 · 4 · 10 = __ · 10 = 240

ɑɢɧɢɥɢɰ ʁɟɭɜɟʄɚɧ 4 ɩɭɬɚ ɢ ɩɪɨɢɡɜɨɞ ɫɟɭɜɟʄɚɨBB ɩɭɬɚ

(6 · 5 · 10 = __ · 10 = 300

ɑɢɧɢɥɢɰ ʁɟɭɜɟʄɚɧ __ ɩɭɬɚ ɢ ɩɪɨɢɡɜɨɞ ɫɟɭɜɟʄɚɨ 5 ɩɭɬɚ

L

6 · (10 · 2 = 6 · __ = 120

TA

ɉ ɍ ɋ ɑ ɉ

ɪɟɞɨɜɚ ɩɨ 10 ɫɚɞɧɢɰɚ ɭʁɟɞɧɨɦɪɟɞɭ

ɭɨɱɚɜɚɲ" Ɉɛʁɚɫɧɢ

Ʉɚɞɚɫɟ ʁɟɞɚɧɱɢɧɢɥɚɰ ɭɜɟʄɚ ɧɟɤɨɥɢɤɨɩɭɬɚ ɢ ɩɪɨɢɡɜɨɞɫɟ ɭɜɟʄɚ ɢɫɬɨ ɬɨɥɢɤɨɩɭɬɚ

R

ɍɫɥɟɞɟʄɨʁɧɟɞɟʂɢ ʁɟ ɛɢɥɨ ɱɟɬɢɪɢ ɪɚɞɧɚ ɞɚɧɚ Ɂɛɨɝ ɤɢɲɧɢɯɩɟɪɢɨɞɚ, ɛɪɨʁɡɚɫɚɻɟɧɢɯ ɫɚɞɧɢɰɚ ɫɟ ɫɦɚʃɢɜɚɨ Ⱦɨɩɭɧɢɡɚɩɢɫɟ ɭ ɬɚɛɟɥɢɢ ɧɚɰɪɬɚʁɲɬɚɧɟɞɨɫɬɚʁɟ 8 · 40 = 320

Ɣ ɒɬɚ

O

ɑɢɧɢɥɢɰ ʁɟɭɦɚʃɟɧ 2 ɩɭɬɚ ɢ ɩɪɨɢɡɜɨɞ ɫɟɭɦɚʃɢɨBB ɩɭɬɚ

(8 : 4 · 40 = __ · 40 = 80

ɑɢɧɢɥɢɰ ʁɟɭɦɚʃɟɧ __ ɩɭɬɚ ɢ ɩɪɨɢɡɜɨɞ ɫɟ ɭɦɚʃɢɨ ɩɭɬɚ

8 · (40 : 8 = 8 · __ = 40

ɑɢɧɢɥɢɰ ʁɟɭɦɚʃɟɧ 8 ɩɭɬɚ ɢ ɩɪɨɢɡɜɨɞ ɫɟɭɦɚʃɢɨBB ɩɭɬɚ

-P

(8 : 2 · 40 = __ · 40 = 160

ɋ ɑ

U KA

ɉ ɍ

ɪɟɞɨɜɚ ɩɨ 40 ɫɚɞɧɢɰɚ ɭʁɟɞɧɨɦɪɟɞɭ

ɭɨɱɚɜɚɲ" Ɉɛʁɚɫɧɢ

Ʉɚɞɚɫɟʁɟɞɚɧɱɢɧɢɥɚɰ ɭɦɚʃɢ ɧɟɤɨɥɢɤɨɩɭɬɚ ɢɩɪɨɢɡɜɨɞɫɟ ɭɦɚʃɢ ɢɫɬɨ ɬɨɥɢɤɨɩɭɬɚ Ʉɨɥɢɤɨ ʄɟɛɢɬɢɫɚɞɧɢɰɚ ɤɚɞɚ ɛɪɨʁ ɪɟɞɨɜɚɭɜɟʄɚɦɨɧɟɤɨɥɢɤɨ ɩɭɬɚ, ɚɛɪɨʁɫɚɞɧɢɰɚ ɭɫɜɚɤɨɦ ɪɟɞɭ ɭɦɚʃɢɦɨ ɢɫɬɨ ɬɨɥɢɤɨ ɩɭɬɚ" Ⱦɨɩɭɧɢɡɚɩɢɫɟ ɭ ɬɚɛɟɥɢ ɢ ɧɚɰɪɬɚʁɲɬɚɧɟɞɨɫɬɚʁɟ

ED

8 · 40 = 320

ɪɟɞɨɜɚ ɩɨ 20 ɫɚɞɧɢɰɚ ɭʁɟɞɧɨɦɪɟɞɭ

(8 · 4 · (40 : 4 = 32 · 10 = 320 (8 · 5 · (40 : 5 = __ · 8 = 320

Ɣ ɒɬɚ ɭɨɱɚɜɚɲ" Ɉɛʁɚɫɧɢ

(8 · 10 · (40 : 10 = 80 · __ = 320

ɉ ɍ

ɋ ɑ ɉ

(8 · 8 · (40 : 8 = 64 · __ = 320

Ʉɚɞɚɫɟ ʁɟɞɚɧɱɢɧɢɥɚɰɭɜɟʄɚ ɚ ɞɪɭɝɢ ɫɦɚʃɢ ɢɫɬɢ ɛɪɨʁ ɩɭɬɚ, ɩɪɨɢɡɜɨɞɫɟ ɧɟʄɟɩɪɨɦɟɧɢɬɢ Ɉɜɨɫɜɨʁɫɬɜɨɧɚɡɢɜɚɦɨɫɬɚɥɧɨɫɬ (ɧɟɩɪɨɦɟɧʂɢɜɨɫɬ ɩɪɨɢɡɜɨɞɚ ɍɧɟɤɢɦ ɡɚɞɚɰɢɦɚ, ɨɜɨ ɩɪɚɜɢɥɨ ɦɨɠɟɲɞɚ ɤɨɪɢɫɬɢɲ ɤɚɨ ɨɥɚɤɲɢɰɭɩɪɢɪɚɱɭɧɚʃɭ ɇɚɩɪɢɦɟɪ: 125 · 8 = (125 · 2 · (8 : 2 = 250 · 4 = 1000 1 Ʉɨɪɢɫɬɢ ɫɜɨʁɫɬɜɨɨ ɫɬɚɥɧɨɫɬɢ ɩɪɨɢɡɜɨɞɚ ɢ ɢɡɪɚɱɭɧɚʁɧɚɥɚɤɲɢɧɚɱɢɧ ɚ 50 · 18 = __ · __ = __ ·2

:2

ɛ 25 · 12 = __ · __ = __ · __

ɜ 14 · 50 = __ · __ = __ : __

: __

119

· __


ɁȺȼɂɋɇɈɋɌ ɉɊɈɂɁȼɈȾȺ ɈȾ ɑɂɇɂɅȺɐȺ; ɋɌȺɅɇɈɋɌ ɉɊɈɂɁȼɈȾȺ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɨ 1000, ɡɚɜɢɫɧɨɫɬ ɩɪɨɢɡɜɨɞɚ ɨɞ ɱɢɧɢɥɚɰɚ, ɫɬɚɥɧɨɫɬ ɩɪɨɢɡɜɨɞɚ

1. ɉɪɨɢɡɜɨɞɞɜɚ ɛɪɨʁɚ ʁɟ 200. Ʉɨɥɢɤɢʄɟɛɢɬɢ ɩɪɨɢɡɜɨɞ: Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨɢɫɩɪɟɞ ɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ. ɚ) ɚɤɨʁɟɞɚɧ ɨɞ ɱɢɧɢɥɚɰɚɭɜɟʄɚɦɨ 2ɩɭɬɚ? ɚ) 202 ɛ) ɚɤɨʁɟɞɚɧ ɨɞɱɢɧɢɥɚɰɚɭɦɚʃɢɦɨ 5ɩɭɬɚ? ɚ) 40

ɛ) 400 ɜ) 404 ɝ) 200 ɛ) 25 ɜ) 100 ɝ) 20

3. Ⱦɭɠɢɧɚɫɬɪɚɧɢɰɟʁɟɞɧɨɝ ɤɜɚɞɪɚɬɚ ɢɡɧɨɫɢ 15 cm. ɚ ɂɡɪɚɱɭɧɚʁɨɛɢɦ ɬɨɝ ɤɜɚɞɪɚɬɚ.

Ɉ = __ · __ = __ cm

TA

ɚ) ɚɤɨ ɨɛɚ ɱɢɧɢɨɰɚɭɜɟʄɚɦɨ 2ɩɭɬɚ? ɚ) 200 ɛ) 400 ɜ) 120 ɝ) 420 ɛ) ɚɤɨ ɨɛɚ ɱɢɧɢɨɰɚɭɦɚʃɢɦɨ 2ɩɭɬɚ? ɚ) 50 ɛ) 25 ɜ) 100 ɝ) 75

L

2. ɉɪɨɢɡɜɨɞ ɞɜɚ ɛɪɨʁɚ ʁɟ 100. Ʉɨɥɢɤɢʄɟɛɢɬɢɩɪɨɢɡɜɨɞ: Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨɢɫɩɪɟɞ ɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ.

Ȅ = 15 cm

ɭɜɟʄɚɦɨ 4ɩɭɬɚ? ____________

Ɣ ɭɦɚʃɢɦɨ

3ɩɭɬɚ? ____________

Ɉɞɝɨɜɨɪ: _____________________________________ Ɉɞɝɨɜɨɪ: _____________________________________

O

Ɣ

R

ɛ) Ʉɨɥɢɤɢ ʄɟɛɢɬɢ ɨɛɢɦ ɬɨɝ ɤɜɚɞɪɚɬɚ, ɚɤɨ ʃɟɝɨɜɭɫɬɪɚɧɢɰɭ:

40 · 10 = 400 Ɣ Ʉɨɥɢɤɢ

ɛɢ ɛɢɨɛɚɤɢɧɩɚɡɚɪɞɚʁɟ:

-P

4. Ȼɚɤɚʁɟɧɚɩɢʁɚɰɢɩɪɨɞɚɥɚ 40ʁɚʁɚ.Ʉɨɥɢɤɢ ʁɟ ɛɢɨʃɟɧɩɚɡɚɪ, ɚɤɨʁɟɰɟɧɚʁɟɞɧɨɝ ʁɚʁɟɬɚ 10ɞɢɧɚɪɚ?

U KA

ɩɪɨɞɚɥɚ 2ɩɭɬɚ ɦɚʃɟʁɚʁɚ? ____________________ ɩɪɨɞɚɥɚ 2ɩɭɬɚɜɢɲɟ ʁɚʁɚ" ____________________ ɰɟɧɚ ʁɟɞɧɨɝʁɚʁɟɬɚɛɢɥɚ 2ɩɭɬɚ ɦɚʃɚ" ______________________ Ɣ Ⱦɨɛɢʁɟɧɟɩɨɞɚɬɤɟ

Ⱥ Ȼ ȼ Ƚ

ɩɪɟɞɫɬɚɜɢɧɚ ɝɪɚɮɢɤɨɧɭ, ɤɚɤɨ ʁɟ ɡɚɩɨɱɟɬɨ.Ʉɨɪɢɫɬɢ ɨɞɝɨɜɚɪɚʁɭʄɟɛɨʁɟ

ED

5. Ʉɨɪɢɫɬɢɩɪɚɜɢɥɨ ɨɧɟɩɪɨɦɟɧʂɢɜɨɫɬɢ ɫɬɚɥɧɨɫɬɢ ɩɪɨɢɡɜɨɞɚ ɢ ɢɡɪɚɱɭɧɚʁɧɚɥɚɤɲɢɧɚɱɢɧ ɚ) 140 · 5 = ________________________________________________________ ɛ) 16 · 50 = ________________________________________________________ ɜ) 24 · 30 = ________________________________________________________ ɝ) 40 · 20 = ________________________________________________________ ɞ) 25 · 8 = ________________________________________________________ 6. ȳɚɧɤɨʁɟɩɪɨɞɚɨ 20 kg ʁɚɛɭɤɚɩɨ ɰɟɧɢɨɞ 40ɞɢɧɚɪɚ ɡɚʁɟɞɚɧɤɢɥɨɝɪɚɦ. Ɣ Ʉɨɥɢɤɨ

ʁɟ ȳɚɧɤɨɞɨɛɢɨɞɢɧɚɪɚ? ________________________ ȳɚɧɤɨʁɟɞɨɛɢɨ ___ɞɢɧɚɪɚ.

Ɣ Ⱦɚʁɟȳɚɧɤɨɩɪɨɞɚɨ

40 kg ʁɚɛɭɤɚ ɩɨ ɞɭɩɥɨ ɦɚʃɨʁɰɟɧɢɤɨɥɢɤɨɛɢ ɬɚɞɚɞɨɛɢɨɞɢɧɚɪɚ?

___________________________________ ȳɚɧɤɨɛɢɬɚɞɚɞɨɛɢɨ ___ɞɢɧɚɪɚ.

120


ɁȺȼɂɋɇɈɋɌ ɄɈɅɂɑɇɂɄȺ ɈȾȾȿȴȿɇɂɄȺ ɂ ȾȿɅɂɈɐȺ; ɋɌȺɅɇɈɋɌ ɄɈɅɂɑɇɂɄȺ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɨ 1000, ɡɚɜɢɫɧɨɫɬ ɤɨɥɢɱɧɢɤɚɨɞ ɞɟʂɟɧɢɤɚ ɢ ɞɟɥɢɨɰɚ ɫɬɚɥɧɨɫɬ ɤɨɥɢɱɧɢɤɚ

600 : 100 = 6

ɞɟʂɟɧɢɤ

ɤɨɥɢɱɧɢɤ

ɞɟɥɢɥɚɰ

Ɇɢɥɢɰɭʁɟ ɡɚɧɢɦɚɥɨ ɤɚɤɨ ɫɟ ɦɟʃɚɞɟʂɟɧɢɤ, ɚ ɤɚɤɨ ɤɨɥɢɱɧɢɤ. ɇɚɩɢɫɚɥɚʁɟɧɟɤɨɥɢɤɨɩɪɢɦɟɪɚ ɢ ɞɨɛɢʁɟɧɟ ɩɨɞɚɬɤɟ ɩɪɟɞɫɬɚɜɢɥɚ ɧɚ ɝɪɚɮɢɤɨɧɢɦɚ. Ⱦɨɩɭɧɢɡɚɩɢɫɟ ɨɞɝɨɜɚɪɚʁɭʄɢɦɛɪɨʁɟɜɢɦɚ.

Ɣ ɒɬɚ

1

(60 · 2) : 2 = 120 : __ = 60

2

(640 : 2) : 2 = 320 : __ = 160

2

(60 · 3) : 2 = ___ : 2 = 90

3

(640 : 4) : 2 = 180 : __ = 80

3

(60 · 4) : 2 = 240 : __ = 120

4

(640 : 8) : 2 = __ : 2 = 40

4

640 : 2 = 320

L

1

TA

1 2 3 4

60 : 2 = 30

ɭɨɱɚɜɚɲ? Ɉɛʁɚɫɧɢ

Ʉɚɞɚɫɟɞɟʂɟɧɢɤɭɦɚʃɢ ɧɟɤɨɥɢɤɨɩɭɬɚ ɢ ɤɨɥɢɱɧɢɤɫɟ ɭɦɚʃɢ ɢɫɬɨ ɬɨɥɢɤɨɩɭɬɚ.

R

Ʉɚɞɚɫɟɞɟʂɟɧɢɤɭɜɟʄɚɧɟɤɨɥɢɤɨɩɭɬɚ ɢ ɤɨɥɢɱɧɢɤ ɫɟɭɜɟʄɚ ɢɫɬɨ ɬɨɥɢɤɨ ɩɭɬɚ.

1 2 3 4

480 : 2 = 240

Ɣ ɒɬɚ

-P

480 : (2 · 2) = 480 : __ = 120

2

480 : (2 · 4) = 480 : __ = 60

3

U KA

1 2 3

1

O

ɇɢɤɨɥɭ ʁɟ ɡɚɧɢɦɚɥɨ ɤɚɤɨ ɫɟ ɦɟʃɚ ɞɟɥɢɥɚɰɚ ɤɚɤɨ ɤɨɥɢɱɧɢɤɇɚɩɢɫɚɨʁɟɧɟɤɨɥɢɤɨɩɪɢɦɟɪɚ. Ⱦɨɩɭɧɢɡɚɩɢɫɟ ɭ ɬɚɛɟɥɢ ɢ ɧɚɰɪɬɚʁ ɲɬɚɧɟɞɨɫɬɚʁɟ.

1 2 3

480 : 8 = 60

1

480 : (8 : 2) = 480 : __ = 120

2

480 : (8 : 4) = 480 : __ = 240

3

ɭɨɱɚɜɚɲ"Ɉɛʁɚɫɧɢ

Ʉɚɞɚɫɟɞɟɥɢɥɚɰɭɜɟʄɚɧɟɤɨɥɢɤɨɩɭɬɚ, ɤɨɥɢɱɧɢɤɫɟ ɫɦɚʃɢ ɢɫɬɨ ɬɨɥɢɤɨ ɩɭɬɚ.

Ʉɚɞɚɫɟɞɟɥɢɥɚɰɭɦɚʃɢ ɧɟɤɨɥɢɤɨɩɭɬɚ, ɤɨɥɢɱɧɢɤɫɟ ɭɜɟʄɚ ɢɫɬɨ ɬɨɥɢɤɨɩɭɬɚ.

ED

ɒɬɚ ɦɢɫɥɢɲ, ɤɚɞɚɫɟ ɤɨɥɢɱɧɢɤɧɟʄɟ ɩɪɨɦɟɧɢɬɢ? ɉɪɨɭɱɢɞɚɬɟ ɩɪɢɦɟɪɟ.

·2

·2

:2

:2

:4

Ɣ ɒɬɚ

ɭɨɱɚɜɚɲ" Ɉɛʁɚɫɧɢ

:4

Ʉɚɞɚ ɫɟɞɟʂɟɧɢɤ ɢ ɞɟɥɢɥɚɰɩɨɦɧɨɠɟ ɢɥɢ ɩɨɞɟɥɟ ɢɫɬɢɦ ɛɪɨʁɟɦ, ɤɨɥɢɱɧɢɤɫɟɧɟʄɟ ɩɪɨɦɟɧɢɬɢ Ɉɜɨɫɜɨʁɫɬɜɨ ɧɚɡɢɜɚɦɨ ɫɬɚɥɧɨɫɬ (ɧɟɩɪɨɦɟɧʂɢɜɨɫɬ) ɤɨɥɢɱɧɢɤɚ. ɍɧɟɤɢɦ ɡɚɞɚɰɢɦɚ, ɨɜɨ ɩɪɚɜɢɥɨ ɦɨɠɟɲɞɚ ɤɨɪɢɫɬɢɲɤɚɨ ɨɥɚɤɲɢɰɭɩɪɢɪɚɱɭɧɚʃɭ. ɇɚ ɩɪɢɦɟɪ: 180 : 5 = (180 · 2) : (5 · 2) = 360 : 10 = 36 1. Ʉɨɪɢɫɬɢɩɪɚɜɢɥɨ ɨɧɟɩɪɨɦɟɧʂɢɜɨɫɬɢ ɫɬɚɥɧɨɫɬɢ ɩɪɨɢɡɜɨɞɚ ɢ ɢɡɪɚɱɭɧɚʁɧɚɥɚɤɲɢɧɚɱɢɧ ɚ) 240 : 12 = __ : __ = __ : __

: __

ɛ) 460 : 20 = __ : __ = __ : __

ɜ) 800 : 5 = __ : __ = __ · __

: __

121

· __


ɁȺȼɂɋɇɈɋɌ ɄɈɅɂɑɇɂɄȺ ɈȾ ȾȿȴȿɇɂɄȺ ɂ ȾȿɅɂɈɐȺ ɋɌȺɅɇɈɋɌ ɄɈɅɂɑɇɂɄȺ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɨ 1000, ɡɚɜɢɫɧɨɫɬ ɤɨɥɢɱɧɢɤɚɨɞ ɞɟʂɟɧɢɤɚ ɢ ɞɟɥɢɨɰɚ ɫɬɚɥɧɨɫɬ ɤɨɥɢɱɧɢɤɚ

1. ɍɱɟɬɢɪɢ ɢɫɬɟɛɨɦɛɨʃɟɪɟ ɢɦɚ ɭɤɭɩɧɨ 144ɛɨɦɛɨɧɟ. Ɣ Ʉɨɥɢɤɨɛɨɦɛɨɧɚ ɢɦɚ ɭʁɟɞɧɨʁɛɨɦɛɨʃɟɪɢ" ____________________________ Ɉɞɝɨɜɨɪ: ___________________________________ Ɣ Ⱦɚɫɟ ɭ ɬɟ 4ɛɨɦɛɨʃɟɪɟɧɚɥɚɡɢ 3ɩɭɬɚɜɢɲɟɛɨɦɛɨɧɚɧɟɝɨɲɬɨ ʁɟɛɢɥɨ, ɤɨɥɢɤɨɛɢɬɚɞɚ ɛɢɥɨ ɛɨɦɛɨɧɚ ɭʁɟɞɧɨʁɛɨɦɛɨʃɟɪɢ" ____________________________ Ɉɞɝɨɜɨɪ: ___________________________________ ɭ ɬɟ 4ɛɨɦɛɨʃɟɪɟɧɚɥɚɡɢ 2ɩɭɬɚ ɦɚʃɟɛɨɦɛɨɧɚɧɟɝɨɲɬɨʁɟɛɢɥɨ, ɤɨɥɢɤɨɛɢɬɚɞɚ ɛɢɥɨ ɛɨɦɛɨɧɚ ɭʁɟɞɧɨʁɛɨɦɛɨʃɟɪɢ" ____________________________ Ɉɞɝɨɜɨɪ: ___________________________________

2. Ɉɞɪɟɞɢ ɛɪɨʁɟɜɟ ɨɡɧɚɱɟɧɟɫɥɨɜɢɦɚ ɚ, b ɢ c. 294 : 7 = 42 (294 · b) : 7 = 84, b = __

774 : 9 = 86 (774 : ɫ) : 9 = 43, ɫ = __

R

245 : 5 = 49 (245 : ɚ) : 5 = 7, ɚ = __

TA

L

Ɣ Ⱦɚɫɟ

Ɉɞɝɨɜɨɪ: ___________________________________

-P

____________________________

O

3. ɍʁɟɞɧɨɦɩɨɡɨɪɢɲɬɭ 48 ɫɬɨɥɢɰɚ ɬɪɟɛɚ ɪɚɡɦɟɫɬɢɬɢ ɭ 4 ɪɟɞɚ, ɬɚɤɨɞɚ ɢɯ ɭɫɜɚɤɨɦ ɪɟɞɭ ɢɦɚ ʁɟɞɧɚɤ ɛɪɨʁ Ɣ Ʉɨɥɢɤɨɫɬɨɥɢɰɚ ʄɟɛɢɬɢ ɭɫɜɚɤɨɦ ɪɟɞɭ"

U KA

ɂɫɬɢ ɛɪɨʁɫɬɨɥɢɰɚ ɬɪɟɛɚ ɪɚɡɦɟɫɬɢɬɢ ɭ 2ɩɭɬɚɜɢɲɟ ɪɟɞɨɜɚ,ɧɚ ɢɫɬɢ ɧɚɱɢɧ Ɣ Ʉɨɥɢɤɨɫɬɨɥɢɰɚ ʄɟɛɢɬɢ ɭɫɜɚɤɨɦ ɪɟɞɭ" ____________________________ Ɉɞɝɨɜɨɪ: ___________________________________ ɂɫɬɢ ɛɪɨʁɫɬɨɥɢɰɚ ɬɪɟɛɚ ɪɚɡɦɟɫɬɢɬɢ ɭ 2ɩɭɬɚ ɦɚʃɟ ɪɟɞɨɜɚ,ɧɚ ɢɫɬɢ ɧɚɱɢɧ Ɣ Ʉɨɥɢɤɨɫɬɨɥɢɰɚ ʄɟɛɢɬɢ ɭɫɜɚɤɨɦ ɪɟɞɭ" ____________________________ Ɉɞɝɨɜɨɪ: ___________________________________ 5.

ED

4. Ⱦɟʂɟɧɢɤʁɟ 250, ɚɞɟɥɢɥɚɰʁɟ 2. ɉɪɨɦɟɧɢɞɟɥɢɥɚɰ, ɬɚɤɨɞɚɫɟ ɤɨɥɢɱɧɢɤɭɦɚʃɢ5ɩɭɬɚ.

_________________________________

Ⱦɟʂɟɧɢɤʁɟ 160, ɚɞɟɥɢɥɚɰʁɟ 8. ɉɪɨɦɟɧɢɞɟɥɢɥɚɰ, ɬɚɤɨ ɞɚɫɟ ɤɨɥɢɱɧɢɤ ɭɜɟʄɚ 4ɩɭɬɚ. _________________________________

6. ɉɨɩɭɧɢɩɪɚɡɧɚɩɨʂɚ ɨɞɝɨɜɚɪɚʁɭʄɢɦɛɪɨʁɟɜɢɦɚ. 130 : 5 = 260 :

=

640 : 16 = 320 :

=

300 : 25 = 60 :

=

240 : 5 = 480 :

=

7. 300 ɨɥɨɜɚɤɚ ɪɚɫɩɨɪɟɻɟɧɨ ʁɟ ɭ 12 ɤɭɬɢʁɚ, ɬɚɤɨɞɚ ɢɯ ɭɫɜɚɤɨʁɤɭɬɢʁɢɢɦɚʁɟɞɧɚɤ ɛɪɨʁ Ʉɨɥɢɤɨ ɨɥɨɜɚɤɚ ɢɦɚ ɭɫɜɚɤɨʁɤɭɬɢʁɢ" ɉɪɢɦɟɧɢɫɜɨʁɫɬɜɨɫɬɚɥɧɨɫɬɢ ɤɨɥɢɱɧɢɤɚ.

____________________________ Ɉɞɝɨɜɨɪ: ____________________________________

122


ȳȿȾɇȺɑɂɇȿ ɋȺ ɇȿɉɈɁɇȺɌɂɆ ɑɂɇɂɈɐȿɆ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɨ 1000,ʁɟɞɧɚɱɢɧɟ ɫɚ ɧɟɩɨɡɧɚɬɢɦ ɱɢɧɢɨɰɟɦ

ɉɨɞɫɟɬɢʄɟɦɨ ɫɟ ɜɟɡɟ ɢɡɦɟɻɭ ɦɧɨɠɟʃɚ ɢɞɟʂɟʃɚ. Ʉɚɤɨʁɟ 8 · 10 = 80 ɑɢɧɢɥɚɰ 8ʁɟɞɧɚɤ ʁɟ ɤɨɥɢɱɧɢɤɭ ɩɪɨɢɡɜɨɞɚ 80 ɢ 10.

ɑɢɧɢɥɚɰ 10ʁɟɞɧɚɤ ʁɟ ɤɨɥɢɱɧɢɤɭ ɩɪɨɢɡɜɨɞɚ 80 ɢ 8.

ɦɚʁɢɰɟ ɯ ɞɢɧɚɪɚ. Ɂɚɩɢɫɭʁɟɦɨʁɟɞɧɚɤɨɫɬ: ɯ · 3 = 975. ȳɟɞɧɚɤɨɫɬɯ · 3 = 975 ʁɟʁɟɞɧɚɱɢɧɚ ɯ ʁɟ ɧɟɩɨɡɧɚɬɢɱɢɧɢɥɚɰ Ɣ Ɋɟɲɚɜɚɦɨ ʁɟɞɧɚɱɢɧɭ ɢ ɨɞɪɟɻɭʁɟɦɨɰɟɧɭʁɟɞɧɟ ɦɚʁɢɰɟ:

O

R

Ɣ ɇɟɤɚʁɟɰɟɧɚʁɟɞɧɟ

TA

Ɍɪɢ ɦɚʁɢɰɟ ɢɦɚʁɭ ɢɫɬɟɰɟɧɟ, ɚ ɡɚʁɟɞɧɨ ɤɨɲɬɚʁɭ 975ɞɢɧɚɪɚ. Ʉɨɥɢɤɨ ɤɨɲɬɚʁɟɞɧɚ ɦɚʁɢɰɚ?

L

ɬɨʁɟ 8 = 80 : 10 ɢ 10 = 80 : 8

ɯ · 3 = 975

-P

ɯ = 975 : 3 ɯ = 325

1.

U KA

ɉɪɨɜɟɪɚ: 325 3 = 975

ɇɟɩɨɡɧɚɬɢɱɢɧɢɥɚɰ ɢɡɪɚɱɭɧɚɜɚɦɨ ɬɚɤɨɲɬɨɩɪɨɢɡɜɨɞ ɩɨɞɟɥɢɦɨ ɫɚɩɨɡɧɚɬɢɦɱɢɧɢɨɰɟɦ

ɐɟɧɚ ʁɟɞɧɟ ɦɚʁɢɰɟʁɟ 325 ɞɢɧɚɪɚ.

ɂɡɪɚɱɭɧɚʁɧɟɩɨɡɧɚɬɢ ɱɢɧɢɥɚɰ. ɉɪɨɜɟɪɢ ɬɚɱɧɨɫɬ ɪɟɲɟʃɚ (ɭɦɟɫɬɨ ɪɟɱɢ ɩɪɨɜɟɪɚ ɩɢɫɚʄɟɦɨ ɫɥɨɜɨɉ). a) 2 · a = 658

ɛ) b · 6 = 816

ɜ) 3 · c = 957

ɝ) m · 5 = 760

ɚ = ________

b = ________

c = ________

m = ________

ɚ = ________

b = ________

c = ________

m = ________

ED

ɉ: ______________

ɉ ______________

ɉ: ______________

2. ɉɟɬ ɤɭɝɥɢ ɫɥɚɞɨɥɟɞɚ ɤɨɲɬɚ 425 ɞɢɧɚɪɚ. Ʉɨɥɢɤɨ ɤɨɲɬɚʁɟɞɧɚ ɤɭɝɥɚɫɥɚɞɨɥɟɞɚ?

ɉ: ______________

3. ȳɟɞɚɧɱɢɧɢɥɚɰʁɟ 9, ɚ ɩɪɨɢɡɜɨɞʁɟ ɡɛɢɪɛɪɨʁɟɜɚ 295 ɢ 470. Ɉɞɪɟɞɢ ɞɪɭɝɢ ɱɢɧɢɥɚɰ.

Ɉɞɝɨɜɨɪ: ________________________________

Ɍɨʁɟɛɪɨʁ ___.

4. Ʉɚɞɚ ɤɨɚɥɚɄɨɥɟɧɟɫɩɚɜɚ, ɨɧɡɚ ʁɟɞɚɧɫɚɬ ɩɨʁɟɞɟ 10 gɥɢɲʄɚ. ɍ ɩɟɬɚɤ ʁɟ Ʉɨɥɟ ɩɨʁɟɨ 100 gɥɢɲʄɚ. ɄɨɥɢɤɨʁɟɄɨɥɟ ɩɪɨɜɟɨ ɫɚɬɢ ɭɫɩɚɜɚʃɭ? ȳɟɞɧɚɱɢɧɚ:

Æ

Æ

Ɉɞɝɨɜɨɪ: ________________________________________________

123


ȳȿȾɇȺɑɂɇȿ ɋȺ ɇȿɉɈɁɇȺɌɂɆ ɑɂɇɂɈɐȿɆ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɨ 1000,ʁɟɞɧɚɱɢɧɟ ɫɚ ɧɟɩɨɡɧɚɬɢɦ ɱɢɧɢɨɰɟɦ

1. Ɋɟɲɢʁɟɞɧɚɱɢɧɟ: ɚ) ɯ · 3 = 792

ɛ) ɯ · 5 = 915

ɜ) ɯ · 7 = 889

ɝ) ɯ · 9 = 711

ɯ = ________

ɯ = ________

ɯ = ________

ɯ = ________

ɯ = ________

ɯ = ________

ɯ = ________

ɯ = ________

ɉ: ______________

ɉ: ______________

ɉ ______________

L

ɉ: ______________

3. ȳɨɜɚɧɚ ʁɟ ɡɚɦɢɫɥɢɥɚ ʁɟɞɚɧɛɪɨʁ Ⱥɤɨ ɝɚ ɭɜɟʄɚɲ 8ɩɭɬɚ, ɞɨɛɢʄɟɲ ɛɪɨʁ912. Ʉɨʁɢ ɛɪɨʁʁɟ ɡɚɦɢɫɥɢɥɚ ȳɨɜɚɧɚ?

TA

2. ȳɟɞɚɧɱɢɧɢɥɚɰʁɟ ɪɚɡɥɢɤɚɛɪɨʁɟɜɚ 683 ɢ 679, ɚɩɪɨɢɡɜɨɞʁɟ 740. ɉɨɫɬɚɜɢ ʁɟɞɧɚɱɢɧɭ ɢ ɢɡɪɚɱɭɧɚʁɞɪɭɝɢ ɱɢɧɢɥɚɰ.

ȳɟɞɧɚɱɢɧɚ:

O

R

ȳɟɞɧɚɱɢɧɚ:

ȳɨɜɚɧɚʁɟ ɡɚɦɢɫɥɢɥɚ ɛɪɨʁ___.

-P

Ⱦɪɭɝɢ ɱɢɧɢɥɚɰʁɟɛɪɨʁ___.

4. ɋɨʃɚ ʁɟ ɤɭɩɢɥɚ ɩɨ ʁɟɞɚɧɤɢɥɨɝɪɚɦʁɚɛɭɤɚ ɢʁɚɝɨɞɚ. ȳɚɝɨɞɟɫɭ 3ɩɭɬɚɫɤɭɩʂɟ ɨɞʁɚɛɭɤɚ. Ʉɭɩʂɟɧɨ ɜɨʄɟ ʁɟɩɥɚɬɢɥɚ 180ɞɢɧɚɪɚ. Ʉɨɥɢɤɚʁɟ ɰɟɧɚ ɤɢɥɨɝɪɚɦɚʁɚɛɭɤɚ, ɚ ɤɨɥɢɤɨʁɚɝɨɞɚ? ɇɟɩɨɡɧɚɬɚʁɟɰɟɧɚʁɚɛɭɤɚ. Ɂɚɬɨɰɟɧɭ 1 kg ʁɚɛɭɤɚ ɨɡɧɚɱɚɜɚɦɨ ɫɚ ɯ ɞɢɧɚɪɚ.

Ɣ

Ɂɧɚɦɨɞɚʁɟɰɟɧɚ 1 kg ʁɚɝɨɞɚ 3 ɩɭɬɚɜɟʄɚ ɨɞ 1 kg ʁɚɛɭɤɚ. Ɂɚɬɨɰɟɧɭ 1 kg ʁɚɝɨɞɚ ɨɡɧɚɱɚɜɚɦɨ ɫɚ 3 · ɯ ɞɢɧɚɪɚ.

Ɣ

ɉɨɫɬɚɜʂɚɦɨʁɟɞɧɚɱɢɧɭɩɨɦɨʄɭ ɤɨʁɟ ɨɞɪɟɻɭʁɟɦɨɰɟɧɭ 1 kg ʁɚɛɭɤɚ:

U KA

Ɣ

Æ 4 · ɯ = 180

ED

ɯ + 3 · ɯ = 180

Æ ɯ = ___ : __

Æ ɯ = ___

4·ɯ

1 kg ʁɚɛɭɤɚʁɟ ɯ ɞɢɧɚɪɚ,ɲɬɨ ɢɡɧɨɫɢ ____ɞɢɧɚɪɚ. 1 kg ʁɚɝɨɞɚʁɟ 3 · ɯ ɞɢɧɚɪɚ, ɲɬɨ ɢɡɧɨɫɢ 3 · ___ɞɢɧɚɪɚ, ɚ ɬɨʁɟ ____ɞɢɧɚɪɚ. 5. ȳɚɧɤɨʁɟ ɪɟɤɟɬ ɢ ɥɨɩɬɢɰɭ ɡɚɫɬɨɧɢ ɬɟɧɢɫɩɥɚɬɢɨ 920 ɞɢɧɚɪɚ. Ɋɟɤɟɬ ʁɟ 7 ɩɭɬɚ ɫɤɭɩʂɢ ɨɞɥɨɩɬɢɰɟ. Ʉɨɥɢɤɨ ɤɨɲɬɚɥɨɩɬɢɰɚ, ɚ ɤɨɥɢɤɨ ɪɟɤɟɬ" ȳɟɞɧɚɱɢɧɚ: ____________________ ____________________ ____________________ _______________________________________________ Ɉɞɝɨɜɨɪ: _____________________________________________________________________

124


ȳȿȾɇȺɑɂɇȿ ɋȺ ɇȿɉɈɁɇȺɌɂɆ ɑɂɇɂɈɐȿɆ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɨ 1000,ʁɟɞɧɚɱɢɧɟ ɫɚ ɧɟɩɨɡɧɚɬɢɦ ɱɢɧɢɨɰɟɦ

Ɂɚɛɚɜɢɬɟɫɟ ɩɨɩɭʃɚɜɚʃɟɦ ɛɪɨʁɟɜɧɢɯ ɭɤɪɲɬɟɧɢɰɚ... 1. ɍɩɢɲɢɭ ɠɭɬɚ ɩɨʂɚ ɨɞɝɨɜɚɪɚʁɭʄɟɛɪɨʁɟɜɟ, ɬɚɤɨɞɚ ʁɟɞɧɚɱɢɧɟ ɭ ɭɤɪɲɬɟɧɢɰɢ ɛɭɞɭ ɬɚɱɧɟ. Ⱦɨɛɢʁɟɧɚ ɪɟɲɟʃɚɩɪɨɜɟɪɢ ɫɚ ɨɫɬɚɥɢɦɱɥɚɧɨɜɢɦɚ ɝɪɭɩɟ. :

+

+

98

152

=

= 2

=

: 4

500

·

387

=

O

= 4

820

U KA

·

ED

200

=

332 ·

168

=

:

5

=

740

·

3

=

:

-P

·

·

R

=

=

TA

·

..5..

L

..3.. ...·.. 128 ..=.. 384 ....

10

= = · 300

:

=

:

100

=

3

=

=

2

738

·

=

8

· ·

9

=

·

·

4

=

900

·

7

=

315

: 5

=

=

900

· = 742

125


ɋȺȾȺ ɁɇȺɆ ɆɇɈȽɈ ȼɂɒȿ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɞɨ 1000,ʁɟɞɧɚɱɢɧɟ ɫɚ ɧɟɩɨɡɧɚɬɢɦ ɱɢɧɢɨɰɟɦ

Ɇɧɨɠɢɦ ɬɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɟ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ: ɋ Ⱦ 2 1

ȳ 6

6

8

4

·

ɋ Ⱦ ȳ 2 4 1

3

9

6

ɋ Ⱦ ȳ ·

4

4

3

2

0

0

0

1 8

6 2

5 5

·

5

Ⱦɟɥɢɦ ɬɪɨɰɢɮɪɟɧɟ ɛɪɨʁɟɜɟ ʁɟɞɧɨɰɢɮɪɟɧɢɦ ɛɪɨʁɟɦ (ɫɚɨɫɬɚɬɤɨɦ ɢ ɛɟɡ ɨɫɬɚɬɤɚ):

5 5 0 –

4 0 4

Ⱦ 1

ɋ 4 – 3 1 – 1

ȳ 0

ɨɫɬɚɬɚɤ

ɉɪɨɜɟɪɚɜɚɦ: (110 · 5) + 4 = 550 + 4 = 554

Ⱦ ȳ ɋ Ⱦ ȳ 5 6 : 3 = 1 5 2

ɋ Ⱦ ȳ Ⱦ ȳ 4 1 5 : 5 = 8 3 – 4 0 1 5 – 1 5 0 – 1 0 0

L

=

ɋ 1

TA

Ⱦ ȳ 5 4 : 5

5 5 0 6 – 6 0

152 · 3 456

ɉɪɨɜɟɪɚɜɚɦ:

O

ɉɪɨɜɟɪɚɜɚɦ:

R

ɋ 5 5 0 –

83 · 5 415

120 307 Ɣ Ɂɧɚɦɞɚ

U KA

-P

ɉɨɲɬɭʁɟɦ ɩɪɚɜɢɥɚɨɪɟɞɨɫɥɟɞɭ ɨɛɚɜʂɚʃɚɪɚɱɭɧɫɤɢɯɨɩɟɪɚɰɢʁɚ. Ɂɚɬɨ ɭɦɟɦ ɞɚ ɪɟɲɚɜɚɦ ɡɚɞɚɬɤɟ ɫɚ ɞɜɟ ɢ ɫɚ ɬɪɢɪɚɱɭɧɫɤɟɨɩɟɪɚɰɢʁɟ.

250

34

70

238

28 196

ɡɚɝɪɚɞɚɦɚ ɨɡɧɚɱɢɦ ɪɚɱɭɧɫɤɭɨɩɟɪɚɰɢʁɭ ɤɨʁɭ ɬɪɟɛɚɞɚ ɨɛɚɜɢɦɩɪɟɞɪɭɝɢɯ ɨɩɟɪɚɰɢʁɚ ɇɚ ɩɪɢɦɟɪ: Ɂɛɢɪɛɪɨʁɟɜɚ 327 ɢ 169 ɭɜɟʄɚʁ2ɩɭɬɚÆ (327 + 169) · __ = 496 · 2 = ___ Ɂɧɚɦɞɚɫɭ ɦɧɨɠɟʃɟ ɢɞɟʂɟʃɟ ɪɚɜɧɨɩɪɚɜɧɟ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ Ɂɚɬɨ ɡɚɝɪɚɞɚɦɚ ɢɫɬɢɱɟɦ ɨɩɟɪɚɰɢʁɟ ɤɨʁɟ ʄɭɩɪɜɨ ɢɡɜɟɫɬɢɇɚɩɪɢɦɟɪ: (225 : 3) · 5 = 75 · 5 = 375

ED

Ɣ

Ɣ Ɂɧɚɦɞɚ ɪɟɲɚɜɚɦ

ɦɚɬɟɦɚɬɢɱɤɟ ɢɡɪɚɡɟɫɚ ɬɪɢ ɪɚɱɭɧɫɤɟ ɨɩɟɪɚɰɢʁɟ, ɛɟɡ ɡɚɝɪɚɞɚ

928 : 4 – 810 : 6 = 232 – 135 = 97 Ɣ Ɂɧɚɦɞɚɩɪɢɦɟɧɢɦɫɜɨʁɫɬɜɚ

50 · 18 = 100 · 9 = 900 ·2

100

:2

9

154 Â 3 + 750 : 2 = 462 + 375 = 837

ɫɬɚɥɧɨɫɬɢɩɪɨɢɡɜɨɞɚ ɢɫɬɚɥɧɨɫɬɢ ɤɨɥɢɱɧɢɤɚ ɡɚ ɛɪɠɟ ɪɚɱɭɧɚʃɟ

14 · 50 = 7 · 100 = 700 :2

7

·2

·2

100

Ɣ Ɂɧɚɦɞɚ

ɢɡɪɚɱɭɧɚɦɧɟɩɨɡɧɚɬɢ ɱɢɧɢɥɚɰ ɯ · 3 = 975 ɯ = 975 : 3 ɯ = 325 ɉɪɨɜɟɪɚɜɚɦ: 325 · 3 = 975

·2

:2

:2

ɇɟɩɨɡɧɚɬɢɱɢɧɢɥɚɰ ɢɡɪɚɱɭɧɚɜɚɦ ɬɚɤɨɲɬɨɩɪɨɢɡɜɨɞ ɩɨɞɟɥɢɦ ɫɚɩɨɡɧɚɬɢɦɱɢɧɢɨɰɟɦ

126


ɉɊɈȼȿɊȺȼȺɆɈ ɇȺɍɑȿɇɈ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɢ ɞɟʂɟʃɟ ɞɨ0 ɩɪɨɜɟɪɚɡɧɚʃɚ

1. ɂɡɪɚɱɭɧɚʁɩɪɨɢɡɜɨɞɟ ɢ ɩɨɩɭɧɢɬɚɛɟɥɭ. ɚ b a·b

148 6

329 3

437 2

225 4

139 7

125 8

374 2

L

2. Ⱦɭʃɢɧɛɪɚɬ ɫɜɚɤɢɞɚɧɩɨɩɢʁɟ225 ml ɦɥɟɤɚ.Ʉɨɥɢɤɨ ɦɥɟɤɚɩɨɩɢʁɟ ɡɚ 4ɞɚɧɚ?

TA

_______________ Ɉɞɝɨɜɨɪ: ___________________________________________

R

3. Ɂɚʁɟɱɚɪʁɟ ɨɞɁɪɟʃɚɧɢɧɚ ɭɞɚʂɟɧ285 km. Ʉɨɥɢɤɨ ʄɟ ɤɢɥɨɦɟɬɚɪɚɩɪɟʄɢ ɜɨɡɚɱɚɭɬɨɦɨɛɢɥɚ ɚɤɨɩɪɟɻɟ ɨɜɚʁɩɭɬ ɭ ɨɛɚɩɪɚɜɰɚ?

4. ɂɡɪɚɱɭɧɚʁɤɨɥɢɱɧɢɤɟ ɩɨɩɭɧɢ ɬɚɛɥɢɰɢ. 430 5

178 2

539 7

-P

258 3

356 4

324 9

800 5

U KA

ɚ b a:b

O

_______________ Ɉɞɝɨɜɨɪ: ___________________________________________

5. Ɍɪɢ ɦɨɥɟɪɚ ɪɚɞɟ ɡɚʁɟɞɧɨ ɢ ɡɚɪɚɞɭɞɟɥɟɧɚʁɟɞɧɚɤɟɞɟɥɨɜɟ.Ɂɚ ʁɟɞɚɧɫɚɬ ɨɧɢ ɡɚɪɚɞɟ 981 ɞɢɧɚɪɚ. Ʉɨɥɢɤɨ ʁɟɞɢɧɚɪɚ ɡɚɪɚɞɢɨɫɜɚɤɢ ɨɞʃɢɯ? _______________ Ɉɞɝɨɜɨɪ: ___________________________________________

ED

6. ɇɚʁɜɟʄɢ ɬɪɨɰɢɮɪɟɧɢɛɪɨʁɭɦɚʃɢ ɡɚɩɪɨɢɡɜɨɞɛɪɨʁɟɜɚ 99 ɢ 9. _______________ Ɉɞɝɨɜɨɪ: ___________________________________________ 7. Ʉɢʄɢɧɱɚɪɨɛʃɚɤ ɭɧɟɬɢ ɛɪɨʁ

ɭɜɟʄɚ ɡɚɛɪɨʁɤɨʁɢʁɟ ɩɭɬɚɜɟʄɢ ɚ ɡɚɬɢɦ ɞɨɛɢʁɟɧɢ ɩɪɨɢɡɜɨɞɭɦɚʃɢ ɡɚɛɪɨʁ . ɍɬɚɛɥɢɰɢ ɫɭɧɚɩɢɫɚɧɢɛɪɨʁɟɜɢ ɤɨʁɟ Ʉɢʄɚ ɠɟɥɢɞɚ ɭɧɟɫɟ ɚ ɬɢ ɧɚɩɢɲɢɛɪɨʁɟɜɟ ɤɨʁɟ ɱɚɪɨɛʃɚɤ ɬɪɟɛɚɞɚ ɢɡɛɚɰɢ.

148

6

699

256

3

592

427

2

365

114

8

905

196

5

666

127


ɉɊɈȼȿɊȺȼȺɆɈ ɇȺɍɑȿɇɈ Ʉʂɭɱɧɟɪɟɱɢ: ɦɧɨɠɟʃɟ ɢ ɞɟʂɟʃɟ ɞɨ000, ɩɪɨɜɟɪɚɡɧɚʃɚ

8. Ȼɪɨʁ650 ɭɦɚʃɢ ɡɚ ɤɨɥɢɱɧɢɤɛɪɨʁɟɜɚ 950 ɢ 2. _______________________________________________________________ 9. ɋɚɪɚ ɭɫɜɨʁɨʁɛɢɛɥɢɨɬɟɰɢ ɢɦɚ 132ɱɚɫɨɩɢɫɚ. ɋɜɚɤɢ ɬɪɟʄɢ ɱɚɫɨɩɢɫʁɟɧɚ ɟɧɝɥɟɫɤɨɦ, ɚ ɨɫɬɚɥɢ ɫɭɧɚɫɪɩɫɤɨɦ ʁɟɡɢɤɭ. Ʉɨɥɢɤɨɋɚɪɚ ɢɦɚɱɚɫɨɩɢɫɚɧɚ ɫɪɩɫɤɨɦ ʁɟɡɢɤɭ? _____________________

Ɉɞɝɨɜɨɪ: ___________________________________________

L

10. Ɋɚɡɥɢɰɢ ɛɪɨʁɟɜɚ 648 ɢ 458ɞɨɞɚʁɩɪɨɢɡɜɨɞɛɪɨʁɟɜɚ 125 ɢ 5. _______________________________________________________________

TA

11. Ʉɨɥɢɱɧɢɤɛɪɨʁɟɜɚ 975 ɢ 5 ɩɨɦɧɨɠɢ ɪɚɡɥɢɤɨɦ ɛɪɨʁɟɜɚ 502 ɢ 497.

_______________________________________________________________

R

12. Ɂɚ 3 kg ɤɪɭɲɚɤɚ ɂɜɚɧʁɟɩɥɚɬɢɨ 195ɞɢɧɚɪɚ. Ʉɨɥɢɤɨ ɤɨɲɬɚ 1 kg ɦɚɥɢɧɚ ɱɢʁɚ ʁɟɰɟɧɚɞɜɚ ɩɭɬɚɜɟʄɚ?

Ɉɞɝɨɜɨɪ: _____________________________________

O

____________________________

-P

13. ɋɬɚɧɨɜɧɢɰɢ ʁɟɞɧɟɲɭɦɟɫɭɫɟɫɚɤɪɢɥɢ ɨɞ ɥɨɜɚɰɚ, ɚɥɢɢɯ ɭɫɧɟɝɭ ɦɨɝɭ ɨɬɤɪɢɬɢʃɢɯɨɜɢɬɪɚɝɨɜɢ. Ɋɟɲɢʁɟɞɧɚɱɢɧɟ. Ⱦɨɛɢʁɟɧɟɛɪɨʁɟɜɟɩɪɨɧɚɻɢ ɭ ɬɚɛɥɢɰɢ. ɍɩɪɚɡɧɚ ɩɨʂɚ ɧɚɩɢɲɢɨɞɝɨɜɚɪɚʁɭʄɚ ɢɦɟɧɚ. Ɍɚɤɨ ʄɟɲɫɚɡɧɚɬɢɤɨʁɢɦ ɫɬɚɧɨɜɧɢɰɢɦɚɩɪɢɩɚɞɚʁɭ ɨɫɬɚɜʂɟɧɢɬɪɚɝɨɜɢ. 5 · ɯ = 695

3 · ɯ = 651

6 · ɯ = 702

ɯ = __________

ɯ = __________

ɯ = __________

ɯ = __________

ɯ = __________

ɯ = __________

ɯ = __________

ɯ = __________

ED

U KA

ɯ · 7 = 952

117

139

136

217

14. ȳɟɞɚɧɛɪɨʁ ɤɚɠɟ: „Ⱥɤɨ ɦɟ ɭɜɟʄɚɲ ɩɭɬɚ, ɞɨɛɢʄɟɲ ɧɚʁɦɚʃɢ ɛɪɨʁɞɟɜɟɬɟ ɫɬɨɬɢɧɟ”. Ʉɨʁɢɛɪɨʁʁɟ ɬɨ ɪɟɤɚɨ?

15. ɇɟɧɚʁɟ ɤɭɩɢɥɚ 4ɫɥɚɝɚɥɢɰɟ ɩɨ ɢɫɬɨʁ ɰɟɧɢȵɟɧɪɚɱɭɧʁɟ ɢɡɧɨɫɢɨ 992ɞɢɧɚɪɚ. ɂɜɚ ɠɟɥɢ ɞɚ ɤɭɩɢɬɪɢ ɬɚɤɜɟɫɥɚɝɚɥɢɰɟ. Ʉɨɥɢɤɢʄɟɛɢɬɢ ɂɜɢɧ ɪɚɱɭɧ"

Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞ ʁɟɞɧɚɱɢɧɟɩɨɦɨʄɭ ɤɨʁɟ ʄɟɲ ɞɨʄɢ ɞɨ ɬɚɱɧɨɝ ɪɟɲɟʃɚ

Ɉɛɨʁ ɞɟɨ ɫɥɚɝɚɥɢɰɟɫɚɬɚɱɧɢɦ ɪɟɲɟʃɟɦ

ɚ) ɯ · 3 = 900 ɛ) ɯ · 3 = 801 ɜ) ɯ · 3 = 901 746

Ɍɨʁɟɛɪɨʁ ___.

128

787

744

704


O

R

TA

L

РАЗЛОМЦИ

-P

ŖʼnŜŠőŅŎš

U KA

ųũųŷźŮƀűŻũƐżűŸűƁżƐŷƁŶŮųűŹũŰŴŷŵſű

ųũųŷźŮżŸŷŹŮƊżƐżŹũŰŴŷŵſűƐŮŭŶũųűžűŵŮŶűŴũſũ

ED

ŭũŸŹűŵŮŶűƁźūŷƐŮŰŶũƒŮŷŹũŰŴŷŵſűŵũ żŹŮƁũūũƒżŹũŰŶűžŰũŭũŻũųũ

ŭũŹŮŰżŴŻũŻŵŮŹŮƒũŭżůűŶŮŰũŸűƁŮƁŭŮſűŵũŴŶűŵŪŹŷƐŮŵ źũƐŮŭŶŷŵŭŮſűŵũŴŷŵ


ɊȺɁɅɈɆɐɂ Ʉʂɭɱɧɟɪɟɱɢ: ɪɚɡɥɨɦɰɢ

(n ” 10) ɩɨɧɚɜʂɚʃɟ ɝɪɚɞɢɜɚ ɞɪɭɝɨɝɪɚɡɪɟɞɚ

Ɣ

TA

L

1. ȺɧɞɪɟʁɄɨɫɬɚ ɋɬɟɮɚɧ ɢ Ɏɢɥɢɩ ɠɟɥɟɞɚɩɨɞɟɥɟ ɱɨɤɨɥɚɞɟɫɚɫɜɨʁɢɦɞɪɭɝɚɪɢɦɚ. Ʉɨʁɢɞɟɱɚɰɢ ɫɭɩɨɞɟɥɢɥɢɱɨɤɨɥɚɞɭɧɚʁɟɞɧɚɤɟɞɟɥɨɜɟ? ɉɨɝɥɟɞɚʁɫɥɢɤɟ. Ɂɚ ɬɚɱɧɭ ɩɨɞɟɥɭ ɨɛɨʁ ɩɨʂɟ ɫɚɫɚɫɥɨɜɨɦ Ɍ. Ⱥɧɞɪɟʁ Ʉɨɫɬɚ ɋɬɟɮɚɧ Ɏɢɥɢɩ

ɉɨɞɟɥɢɬɢɧɟɤɭɰɟɥɢɧɭ ɡɧɚɱɢ ɢɡɜɪɲɢɬɢ ɩɨɞɟɥɭɧɚʁɟɞɧɚɤɟɞɟɥɨɜɟ.

_____________

_____________

-P

ʁɟɞɧɚɩɨɥɨɜɢɧɚ

O

R

2. ɋɜɚɤɭɮɢɝɭɪɭɫɦɨɩɨɞɟɥɢɥɢɧɚ ʁɟɞɧɚɤɟɞɟɥɨɜɟ ɚ ɡɚɬɢɦɫɦɨ ɨɛɨʁɢɥɢ ɫɚɦɨ ʁɟɞɚɧɞɟɨ. ɇɚɩɢɲɢ ɧɚɡɢɜɟ ɨɛɨʁɟɧɨɝɞɟɥɚɮɢɝɭɪɟ.

ɉɢɰɚ ʁɟ ɩɨɞɟʂɟɧɚɧɚ

8 ʁɟɞɧɚɤɢɯɞɟɥɨɜɚ

_____________

_____________

Ⱦɨɛɢɨɫɚɦ ʁɟɞɧɭ ɨɫɦɢɧɭɩɢɰɟ

U KA

Ⱥɰɢ ɫɚɦ ɞɚɥɚʁɟɞɧɨ ɩɚɪɱɟ.

ED

Ɂɚɩɢɫɢɤɚɨɲɬɨɫɭ:

ȳɟɞɧɨ ɰɟɥɨ ɢɦɚ 8 ɨɫɦɢɧɚ.











ȳɟɞɧɚ ɨɫɦɢɧɚ ɩɢɲɟɦɨ: 





... ɧɚɡɢɜɚʁɭɫɟ ɪɚɡɥɨɦɰɢ.

Ȼɪɨʁɢɡɧɚɞɰɪɬɟ ɡɨɜɟ ɫɟ ɛɪɨʁɢɥɚɰ.Ɉɡɧɚɱɚɜɚɛɪɨʁ ɢɡɞɜɨʁɟɧɢɯɞɟɥɨɜɚ Ɋɚɡɥɨɦɚɱɤɚɰɪɬɚ ɨɡɧɚɱɚɜɚɞɟʂɟʃɟ. Ȼɪɨʁɢɫɩɨɞɰɪɬɟ ɡɨɜɟ ɫɟ ɢɦɟɧɢɥɚɰ. Ɉɡɧɚɱɚɜɚ ɧɚ ɤɨɥɢɤɨʁɟɞɧɚɤɢɯɞɟɥɨɜɚ ʁɟ ɩɨɞɟʂɟɧɨ ʁɟɞɧɨ ɰɟɥɨ.

3. ɍ ɤɨɪɩɢ ɢɦɚ 28ʁɚɛɭɤɚ. Ɂɟɥɟɧɢɯʁɚɛɭɤɚ ʁɟ ɱɟɬɜɪɬɢɧɚ ɬɨɝɛɪɨʁɚ.Ʉɨɥɢɤɨʁɟ ɬɨ ʁɚɛɭɤɚ? ȳɟɞɧɨ ɰɟɥɨ ɢɦɚ __________ɱɟɬɜɪɬɢɧɟ. ɑɟɬɜɪɬɢɧɭɛɪɨʁɚ 28ɞɨɛɢʁɚɦɨɞɟʂɟʃɟɦ ɬɨɝɛɪɨʁɚ ɫɚ 4. Ɂɧɚɱɢ ɡɟɥɟɧɢɯʁɚɛɭɤɚ ɢɦɚ __ : __ = __.

130


ɊȺɁɅɈɆɐɂ Ʉʂɭɱɧɟɪɟɱɢ ɪɚɡɥɨɦɰɢ

(n ” 10), ɩɨɧɚɜʂɚʃɟ ɝɪɚɞɢɜɚ ɞɪɭɝɨɝɪɚɡɪɟɞɚ

4. Ʉɨɥɢɤɨ ɢɡɧɨɫɢ ɚ)

ɛɪɨʁɚ 40?

ɛ)

______________

ɛɪɨʁɚ 63?

ɜ)

ɛɪɨʁɚ 40?

ɝ)

______________ ______________

ɛɪɨʁɚ 40?

______________

ɛɪɨʁɚ 80?

______________

R

TA

L

5. Ɉɛɨʁʁɟɞɧɭɫɟɞɦɢɧɭ ɨɞ ɭɤɭɩɧɨɝ ɛɪɨʁɚ ɰɜɟɬɨɜɚ

ɞ)

ɚ)

18

ɛ)

54

ɨɞ 54 ɢɡɧɨɫɢ ________________

-P

ɨɞ 18 ɢɡɧɨɫɢ ________________

O

6. ɂɡɪɚɱɭɧɚʁɬɪɟʄɢɧɭ, ɲɟɫɬɢɧɭ ɢɞɟɜɟɬɢɧɭɧɚɩɢɫɚɧɢɯɛɪɨʁɟɜɚ

ɨɞ 54 ɢɡɧɨɫɢ________________

ɨɞ 18 ɢɡɧɨɫɢ ________________

ɨɞ 54 ɢɡɧɨɫɢ ________________

U KA

ɨɞ 18 ɢɡɧɨɫɢ ________________

7. Ɏɢɥɢɩʁɟ ɩɪɟɲɚɨ 15 km,ɲɬɨ ɢɡɧɨɫɢ ɬɪɟʄɢɧɭɞɭɠɢɧɟ ɩɭɬɚ ɤɨʁɢɬɪɟɛɚɞɚɩɪɟɻɟ. Ʉɨɥɢɤɚʁɟ ɞɭɠɢɧɚɰɟɥɨɝ ɩɭɬɚ? Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞ ɡɚɩɢɫɚ ɩɨɦɨʄɭ ɤɨʁɟɝ ʄɟɲɞɨʄɢɞɨ ɬɚɱɧɨɝ ɪɟɲɟʃɚ. 15 km

ɛ) 15 + 3

ED

ɚ) 15  3

ɜ) 15 · 3

ɝ) 15 · 3

8. Ɉɞɪɟɞɢ ɛɪɨʁ

ɚ ɱɢʁɚ ʁɟ ʁɟɞɧɚ ɩɨɥɨɜɢɧɚ 6;

ɛ) ɱɢʁɚʁɟ ʁɟɞɧɚɱɟɬɜɪɬɢɧɚ 20;

ɜ) ɱɢʁɚ ʁɟ ʁɟɞɧɚ ɨɫɦɢɧɚ 12.

_____________

______________

______________

Ɍɨʁɟɛɪɨʁ__.

Ɍɨ ʁɟɛɪɨʁ__.

Ɍɨʁɟɛɪɨʁ __.

9. Ⱦɟɜɟɬɢɧɚ ʁɟɞɧɨɝɛɪɨʁɚ ʁɟ 7, ɚ ʃɟɝɨɜɚ ɫɟɞɦɢɧɚ ʁɟ 9. Ʉɨʁɢ ʁɟ ɬɨɛɪɨʁ" Ɉɛɨʁɩɨɫɭɞɭɫɚɩɪɢɛɨɪɨɦ ɧɚ ɤɨʁɨʁɫɟɧɚɥɚɡɢ ɬɚɱɧɨ ɪɟɲɟʃɟ.

131


ɊȺɁɅɈɆɐɂ Ʉʂɭɱɧɟɪɟɱɢ: ɪɚɡɥɨɦɰɢ

(m ” n ”10)

ɋɨʃɚ ɫɥɚɜɢ ɪɨɻɟɧɞɚɧɉɨɞɟɥɢɥɚ ʁɟ ɲɟɫɬ ɞɟɫɟɬɢɧɚ ɬɨɪɬɟɫɜɨʁɢɦɝɨɫɬɢɦɚ Ʉɚɤɨʁɟ ɬɨ ɭɪɚɞɢɥɚ" Ɉɧɞɚʁɟ 6ɩɚɪɱɚɞɢɫɬɚɜɢɥɚɧɚ ɬɚɰɧɟ ɢ ɩɨɞɟɥɢɥɚ ɢɯ ɝɨɫɬɢɦɚ

Ɋɚɡɥɨɦɚɤ ɤɨʁɢɨɞɝɨɜɚɪɚ ɫɜɚɤɨɦ ɞɟɥɭʁɟ 

Ɋɚɡɥɨɦɚɤ ɤɨʁɢɨɞɝɨɜɚɪɚ ɪɚɫɩɨɞɟʂɟɧɢɦɞɟɥɨɜɢɦɚ ʁɟ 

Ɉɫɬɚɥɨʁɟ ʁɨɲ4ɩɚɪɱɟɬɚ ɬɨɪɬɟ

TA

L

ɉɪɜɨ ʁɟ ɩɨɞɟɥɢɥɚ ɬɨɪɬɭ ɧɚ 10 ʁɟɞɧɚɤɢɯɞɟɥɨɜɚ

R

Ɋɚɡɥɨɦɚɤ ɤɨʁɢɨɞɝɨɜɚɪɚ ɩɪɟɨɫɬɚɥɢɦ ɞɟɥɨɜɢɦɚ ʁɟ 

O

ɇɚɰɪɬɚɧɟ ɮɢɝɭɪɟɩɪɟɞɫɬɚɜʂɚʁɭʁɟɞɧɨ ɰɟɥɨ

-P

1 ɉɨɫɦɚɬɪɚʁɰɪɬɟɠɟ ɢɧɚɩɢɲɢ ɲɬɚ ɧɟɞɨɫɬɚʁɟ



Ɏɢɝɭɪɚʁɟɩɨɞɟʂɟɧɚ __ʁɟɞɧɚɤɢɯɞɟɥɨɜɚ Ɉɛɨʁɟɧɨ ʁɟ __ɞɟɥɚ Ɋɚɡɥɨɦɚɤ ɤɨʁɢɨɞɝɨɜɚɪɚ ɨɛɨʁɟɧɢɦɞɟɥɨɜɢɦɚʁɟ



U KA

Ɏɢɝɭɪɚʁɟɩɨɞɟʂɟɧɚ __ʁɟɞɧɚɤɢɯɞɟɥɨɜɚ Ɉɛɨʁɟɧɨ ʁɟ __ɞɟɥɨɜɚ Ɋɚɡɥɨɦɚɤ ɤɨʁɢɨɞɝɨɜɚɪɚ ɨɛɨʁɟɧɢɦɞɟɥɨɜɢɦɚʁɟ

ED

2 Ɉɛɨʁɞɟɨɮɢɝɭɪɟ ɤɨʁɢʁɟ ɨɡɧɚɱɟɧɪɚɡɥɨɦɤɨɦ

132

3 ɂɡɪɚɡɢ ɪɚɡɥɨɦɤɨɦ ɨɛɨʁɟɧɢ ɞɟɨɮɢɝɭɪɟ


ɊȺɁɅɈɆɐɂ Ʉʂɭɱɧɟɪɟɱɢ: ɪɚɡɥɨɦɰɢ

(m ” n ”10)

L

1. ɇɟɦɚʃɚʁɟ ɬɚɱɧɨɫɥɨɠɢɨ ɬɪɢɞɟɥɚɫɥɚɝɚɥɢɰɟɧɚɫɥɢɰɢ. ɇɢʁɟɫɢɝɭɪɚɧɤɨʁɢʁɟ ɱɟɬɜɪɬɢ ɞɟɨ. Ⱦɟɨɫɥɚɝɚɥɢɰɟ ɤɨʁɢ ɨɞɝɨɜɚɪɚ ɬɚɱɧɨɦ ɪɟɲɟʃɭ ɨɛɨʁɠɭɬɨɦ ɛɨʁɨɦ.

TA

2. ɇɚɩɢɲɢɪɚɡɥɨɦɚɤ ɤɨʁɢɨɞɝɨɜɚɪɚ ɞɨɦɢɧɚɦɚ ɫɚɫɥɢɤɟ. ɂɫɬɢɪɚɡɥɨɦɚɤɩɪɟɞɫɬɚɜɢɰɪɬɟɠɨɦ ɤɚɤɨʁɟɩɨɤɚɡɚɧɨ ɧɚɩɪɢɦɟɪɭ. ɚ)

ɚ)

O

R

ɉɪɢɦɟɪ

ɚ)

ɚ)

-P

ɚ)

ED

U KA

3. Ɂɚɨɤɪɭɠɢ ɪɚɡɥɨɦɚɤ ɤɨʁɢ ɨɞɝɨɜɚɪɚ ɨɛɨʁɟɧɨɦ ɞɟɥɭɮɢɝɭɪɟ.

4. Ⱥɧɻɟɥɚʁɟ ɧɚɰɪɬɟɠɭ ɨɛɨʁɢɥɚɞɟɨɧɨɜɰɚ ɤɨʁɢʁɟɩɨɬɪɨɲɢɥɚ. ɚ) Ⱦɟɨɩɨɬɪɨɲɟɧɨɝɧɨɜɰɚ ɢɡɪɚɡɢ ɪɚɡɥɨɦɤɨɦ ɛ ɐɪɜɟɧɨɦ ɛɨʁɨɦ ɨɛɨʁɞɟɨɩɪɟɨɫɬɚɥɨɝɧɨɜɰɚ. ɂɡɪɚɡɢ ɝɚ ɪɚɡɥɨɦɤɨɦ

5. Ⱦɟɨɮɢɝɭɪɟ ɤɨʁɢʁɟ ɞɨɩɭɧɚ ɞɨʁɟɞɧɨɝɰɟɥɨɝ ɨɛɨʁɰɪɜɟɧɨɦ ɛɨʁɨɦ. ɂɡɪɚɡɢ ɬɚʁɞɟɨ ɪɚɡɥɨɦɤɨɦ ɚ)

ɛ)

ɜ)

133

ɝ)


ɍɉɈɊȿȭɂȼȺȵȿ ɊȺɁɅɈɆȺɄȺ ȳȿȾɇȺɄɂɏ ɂɆȿɇɂɅȺɐȺ (m ” n ”10), ɭɩɨɪɟɻɢɜɚʃɟ ɪɚɡɥɨɦɚɤɚ ʁɟɞɧɚɤɢɯ ɢɦɟɧɢɥɚɰɚ

Ʉʂɭɱɧɟɪɟɱɢ: ɪɚɡɥɨɦɰɢ

Ɣ

Ʉɚɤɨ ɦɨɠɟɲɞɚ ɭɩɨɪɟɞɢɲɪɚɡɥɨɦɤɟ ɫɚ ɢɫɬɢɦ ɢɦɟɧɢɨɰɟɦ" Ɂɟɦʂɚʁɟʁɟɞɢɧɚɩɥɚɧɟɬɚ ɡɚ ɤɨʁɭ ɡɧɚɦɨɞɚ ɢɦɚɜɨɞɭ. Ɉɤɨ ɩɨɜɪɲɢɧɟɁɟɦʂɟʁɟ ɩɨɤɪɢɜɟɧɨ ɜɨɞɢɦ, ɚ ɨɤɨ ʁɟ ɤɨɩɧɨ. ɡɚɭɡɢɦɚ ɜɟʄɢ ɞɟɨ, ɜɨɞɚ ɢɥɢ ɤɨɩɧɨ"

L

Ɣ ɒɬɚ

ɋɜɨʁɨɞɝɨɜɨɪ ɦɨɠɟɲ ɞɚɩɪɨɜɟɪɢɲɚɤɨ ɪɚɡɥɨɦɤɟ ɢ ɩɪɢɤɚɠɟɲɧɚ ɰɪɬɟɠɢɦɚ ɮɢɝɭɪɚ.

ɍɩɨɪɟɞɢʄɟɦɨ ɪɚɡɥɨɦɤɟ

ɢ

TA

ɍɩɨɪɟɻɢɜɚʃɟ ɪɚɡɥɨɦɚɤɚ .

1 < 3 Ɂɧɚɱɢ

<

R

ɂɦɟɧɢɨɰɢɨɜɢɯ ɪɚɡɥɨɦɚɤɚɫɭʁɟɞɧɚɤɢ Ɂɚɬɨ ʄɟɦɨ ɭɩɨɪɟɞɢɬɢ ʃɢɯɨɜɟ ɛɪɨʁɢɨɰɟ. .

<

O

Ʉɚɞɚ ɭɩɨɪɟɻɭʁɟɦɨ ɪɚɡɥɨɦɤɟ ɫɚ ɢɫɬɢɦ ɢɦɟɧɢɨɰɢɦɚ, ɦɨɪɚɦɨɞɚ ɭɩɨɪɟɞɢɦɨ ʃɢɯɨɜɟ ɛɪɨʁɢɨɰɟ.

ɨɞɝɨɜɚɪɚʁɭʄɢ ɡɧɚɤ: ,  ɢɥɢ=. ɜ  ɝ)

U KA

1. ɍɩɨɪɟɞɢ ɞɚɬɟ ɪɚɡɥɨɦɤɟ.ɍɩɢɲɢ ɭ ɚ) ɛ)

-P

Ɉɞɞɜɚ ɪɚɡɥɨɦɤɚɫɚ ɢɫɬɢɦ ɢɦɟɧɢɨɰɢɦɚ,ɜɟʄɢʁɟ ɨɧɚʁɪɚɡɥɨɦɚɤ ɱɢʁɢʁɟɛɪɨʁɢɥɚɰɜɟʄɢ

ɍɨɱɚɜɚɦɨɞɚɫɭ ɪɚɡɥɨɦɰɢ ɫɚ ɢɫɬɢɦ ɢɦɟɧɢɨɰɢɦɚ ɢɫɬɢɦ ɛɪɨʁɢɨɰɢɦɚʁɟɞɧɚɤɢ:

ED

Ɣ ɉɨɞɫɟɬɢɫɟ:

ɋɨʃɚʁɟʁɟɞɧɭ ɬɨɪɬɭɩɨɞɟɥɢɥɚ ɧɚ 10ʁɟɞɧɚɤɢɯɞɟɥɨɜɚ. Ɋɚɡɥɨɦɰɢ ɤɚɨɲɬɨɫɭ:

,

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, ,

ɢ

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Æ

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,ɩɪɟɞɫɬɚɜʂɚʁɭʁɟɞɧɭɰɟɥɢɧɭ ɢɥɢ ʁɟɞɚɧɰɟɨ.

Ɂɚɬɨɫɭ ɨɧɢ ɢ ɦɟɻɭɫɨɛɧɨ ʁɟɞɧɚɤɢ. ɇɚɩɪɢɦɟɪ:

ɨɞɝɨɜɚɪɚʁɭʄɢ ɡɧɚɤ: ,  ɢɥɢ=.

2. ɍɩɨɪɟɞɢ ɫɥɟɞɟʄɟ ɪɚɡɥɨɦɤɟ. ɍɩɢɲɢɭ Ɣ

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Ɣ

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Ɣ

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ɍɉɈɊȿȭɂȼȺȵȿ ɊȺɁɅɈɆȺɄȺȳȿȾɇȺɄɂɏ ɂɆȿɇɂɅȺɐȺ Ʉʂɭɱɧɟɪɟɱɢ: ɪɚɡɥɨɦɰɢ (m ” n ”10), ɭɩɨɪɟɻɢɜɚʃɟ ɪɚɡɥɨɦɚɤɚ ʁɟɞɧɚɤɢɯ ɢɦɟɧɢɥɚɰɚ

ɨɞɝɨɜɚɪɚʁɭʄɢ ɡɧɚɤ: <, > ɢɥɢ=.

U KA

-P

O

2. ɍɩɨɪɟɞɢ ɫɥɟɞɟʄɟ ɪɚɡɥɨɦɤɟ. ɍɩɢɲɢɭ

R

TA

L

1. Ɉɛɨʁɞɟɨɮɢɝɭɪɟ ɢɡɪɚɠɟɧ ɪɚɡɥɨɦɤɨɦ.Ɂɚɨɤɪɭɠɢ ɜɟʄɢ ɪɚɡɥɨɦɚɤ.

3. ȳɨɜɚɧ, ɍɪɨɲɢɊɚɲɚ ɫɟ ɬɚɤɦɢɱɟ ɤɨ ʄɟɛɪɠɟɫɥɨɠɢɬɢ ɫɥɚɝɚɥɢɰɭ. Ɂɚ 15 ɦɢɧɭɬɚ, ȳɨɜɚɧʁɟ ɫɥɨɠɢɨ

ɫɥɚɝɚɥɢɰɟ,ɍɪɨɲ , ɚ Ɋɚɲɚʁɟɫɥɨɠɢɨ

.

ED

ɚ) Ʉɨʁɢɞɟɱɚɤ ʁɟ ɫɥɨɠɢɨɰɟɥɭɫɥɚɝɚɥɢɰɭ? Ɉɞɝɨɜɨɪ: _____________________________________________________ ɛ) Ʉɨʁɢʁɟ ɞɟɱɚɤʁɟ ɡɚ ɢɫɬɨɜɪɟɦɟ ɫɥɨɠɢɨɧɚʁɦɚʃɢɞɟɨ ɫɥɚɝɚɥɢɰɟ" Ɉɞɝɨɜɨɪ: _____________________________________________________ ɜ) ɍɩɢɲɢ ɢɡɨɫɬɚɜʂɟɧɟ ɛɪɨʁɢɨɰɟ ɪɚɡɥɨɦɚɤɚ, ɬɚɤɨɞɚ ɞɚɬɢ ɡɚɩɢɫɢ ɛɭɞɭ ɬɚɱɧɢ < 4. ɏɜɚɥɢɲɭɫɟɞɜɟ ɤɚɦɢɥɟ. ɉɪɨɱɢɬɚʁ ɞɟɨʃɢɯɨɜɨɝ ɪɚɡɝɨɜɨɪɚ.

<

ȳɚɫɚɦ Ⱥɪɚ. Ɂɚ ɱɚɫɚ ɩɨɩɢʁɟɦ 180 l ɜɨɞɟ

ȳɚɫɚɦȿɪɚ. Ɂɚ ɱɚɫɚ ɩɨɩɢʁɟɦ 180 l ɜɨɞɟ.

Ʉɨʁɚ ɤɚɦɢɥɚ ɛɪɠɟɩɢʁɟɜɨɞɭ? Ɂɚɨɤɪɢɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞ ɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ

ɚ Ⱥɪɚ

135

ɛ ȿɪɚ


ɍɉɈɊȿȭɂȼȺȵȿ ɊȺɁɅɈɆȺɄȺȳȿȾɇȺɄɂɏ ɂɆȿɇɂɅȺɐȺ Ʉʂɭɱɧɟɪɟɱɢ: ɪɚɡɥɨɦɰɢ

(m ” n ”10), ɭɩɨɪɟɻɢɜɚʃɟ ɪɚɡɥɨɦɚɤɚ ʁɟɞɧɚɤɢɯ ɢɦɟɧɢɥɚɰɚ

Ɂɚɛɚɜɢɬɟɫɟ ɩɪɚɜʂɟʃɟɦ ɦɨɞɟɥɚ ɪɚɡɥɢɱɢɬɢɯɞɟɥɨɜɚ ɰɟɥɢɧɟ, ɨɞ ɪɚɡɧɢɯ ɦɚɬɟɪɢʁɚɥɚ...

dzȒȖȔȉȅȄȑ ȐȄȖȉȔȌȫȄȏ: ȹ 10 ȓȔȒȆȌȈȑȌșȓȏȄȕȖȌțȑȌș țȄȜȄ (ȋȄȓȔȐȌȑȉ 1 dl

ȹ 1 ȕȗȓȉȑȄ ȎȄȜȌȎȄ ȌȏȌ ȑȉȎȄ ȐȄȏȒ ȐȄȭȄ ȐȉȔȄ ȹ ȓȒȕȗȈȄ ȕȄ ȆȒȈȒȐ ȹ ȆȒȈȉȑȉ ȅȒȫȌȚȉ (ȖȉȐȓȉȔȉ, ȌȏȌ ȅȒȫȄ ȋȄ ȎȒȏȄțȉ

ȹ ȐȄȔȎȉȔȋȄȓȌ

L

1. ȓȔȉȈȏȒȇ

ǷȓȗȖȕȖȆȒȋȄȔȄȈ:

-P

O

R

TA

ȹ ǦȄȊȑȒ ȫȉ ȈȄ ȗȆȉȎ ȐȉȔȌȖȉ ȌȕȖȒȐ ȫȉȈȌȑȌȚȒȐ ȐȉȔȉ (ȖȒ ȐȒȊȉ ȈȄ ȅȗȈȉ ȎȄȜȌȎȄȌȏȌ ȋȄȖȆȄȔȄțȄț ȒȈ ȑȉȎȉ ȘȏȄȜȌȚȉ ȌȏȌȑȉȎȄ ȈȔȗȇȄ ȐȄȭȄ ȐȉȔȄ . ȹ ǤȎȒ ȐȉȔȌȖȉȒȕȐȌȑȉ ȎȒȔȌȕȖȌȖȉ 8 țȄȜȄ, ȋȄ ȓȉȖȌȑȉ ȎȒȔȌȕȖȌȖȉ 5 țȄȜȄ, ȋȄ ȈȉȕȉȖȌȑȉ 10 țȄȜȄ... ȹ DZȄ ȓȔȄȋȑȌȐ țȄȜȄȐȄ ȑȄȓȌȜȉȖȉ ȔȄȋȏȒȐȎȉ, ȎȄȒ ȜȖȒ ȫȉ ȓȒȎȄȋȄȑȒ ȑȄ ȕȏȌȚȌ. ȹ DZȄ ȓȔȌȐȉȔ: ȗ țȄȜȗ ȕȄ ȑȄȖȓȌȕȒȐ ȕȌȓȄȖȉ 1 ȎȄȜȌȎȗ ȆȒȈȉ (ȫȉȈȑȌȚȗ ȐȉȔȉ , ȕȄ ȑȄȖȓȌȕȒȐ ȕȌȓȄȖȉ 2 ȎȄȜȌȎȉ ȆȒȈȉ Ȍ ȖȄȎȒ ȔȉȈȒȐ. DZȄ ȎȔȄȫȗ ȒȅȒȫȖȉ ȆȒȈȗ ȗ țȄȜȄȐȄ ȔȄȋȏȌțȌȖȌȐ ȅȒȫȄȐȄ

U KA

dzȒȖȔȉȅȄȑ ȐȄȖȉȔȌȫȄȏ: ȹ ȓȏȄȕȖȉȏȌȑȗ ȅȒȫȌ ȹ ȔȄȆȑȄȓȒȈȏoȇȄ ȹ ȒȆȄȏȑȌ ȓȔȉȈȐȉȖ (ȋȄȐȉȑȄ ȋȄ ȒȎȏȄȇȌȫȗ

ȹ ȓȏȄȕȖȌțȑȌȑȒȊ ȋȄ ȕȉțȉȭȉ ȹ șȄȔȖȌȫȄ

ED

2. ȓȔȉȈȏȒȇ

3. ȓȔȉȈȏȒȇ

dzȒȖȔȉȅȄȑ ȐȄȖȉȔȌȫȄȏ: ȹ ȓȏȄȕȖȌțȑȌ ȌȏȌ ȎȄȔȖȒȑȕȎȌ ȖȄȭȌȔȌ ȔȄȋȑȌș ȅȒȫȄ ȹ ȐȄȎȄȋȉ ȹ ȏȉȓȌȏȒ ȹ ȐȄȔȎȉȔ ȋȄ ȓȌȕȄȭȉȑȄ ȓȏȄȕȖȌȚȌ ȌȏȌ ȘȒȏȌȫȌ

136


ȾȿɐɂɆȺɅɇɂ ɁȺɉɂɋ ȻɊɈȳȺ ɋȺ ȳȿȾɇɈɆ ȾȿɐɂɆȺɅɈɆ Ʉʂɭɱɧɟɪɟɱɢ: ɞɟɰɢɦɚɥɧɢɡɚɩɢɫ ɛɪɨʁɚɫɚ ʁɟɞɧɨɦ ɞɟɰɢɦɚɥɨɦ, ʁɟɞɢɧɢɰɟ ɦɟɪɟɡɚ ɞɭɠɢɧɭ

ɉɨɞɫɟɬɢʄɟɦɨɫɟ ɤɨʁɟɫɭʁɟɞɢɧɢɰɟ ɦɟɪɟ ɡɚɞɭɠɢɧɭ ɦɚʃɟ ɨɞʁɟɞɧɨɝ ɦɟɬɪɚ. Ɉɫɧɨɜɧɚ ʁɟɞɢɧɢɰɚ

Ɇɚʃɟ ʁɟɞɢɧɢɰɟ

dm - ɞɟɰɢɦɟɬɚɪ

m ɦɟɬɚɪ

1 ɫm = 10 mm

1ɫm ʁɟɞɟɫɟɬɩɭɬɚ ɦɚʃɢɨɞ 1 dm.

1 mm ʁɟɞɟɫɟɬ ɩɭɬɚ ɦɚʃɢɨɞ 1 ɫm.

Ɂɚɬɨ ɤɚɠɟɦɨɞɚʁɟ

Ɂɚɬɨ ɤɚɠɟɦɨɞɚʁɟ

Ɂɚɬɨ ɤɚɠɟɦɨɞɚʁɟ

1 dm ɞɟɫɟɬɢ ɞɟɨ ɦɟɬɪɚ.

1ɫm ɞɟɫɟɬɢɞɟɨ ɞɟɰɢɦɟɬɪɚ.

1 mm ɞɟɫɟɬɢɞɟɨ ɰɟɧɬɢɦɟɬɪɚ.

Ɂɚɩɢɫɭʁɟɦɨ ɨɜɚɤɨ:

Ɂɚɩɢɫɭʁɟɦɨ ɨɜɚɤɨ:

Ɂɚɩɢɫɭʁɟɦɨ ɨɜɚɤɨ:

1dm = 0,1 m

ɫP 0,1 dm

TA

L

1 dm ʁɟ ɞɟɫɟɬ ɩɭɬɚ ɦɚʃɢɨɞ 1 m.

1 mm = 0,1 ɫm

ɇɚ ɰɪɬɟɠɭɫɦɨ 1 m ɩɪɟɞɫɬɚɜɢɥɢ ɤɚɨ ɬɪɚɤɭ ɢɡɞɟʂɟɧɭ ɧɚ 10ʁɟɞɧɚɤɢɯɞɟɥɨɜɚ. ɋɜɚɤɢɞɟɨ ɩɪɟɞɫɬɚɜʂɚ 1 dm ɢɥɢ ɞɟɫɟɬɢɞɟɨɰɟɥɢɧɟ.

O

Ɣ

1 dm = 10 ɫm

mm - ɦɢɥɢɦɟɬɚɪ

R

1m

1 m = 10 dm

cm - ɰɟɧɬɢɦɟɬɚɪ

-P

1 dm

1 dm = 0,1 m (ɱɢɬɚɦɨ: 1 dm ʁɟ ɧɭɥɚɰɟɥɢɯ ɢʁɟɞɚɧɞɟɫɟɬɢ ɞɟɨ ɦɟɬɪɚ) Ɣ ɍɨɱɚɜɚɦɨɞɚʁɟ ɨɛɨʁɟɧʁɟɞɚɧɞɟɫɟɬɢ ɞɟɨ ɤɨʁɢɨɞɝɨɜɚɪɚ ɡɚɩɢɫɭ 0,1.

U KA

Ɂɚɩɢɫ0,1ɫɟ ɡɨɜɟ ɞɟɰɢɦɚɥɧɢɡɚɩɢɫɛɪɨʁɚ ɢɥɢ ɞɟɰɢɦɚɥɧɢɛɪɨʁ ɛɪɨʁɰɟɥɢɯɞɟɥɨɜɚ

0 1

ɛɪɨʁɞɟɰɢɦɚɥɧɢɯ (ɞɟɫɟɬɢɯ) ɞɟɥɨɜɚ

ɡɚɪɟɡ ɨɞɜɚʁɚ ɰɟɨɞɟɨ ɨɞɞɟɰɢɦɚɥɧɨɝɞɟɥɚ

ED

ɉɪɢ ɩɢɫɚʃɭɞɟɰɢɦɚɥɧɨɝɛɪɨʁɚ ɤɨɪɢɫɬɢɦɨ ɡɚɪɟɡ ɤɨʁɢɨɞɜɚʁɚ ɰɟɨɞɟɨ ɨɞɞɟɰɢɦɚɥɧɨɝɞɟɥɚ. 1. ɉɪɨɱɢɬɚʁɫɥɟɞɟʄɟɞɟɰɢɦɚɥɧɟ ɡɚɩɢɫɟɛɪɨʁɟɜɚ: 0,1 0,5 0,8 1,6 1,9 0,4 5,7 4,9. ɂɡɞɜɨʁɢɡɚɩɢɲɢ ɞɟɰɢɦɚɥɧɟ ɡɚɩɢɫɟ ɤɨʁɢɫɭɜɟʄɢ ɨɞʁɟɞɧɨɝɰɟɥɨɝ. ___, ___, ___, ___. Ʉɪɨʁɚɱɢɰɚ ʁɟ ɨɞɫɟɤɥɚ ɬɪɢ ɬɪɚɤɟ. ɐɪɜɟɧɚ ɬɪɚɤɚʁɟɞɭɠɢɧɟ ɞɭɠɢɧɟ 1 m 5 dm, ɩɥɚɜɚ 3 dm 8ɫm, ɚ ɡɟɥɟɧɚ 9 cm 5 mm. Ⱦɭɠɢɧɟ ɨɜɢɯ ɬɪɚɤɚ ɦɨɠɟɦɨɞɚ ɢɡɪɚɡɢɦɨ: ɚ) ɦɚʃɨɦ ʁɟɞɢɧɢɰɨɦ ɦɟɪɟ: 1 m 5 dm = 15 dm; 3 dm 8ɫm = ___ɫm;

9 cm 5 mm = ___ mm.

ɚ ɜɟʄɨɦʁɟɞɢɧɢɰɨɦ ɦɟɪɟ: 1 m 5 dm = 1,5 m;.. 3 dm 8ɫm = ___ 8 dm; 9 cm 5 mm = ___ɫm. Ɣ

Ⱦɟɰɢɦɚɥɧɢ ɡɚɩɢɫ1,5ɱɢɬɚɦɨ: 1 ɰɟɨ ɢ 5ɞɟɫɟɬɢɯ.

2. ɋɬɟɮɚɧʁɟ ɧɚɰɪɬɚɨ ɬɪɢ ɞɭɠɢ ɢ ɡɚɩɢɫɚɨʃɢɯɨɜɟ ɞɭɠɢɧɟ. ɂɡɪɚɡɢɫɜɚɤɭɞɭɠɢɧɭ ɜɟʄɨɦ ʁɟɞɢɧɢɰɨɦ ɦɟɪɟ, ɬɚɤɨɲɬɨ ʄɟɲɧɚ ɥɢɧɢʁɭ ɧɚɩɢɫɚɬɢ ɨɞɝɨɜɚɪɚʁɭʄɢ ɞɟɰɢɦɚɥɧɢɛɪɨʁ Ɣ SO = 4 cm = ____ dm; Ɣ AB = 12 cm = ____ dm;

137

Ɣ MN = 86 mm = ____ cm.


ȾȿɐɂɆȺɅɇɂ ɁȺɉɂɋ ȻɊɈȳȺ ɋȺ ȳȿȾɇɈɆ ȾȿɐɂɆȺɅɈɆ Ʉʂɭɱɧɟɪɟɱɢ: ɞɟɰɢɦɚɥɧɢɡɚɩɢɫ ɛɪɨʁɚɫɚ ʁɟɞɧɨɦ ɞɟɰɢɦɚɥɨɦ, ʁɟɞɢɧɢɰɟ ɦɟɪɟɡɚ ɞɭɠɢɧɭ

1. ɉɨɜɟɠɢ ɥɢɧɢʁɚɦɚʁɟɞɚɧɚɤɟɞɟɰɢɦɚɥɧɟ ɡɚɩɢɫɟ. ɇɟɤɢ ɡɚɩɢɫɢʄɟ ɨɫɬɚɬɢɧɟɩɨɜɟɡɚɧɢ

40,0

5,7

1,23

12 ɰɟɥɢɯ ɢ 3 ɞɟɫɟɬɚ

12,3

2,79

2. Ɋɟɡɭɥɬɚɬ ɦɟɪɟʃɚɞɭɠɢɧɟ ɢɡɪɚɡɢɞɟɰɢɦɚɥɧɢɦɛɪɨʁɟɦ.

27,9

27 ɰɟɥɢɯ ɢ 9 ɞɟɫɟɬɢɯ

7,5

L

0,4

0 ɰɟɥɢɯ ɢ 4 ɞɟɫɟɬɚ

TA

7ɰɟɥɢɯ ɢ 5 ɞɟɫɟɬɢɯ

____ m

4 dm 4 cm

____ dm

6 mm

____ cm

4 dm

____ m

3 cm

____ dm

14 mm

____ cm

13 m 4 dm

____ m

9 cm

____ dm

2 cm 5 mm

____ cm

8 dm

____ m

28 dm 1 cm

____ dm

16 cm 8 mm

____ cm

O

R

5 m 7 dm

3. ɇɚɰɪɬɚʁɞɭɠ:

-P

ɚ) Ⱥȼ = 1,2 dm;

U KA

ɛ) ɋD = 5,8 cm.

ED

4. ɉɨɩɭɧɢɬɚɛɟɥɭ. ɇɚɩɢɲɢɤɨɥɢɤɨ ɞɟɰɢɦɟɬɚɪɚ,ɰɟɧɬɢɦɟɬɚɪɚ ɢ ɦɢɥɢɦɟɬɚɪɚ ɨɞɝɨɜɚɪɚɞɭɠɢɧɢ ɞɪɜɟɧɢɯɛɨʁɢɰɚ. ɇɚɩɪɢɦɟɪ: Ɣ ɚɤɨʁɟ ɦɟɪɧɚʁɟɞɢɧɢɰɚɰɟɧɬɢɦɟɬɚɪ, ɤɚɠɟɦ ɞɚʁɟ ɛɨʁɢɰɚ ɞɭɝɚɱɤɚ 8 cm; Ɣ ɚɤɨʁɟ ɦɟɪɧɚ ʁɟɞɢɧɢɰɚ ɦɢɥɢɦɟɬɚɪ, ɤɚɠɟɦ ɞɚʁɟɛɨʁɢɰɚ ɞɭɝɚɱɤɚ 80 mm. Ɣ ɚɤɨʁɟ ɦɟɪɧɚ ʁɟɞɢɧɢɰɚɞɟɰɢɦɟɬɚɪ, ɤɚɠɟɦ ɞɚʁɟɛɨʁɢɰɚ ɞɭɝɚɱɤɚ 0,8 dm.

dm

cm

mm 50

7 0,9 100 11 1,2

138


ɋȺȾȺ ɁɇȺɆ ɆɇɈȽɈ ȼɂɒȿ Ʉʂɭɱɧɟɪɟɱɢ: ɪɚɡɥɨɦɰɢ

(m ” n ”10), ɞɟɰɢɦɚɥɧɢ ɡɚɩɢɫ ɛɪɨʁɚ ɫɚ ʁɟɞɧɨɦɞɟɰɢɦɚɥɨɦ

Ɣ Ɂɧɚɦ ɞɚɪɚɡɥɨɦɤɨɦ ɢɡɪɚɡɢɦ ɨɛɨʁɟɧɢ ɞɟɨɰɟɥɢɧɟ. Ɏɢɝɭɪɚʁɟɩɨɞɟʂɟɧɚ 6ʁɟɞɧɚɤɢɯɞɟɥɨɜɚ. Ɉɛɨʁɟɧɨ ʁɟ 4ɞɟɥɚ. Ɋɚɡɥɨɦɚɤ ɤɨʁɢɨɞɝɨɜɚɪɚ ɨɛɨʁɟɧɢɦɞɟɥɨɜɢɦɚʁɟ

TA

L

.

Ɣ Ɂɧɚɦ ɞɚ ɭɩɨɪɟɞɢɦɪɚɡɥɨɦɤɟ ʁɟɞɧɚɤɢɯ ɢɦɟɧɢɥɚɰɚ. Ɋɚɡɥɨɦɤɟ

ɢ

ɂɦɟɧɢɨɰɢ ɪɚɡɥɨɦɤɚ

ɩɪɟɞɫɬɚɜʂɚɦɧɚɰɪɬɟɠɭ,

R

ɚ ɡɚɬɢɦ ɢɯ ɭɩɨɪɟɻɭʁɟɦ.

ɢ

ɫɭʁɟɞɧɚɤɢ

Ɂɚɬɨ ʄɭ ɭɩɨɪɟɞɢɬɢ ʃɢɯɨɜɟ ɛɪɨʁɢɨɰɟ:

<

O

1<3

<

.

-P

<

Ɂɧɚɱɢ

Ʉɚɞɚ ɭɩɨɪɟɻɭʁɟɦɨ ɪɚɡɥɨɦɤɟɫɚ ɢɫɬɢɦ ɢɦɟɧɢɨɰɢɦɚ, ɦɨɪɚɦɨɞɚ ɭɩɨɪɟɞɢɦɨ ʃɢɯɨɜɟ ɛɪɨʁɢɨɰɟ.

U KA

Ɉɞɞɜɚ ɪɚɡɥɨɦɤɚɫɚ ɢɫɬɢɦ ɢɦɟɧɢɨɰɢɦɚ,ɜɟʄɢʁɟ ɨɧɚʁɪɚɡɥɨɦɚɤ ɱɢʁɢʁɟɛɪɨʁɢɥɚɰɜɟʄɢ

ƔɁɧɚɦɞɚ ɪɟɡɭɥɬɚɬ ɦɟɪɟʃɚ ɞɭɠɢɧɟɡɚɩɢɲɟɦ ɞɟɰɢɦɚɥɧɢɦ ɛɪɨʁɟɦ ɫɚʁɟɞɧɨɦɞɟɰɢɦɚɥɨɦ. Ɣ 1 dm = 0,1 m;

Ɣ 1 cm = 0,1 dm;

Ɣ 1 mm = 0,1 cm.

ED

Ɂɚɩɢɫɫɟɡɨɜɟɞɟɰɢɦɚɥɧɢ ɡɚɩɢɫɛɪɨʁɚɢɥɢ ɞɟɰɢɦɚɥɧɢ ɛɪɨʁ ɛɪɨʁɰɟɥɢɯ

ɛɪɨʁɞɟɰɢɦɚɥɧɢɯ (ɞɟɫɟɬɢɯ)

0 1

ɡɚɪɟɡ ɨɞɜɚʁɚɰɟɨɞɟɨ ɨɞɞɟɰɢɦɚɥɧɨɝ

M 1 m 5 dm = 1,5 m.. N 3 dm 8 ɫm = 3,8 dm O 9 cm 5 mm = 9,5 ɫm P 38 m 6 dm = 38,6 m

139


ɉɊɈȼȿɊȺȼȺɆɈ ɇȺɍɑȿɇɈ Ʉʂɭɱɧɟɪɟɱɢ: ɪɚɡɥɨɦɰɢ

(m ” n ”10), ɞɟɰɢɦɚɥɧɢ ɡɚɩɢɫ ɛɪɨʁɚ ɫɚ ʁɟɞɧɨɦɞɟɰɢɦɚɥɨɦ

1. Ɂɚɨɤɪɭɠɢ ɪɚɡɥɨɦɚɤ ɤɨʁɢɨɞɝɨɜɚɪɚ ɨɛɨʁɟɧɨɦɞɟɥɭɮɢɝɭɪɟ. ɚ)

ɛ)

ɜ)

R

TA

L

2. Ɉɛɨʁɞɟɨɮɢɝɭɪɟ ɤɨʁɢɨɞɝɨɜɚɪɚɧɚɩɢɫɚɧɨɦ ɪɚɡɥɨɦɤɭ.

ɨɞɝɨɜɚɪɚʁɭʄɢ ɡɧɚɤ: <, > ɢɥɢ=. ɜ)

O

2. ɍɩɨɪɟɞɢ ɞɚɬɟ ɪɚɡɥɨɦɤɟ.ɍɩɢɲɢ ɭ ɚ) ɛ)

-P

ɝ)

Ɣ

;

Ɣ

Ɣ

ED

;

Ɣ

U KA

3. ɍɩɨɪɟɞɢ ɫɥɟɞɟʄɟ ɪɚɡɥɨɦɤɟ. ɍɩɢɲɢɭ ;

Ɣ

;

Ɣ

;

;

ɨɞɝɨɜɚɪɚʁɭʄɢ ɡɧɚɤ: ,  ɢɥɢ=.

Ɣ

;

Ɣ

;

Ɣ

;

Ɣ

Ɣ

;

Ɣ

;

Ɣ

;

Ɣ

4. Ʉɨʁɢɪɚɡɥɨɦɚɤ ɬɪɟɛɚɞɚɫɬɨʁɢɧɚ ɦɟɫɬɭ M

>

ɚ)

ɛ)

N

<

? Ɂɚɨɤɪɭɠɢ ɫɥɨɜɨ ɢɫɩɪɟɞ ɬɚɱɧɨɝ ɨɞɝɨɜɨɪɚ ɚ)

ɛ)

O

<

ɚ)

ɛ)

5. ɂɡɦɟɪɢ ɞɭɠɢɧɟ ɧɚɰɪɬɚɧɢɯɞɭɠɢ. ɉɨɩɭɧɢ ɬɚɛɥɢɰɭ ɨɞɝɨɜɚɪɚʁɭʄɢɦ ɦɟɪɧɢɦɛɪɨʁɟɜɢɦɚ. dm

cm

mm

AB CD EK OT

140

; .

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Математика 3Б, уџбеник за трећи разред основне школе  

Уџбеник за трећи разред основне школе Аутори: Софија Зарупски, Бошко Влаховић

Математика 3Б, уџбеник за трећи разред основне школе  

Уџбеник за трећи разред основне школе Аутори: Софија Зарупски, Бошко Влаховић

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