Dear students, We are pleased to introduce this book â&#x20AC;&#x153; Mathematics for Primary stage - Year 4 â&#x20AC;&#x153; to our children. We have done all what we can to make studying mathematics an interesting job for you. We are confident in your abilities in understanding the subject of the book, but even seeking for more. Besides the interesting figures and drawings, we took into consideration to increase crosscurricular and real life mathematics applications, where you sense the value and importance of studying mathematics. In many situations, you will find that we ask you to use a calculator to check mathematical operations, and invite you to use the computer to conduct some operations and draw some figures and decorate them. Towards the end of every unit, you will find some activities (sometimes may be closer to puzzles), in order to enjoy studying mathematics, where you will find great, but calculated, challenges that alerts your minds and develops your tendencies. Be careful to follow all what is written, conduct all activities and do not hesitate to question your teacher in all what you may face of any difficulties. Remember that many of the mathematics questions which have more than one correct answer, and studying it bears values that reflect this great humanitarian effort.

May God help you and us to acheive what is good for our beloved nation Egypt.

The authors

Measurement Lesson 1:

The Length

Lesson 2:

The Area

General Exercises on Unit 4

........................................................................................ ....................................................................................... ....................................................................................... .......................................................................................

General Exercises

....................................................................................... 89

Unit 4 Activities

74 80 87 88

General Revision - For the first Term ............................................................................. 94 Model eixam - For the first Term ................................................................................... 101

74 80 87 88 89

Hundred thousands Millions, Milliards (Billions) Operations on Large Numbers Unit 1 Activities General Exercises on Unit 1

Lesson 1 Hundred Hundred Thousand Thousands

Lesson 1

Hundred Thousands

+

1

0

0

9 0

9 0

0

9 0

This is read 1 number 0 0 0 as ‘hundred 0 0 thousand’ and can be represented on This number is read as ‘hundred the abacus as in the This number is figure read opposite. as ‘hundred

9 0

Tens

Hundreds

Thousands Units

9 0

0

Hundreds

0

Units Thousands

1

Thousands Thousands

Tens Ten Thousands

Hundred Ten Thousands Hundreds Hundred Ten Thousands Thousands Thousands Hundreds Tens Units

Units

Hundred Thousands

Hundred 99 999 +Hundreds 1 = 100Tens 000 Thousands Thousands Thousands

Hundred Thousands

99 999 + 1 = 100 + « 000 « This number is read as hundred thousand100 000 Ten

Ten Thousands

99999 100 000 99 999 + 1 1 100000

99 999 + 1 = 100 000

Tens

Lesson 1

99 999 1

1 0on

thousand’ and can be represented on thethousand’ abacus as in the and figure can opposite. be represented

1

Thousands

Ten Thousands

Thousands

Units

Tens

Hundreds

Units

Tens

Hundreds

Thousands Hundred

Ten Thousands

Hundred Thousands

Units

Tens

Hundreds

Units

Tens

Exercise 1

Ten Thousands

Ten Thousands

Hundred Thousands

Units

Hundred Thousands Tens

Hundreds

Units

Thousands

Ten Thousands Tens

Hundreds

Thousands

Hundred Thousands

Ten Thousands

Units Units

Hundred Thousands

Tens Tens

Hundreds Units

Hundreds

Thousands Thousands

Tens

Units

Tens

Hundreds

Ten Thousands Hundreds Thousands

Ten Thousands

Ten Thousands Thousands

Hundred Thousands

Hundred Ten Thousands Thousands

Hundred Thousands

Write the numbers.

Hundred Thousands

2

Hundreds Thousands

Ten Thousands Thousands

Hundred

Ten Thousands Thousands

Write the numbers.

1

2

0Exercise 0 0 1

the abacus as in the figure opposite. Exercise 1 1 Write the numbers. Hundred Thousands

1

0

2 2

Complete Complete according according to to the the place place value value of of each each digit. digit.

Number Number 752 752 341 341 605 605 618 618 78 78 539 539 58 58 002 002

Hundred Ten Hundred Ten Thousands Hundreds Thousands Thousands Thousands Hundreds Thousands Thousands

Tens Tens

Units Units

3 3

Write the the following Underline correct number, Underline the correctnumber number, in in digits, digits, which which express express each each of of

4

c seventy thousand, five hundred and ninty- three (70 593 , 700 593 , 59 370 , 750 093) Complete as the example.

4

the words. the following following in words. a a one one hundred hundred sixty sixty thousand, thousand, seven seven hundred hundred and and forty forty ......... (16 740 , 740 160 , 167 040 , 160 740) b one hundred thousand, three hundred and seventy-ﬁve ...... b one hundred thousand, three hundred and seventy-five c seventy thousand,(10 ﬁve hundred and ,nintythree ................. 375 , 100 375 1 375 , 375 100)

Complete as the Example: 147 962example. = 962 + 147 000 = 2 + 60 + 900 + 7 000 + 40 000 + 100 000 Example: 147 962 = 962 + 147 000 = 2 + …………………………………………… 60 + 900 + 7 000 + 40 000 + 100 000 a 672 384 = 384 = 4 + 80 + ………………………………………… a 672 384 = 384 + …………………………………………… + 80 + ………………………………………… b 126 459 == 4459 + …………………………………………… = 9 + ……………………………………………… b 126 459 = 459 + …………………………………………… 9 + ……………………………………………… c 35 608 = 608 + …………………………………………… = …………………………………………………… c 35 608 = 608 + …………………………………………… = ……………………………………………………

3 3

5

Read the following numbers, then write them in as words. the example. a 712365 Example: 370 634 three hundred seventy thousand, six hundred thirty-four b 105206 c 712 300418 a 365 d 740 740

b e

105 206 85 069

c

300 418

6

Write the value of the circled digit in each of the following numbers. a 27 351 b 156 348 c 723 608 d 543 092 e 230 045 f 467 900

7

Complete using the suitable sign < , > or = in each a 132 045 93 245 b 85 679 302 c 100 074 74 001 d 321 587 321 e 20 864 20 531 f 437 786 437

8

Write the greatest and the smallest number that can be formed from the number cards in each of the following. a 4 1 5 3 2 6 greatest …………………… smallest …………………… b 7 6 4 3 9 1 greatest …………………… smallest …………………… c 3 3 2 6 7 7 greatest …………………… smallest ……………………

9

Arrange the following numbers in an ascending order, then in a descending order. a 654 321 , 143 265 , 142 365 , 645 321 b 325 604 , 302 564 , 325 046 , 325 064 c 515 115 , 151 155 , 551 115 , 115 515

4

. 001 587 876

10 Complete in the same pattern. a 710 654 , 720 654 , 730 654 , ………… , ………… b 80 000 , 280 000 , 480 000 , ………… , ………… c 100 568 , 100 578 , 100 588 , ………… , ………… 10 Complete in the same d 220 300 , 210 300pattern. , 200 300 , ………… , ………… a 710 654 , 720 654pattern. , 730 654 , ………… , ………… 10 Complete in the same b 80 000 ,pattern. 000 10 Complete in, the same 654 , 280 720 654 , 480 730 654, , ………… …………, , ………… ………… 11 a Join710 the000 cards with equal numbers. 10 b Complete in, the same c 80 100 568 100 578,pattern. 100000 588 a 710 654 , 280 720 654 , 480 730 654 , ………… ………… ………… 000 , , ………… 710000 710 1 ,710 + 70 000 a 710 654 720 654 730 654 d 100 220000 300, , 280 210000 300, , 480 200000 300, , ………… b 80 c 568 100 578 100 588 …………, , ………… ………… b 80 000 , , 280 , ,+ 480 000 , , ………… ………… c 100 568 100000 578 100 588 d 300 210 300 200 300 …………, ,71 ………… 710 220 + 71 000 710 710 000 710 c 100 568 100 578 100 588 , ………… , ………… 11 d Join220 the 300 cards with 300 equal numbers. , 210 , 200 300 10 +220 700300 + 710 000300 10300 +1700 ++71 d , with 210 , numbers. 200 , ………… 11 Join the cards equal 710 710 710 70000 000, ………… 11 Join710 the 710 cards with equal numbers. 1 710 + 70 000 12 Join Underline the nearest number each case. 11 cards with equal 710 +the 71710 000 710 +numbers. 710 to 000 71 710 710 1 100 710 000 + 70in000 a 710 90 000 and 109710 000+ 710 000 b 710101 000 and 100 900 710 + 71 000 71 710 710 1 + 70 000 10 + 710 10 000 + 700 + 71 000 71 710 c +200 and000 90710 000+ 710 710 +700 71000 000 10 710 000 710 + 710 10 000 + 700 + 71 000 71 710 710++700 71 + 000 12 Underline nearest to 100 000 in each case. + 700 +the 710 000 number 10 the + 700 + 71rectangles 000 13 10 Write suitable numbers inside empty on the 10 +90 700 +the 710 000 10 to +b700 + 71000 a 000 and 109 000 and 100 12 Underline nearest number 100101 000 in000 each case.900 number line according to thier places. c 90 200000 000 and 90 000 12 a Underline the nearest number tob100101 000000 in each case. and 109 and 100 900 12 Underline the nearest number tob100101 000000 in each case. a 90 000 and 109 and 100 900 000 and 90 000 400c 000200 500 000 a 90suitable 000 109 b empty 101 000 and 100 13 c Write numbers rectangles on900 the 200 000and and 90 000inside the c 000 and 90 000 number line toinside thiernumber. places. 13 suitable numbers the empty rectangles on the 14 Write a 200 Write theaccording greatest 6-digit 13 number Write suitable numbersdifferent empty rectangles on the line toinside thier the places. b Write theaccording greatest 6-digit number. 13 Write suitable numbers6-digit the empty rectangles on the line toinside thiernumber. places. c000Write theaccording smallest 400number 500 000 to thier places. d000Writeline theaccording smallest different 6-digit number. 400number 500 000 14 numbernumber. different 6-digit number and 5 ae000Write the greatest 6-digit 400 500 000 b000Write different 6-digit number. 14 the greatest number. their sum is 15. 6-digit 400a 500 000 c smallest different 14 b a 6-digit number. 6-digit f Write the greatest different 6-digit number. number and their sum is 14 c a 6-digit number. d Write b greatest different 6-digit number. 17. the smallest b greatest different 6-digit number. e number different 6-digit number and of c 6-digit number. d g Write the smallest number and the sum c Write 6-digitis number. their sum is 15. d smallest different 6-digit number. e theand greatest number 6-digit number and its units tens digits 7.different d smallest differentdifferent 6-digit number. fh their number and their sumofis e Writesum the greatest 6-digit number is 15. number the and sum greatest number 6-digit number 17. their sum is 15. fe Write theand smallest different 6-digit number and theirand sum is its units tens digits is 7.different their sum is 15. different 6-digit number and the greatest fg 17. Write the smallest theirsum sumofis5 f Write smallest theirsum sumofis its units tens digits is 7.6-digit number and the 17. g theand greatest different 17.units h its smallest g Write theand greatest different tens digits is 7.6-digit number and the sum of

Second:

Ten Millions

Lesson Millions, and Complete2 the following table to Ten find theMillions sum of: 9 999 999 + 1 Hundred Millions Tens

Units

Units

Hundreds

Thousands

Ten Thousands

9

Hundreds

Hundred Ten Thousands Hundreds Tens Units Thousands Thousands

Tens

Thousands

Millions

9

Hundred Thousands

Millions 9 9 9 9 Complete the following table to find the sum of: 999 999 + 1

Millions

First:

Hundred Ten Thousands Hundreds Thousands Thousands

Ten Thousands

Millions

Hundred Thousands

Ten Millions

9 + 1

Units

Tens

Millions

Ten Millions

The sum is 1 000 000, and 9 is 109000 000, 9 8-digit 9 9 9 it is read as ‘one million’ The sum +1 number and is read as ‘ten million’, and can be represented and can be represented on the on the abacus as in the abacus as in the figure opposite. figure above.

Units

Tens

Hundreds

Thousands

Ten Thousands

Millions

Millions Thousands Units

Hundred Thousands

Units

Tens

Hundreds

Thousands

Ten Thousands

Millions

Hundred Thousands

Exercise 2 its digits as shown To read the number 49 136 527, we separate below 1 Write the numbers. 49 136 527 it is read from left to right as: 49 million, 136 thousand and 527

8 6

Units

and and and and

Tens

Hundreds

Ten Thousands

Millions

Hundred Thousands

numbers, then complete. …… million, …… thousand …… million, …… thousand …… million, …… thousand …… million, …… thousand

Units

Tens

Hundreds

Thousands

Ten Thousands

Millions

Read the following a 73 421 685 b 22 153 027 c 50 200 366 d 68 730 050 Hundred Thousands

1

Thousands

Exercise 3 …… …… …… ……

Units

Tens

Hundre

Thousan

Units Units

Tens Tens

Units

Hundreds Hundreds

Tens

Hundreds Thousands Thousands

Ten Thousands Thousands Thousands Ten

Hundred Ten Hundred Thousands Thousands Thousands

Millions

Units Units

Units

Tens Tens

Tens

Hundreds Hundreds

Hundreds

Thousands Thousands

Thousands

Thousands Thousands

Thousands

Ten Ten Ten Thousands

Millions Millions

Millions

Hundred Hundred Hundred Thousands Thousands

Ten Thousan

Million

Hundred Ten Thousands Hundreds Tens Units thousands thousands

Write the the numbers. numbers. 11 1 Write 7 354 621 923 508 4 561 009 8 000 300 3

Hundre Thousan

Tens

Units

Exercise 22 Exercise

Millions

Hundred Millions Millions Thousands

Number

Hundre

Thousan

Ten Thousan

Million

2

Hundre Thousan

is read read as as ‘one ‘one million’ million’ itit is and can can be be represented represented and on the the abacus abacus as as in in the the on figure above. above. figure Complete according to the place value of each digit. ++ 11

Join the two cards which express the same number

1 170 650 one million, one hundred and fifty thousand, six hundred and seventy 6 Second: Ten Millions

Millions 560

Units Units

Tens Tens

Hundred Ten Units one million, oneThousands hundredHundreds and fifty Tens thousand, Thousands Thousands

seven hundred and sixty 9 9 9 9 9 Third: Hundred Millions

9

9 + 1

Hundreds

Thousands

Ten Thousands

1 150 670 one million , one hundred and seventy Complete the following table to find the sum of:sixty thousand, five hundred and 99 (b) 999105 999million + 1 and 11 Hundred Thousands

66

Hundreds Hundreds

Thousands Thousands

Hundred Hundred Thousands Thousands Ten Ten Thousands Thousands

Millions Millions

Units Units

Tens Tens

Hundreds Hundreds

Thousands Thousands

Millions Millions

Ten 1 170 Millions

Hundred Hundred Thousands Thousands Ten Ten Thousands Thousands

Write each of the following number in digits then put it in the corresponding table according tothe thesum placeand value of each digit. 1 150 760 one million, Complete the following table to one find hundred of: seventy six hundred (a) 999 17 million 450 thousand and 46 and fifty 9 999 + 1 andthousand,

2

Tens

Millions

Units

Units

Tens

Hundreds

Thousands

Ten Thousands

Hundred Thousands

Millions

Ten Millions

Hundred Millions

Ten Millions

4 Hundred Complete as the example Hundred Ten Ten Units Millions The sum Millions is 10 000 000,Thousands 8-digit Thousands Thousands Hundreds Tens Millions number and is read ‘ten Example: 7 435as218 = 7million’, million + 435 thousand + 218 9 9 9 9 9 9 9 and can be represented on the 9 + 1 abacus the figure opposite. a 2 as 405in396 = ……… million + ……… thousand + ……… b 4 691 508 = ……… million + ……… thousand + ……… 3To Write the following number inwe digits. read 136 527, its digits as shown c 8the 300number 597 =49 ……… million +separate ……… thousand + ……… (a) One million , one hundred and fifty thousand and twenty seven. below dsum …………… = 000, 6 million + 412 thousand + 576 The(b) is 100 000 9-digit Twenty four million, thirty thousand and five. 49 136 527two+hundred e …………… = 9 million + 18 thousand 72 number and is read as ‘hundred (c) hundred = million and six thousand f Five …………… 4represented million + 4hundred thousand +4 . million’, and can be on Millions Thousands Nine hundred thousand eighty. Units the(d) abacus as in the figure and opposite. it is read from left to right as: 49 million, 136 thousand and 527 To read the number 714 326 518, we separate its digits as shown below Exercise 3518 714 326

7

Second:

Write the following sum in digits.

4

9

9

9

9

Tens

9

Write the following sum in digits.

Units

9

Complete according to the place value of each digit. Ten +Thousands Hundreds 7 millionHundred aNumber 7435218 =Millions + 435thousand 218. thousands thousands

Hundred Thousands

Millions

Ten Millions

b7 4691508 354 621 = ...million + ........thousand + ......... The csum is 10 000 000, 8-digit 734216858 923 508 = ...million + ........thousand + ......... number and is read as ‘ten million’, 561 009 = ...million + ........thousand + ......... d4 168730050 and can be represented on the 8 000 300 abacus as in the figure opposite.

Hundreds

2

million

Hundred Ten Thousands Hundreds Thousands Thousands pound.

Ten Thousands

5

Millions

9 + 1 Tens Units Tens

Ten Millions c 3

Units

Complete the following a 41 million pound. table to find the sum of: 9 999 999 +1 1 b 2 million pound.

Thousands

4

Ten Millions

63 Join the two cards which express the same number To read the number 49 136 527, we separate its digits as shown below 1 170 650 one million, one hundred and fifty 49 136 527 thousand, six hundred and seventy 1 150 760

Millions Thousands Units

one million, one hundred and seventy thousand, six hundred and fifty it is read from left to right as: 49 million, 136 thousand and 527 1 170 560

one million, one hundred and fifty thousand, Exercise 3 seven hundred and sixty

1

Read the following numbers, then complete. 1 150 670 one million , one hundred and seventy a 73 421 685 …… million, …… thousand and …… thousand, five hundred and sixty b 22 153 027 …… million, …… thousand and …… c 50 200 366 …… million, …… thousand and …… 4 Complete as the example d 68 730 050 …… million, …… thousand and …… Example:

8

a b c

7 435 218 = 7 million + 435 thousand + 218

2 405 396 = ……… million + ……… thousand + ……… 4 691 508 = ……… million + ……… thousand + ……… 8 300 597 = ……… million + ……… thousand + ………

Lesson 3 two cards Milliards (Billions) 2 Join the expressing the same number. Lesson 3 Milliards (Billions) Lesson 3 Milliards Milliards24(Billions) ( Billions ) 24 482 000 million and 482 Complete the following table to find the sum of: 24 082 24 million and Complete the following table to find the sum of:482 thousand 999 999400 999 1 Complete the+ following table to find the sum of: 999 999 999 + 1 999 999 999 + Ten 1 Hundred Ten Hundred Thousands Hundreds Tens Units Milliards Millions 24 040 082 24 million, 48 thousand and 200 Hundred Thousands Ten Hundred Ten Thousands Millions Millions Tens Milliards Hundred Hundred Thousands Ten Thousands Hundreds Ten Millions Thousands Thousands Hundreds Tens Milliards Millions Millions Millions Thousands Thousands Millions Millions 9 9 9 9 9 9 9 9

Thousands Thousands Thousands

Units Units Units

Milliards Milliards Milliards Hundred Hundred Hundred Millions Millions Millions Ten Ten TenMillions Millions Millions

3 Add one million to each of the following numbers. The sum is 1 000 000 000 which is 530 000 247 000 , which 28 900 The sum is 1610-digit 000 is 420 , 39 410 560 the smallest number and The sum is……………… 1 000 000 000 ……………… which is ……………… the smallest 10-digit number and isthe read as ‘milliard’, and can be smallest 10-digit number and is read as ‘milliard’, and can represented on the abacus asbe in is read as ‘milliard’, and can be 4 Add ten millions to each of the represented on the abacus as in following numbers. the figure opposite. represented 49 on 136 the abacus 500 , as 756in382 , 82 356 004 the figure opposite. the figure opposite. ……………… ……………… ………………

Units Units Units

Millions Millions Millions

Tens Tens Tens

Milliards Milliards Milliards

Hundreds Hundreds Hundreds

24 048 200

9 9

9 9 24 million, 9 9 thousand 9 9 82 9 40 and 9 9 9 9 9 + 19 + 1 + 1 24 million, 400 thousand and 82

Millions Millions Millions Hundred Hundred Hundred Thousands Thousands Thousands Ten Ten Ten Thousands Thousands Thousands Thousands Thousands Thousands

9 482 9 24 000 9 9

Units Units

To read the number 6 408 192 357, we separate its digits as 5 read Complete as the6example. To the number 408 192 357, we separate its digits as shown below To read the number 6 408 192 357, we separate its digits as shown below 408 192 357 shown below 98 6230 156 Example: = 156 + 230 000 + 98 000 000 6 408 192 357 6 408 192 357 Milliards Millions Thousands Units

a 52 936 Milliards 147 = 147 + …………… + …………… Millions Thousands Units Milliards Millions Thousands Units b 23 600 156 = …………… + …………… + …………… and it is read from left to right as: 6 Milliard, 408 million, 192 c 3 651 028left = …………… …………… …………… and it is read from to right as: 6+ Milliard, 408 +million, 192 thousand and 357 anddit is10 read from left to right as: 6 Milliard, 408 million, 192 800357 900 = …………… + …………… + …………… thousand and thousand e 6and 000357 834 = …………… + …………… + ……………

12 12 12

9

milliard?Millions Represent the numbers Thousands Units on the number line. 1 000 000 090 , 999 999 990 or 1 100 000 000 Which ofright the following numbers the nearest two it is readbfrom left to as: 49 million, 136isthousand andto 527 milliard? Third: Hundred Millions 2 000 000 020 , 299 999 3 999 or 1 999 999 900 Exercise

Exercise 5

13

Units

Tens

Hundreds

Thousands

Ten Thousands

Hundred Thousands

Millions

Ten Millions

Hundred Millions

the following table numbers to find thecomplete. sumthe of:difference between 4 a the Find two 10-digit with 1Complete Read following numbers, then 1 999 Read the following numbers, then complete. 99 999 + 1685 them is one milliard. a 73 421 …… million, …… thousand and …… a 8two 71910-digit 645 302 …… milliard, …… million, Find027 numbers with the difference between b b 22Ten 153 …… million, …… thousand and …… Hundred Ten Hundred …… thousand andTens …… Thousands Hundreds Millions them is oneThousands million. c 50 200 366 …… million, …… thousand and …… Units Thousands Millions Millions b 6two 539 006 475 …… milliard, …… million, Find numbers with the difference between d c 68 730 050 10-digit …… million, …… thousand and …… 9them is9 one thousand. 9 9 …… 9thousand 9 and …… 9 9 c 2 163 900 800 …… milliard, …… million,+ 1 …… thousand and …… 8 d 5 180 070 506 …… milliard, …… million, …… thousand and …… The sum is 100 000 000, 9-digit number and is ‘hundred 2 Join theread two as cards expressing the same number. million’, and can be represented on 7 000 600 900 7 million, 6 thousand and 900 the abacus as in the figure opposite. 7 million, 600 thousand and 900 70 600 900 To read the number 714 326 518, we separate its digits as 7 006 900 7 milliard, 600 thousand and 900 shown below 714 326 518 7 000 000 + 6 000 + 900 Millions Thousands Units

3

a

a 4 b c d e f

564 253 601 …… million, …… thousand and …… a Find two 10-digit with thousand the difference between 901 420 368 ……numbers million, …… and …… is one milliard. 987 them 654 321 …… million, …… thousand and …… b Find two 10-digit with thousand the difference between 123 456 789 ……numbers million, …… and …… is one million. 600 them 400 200 …… million, …… thousand and …… c Find two 10-digit with thousand the difference between 809 005 000 ……numbers million, …… and …… them is one thousand.

Which of the following numbers is the nearest to one milliard? Represent the numbers the number line. it is read from left to right as: 417 million, 326on thousand and 518 1 000 000 090 , 999 999 990 or 1 100 000 000 b Which of theExercise following numbers 4 is the nearest to two milliard? 2 following 000 000 020 , 299then 999complete. 999 or 1 999 999 900 1 Read the numbers,

10

13

b

2 4

5

Which of the following numbers is the nearest to two milliard? 2 000 000 020 , 299 999 999 or 1 999 999 900

Join the two expressing number. between a Find two cards 10-digit numbers the withsame the difference them is one milliard. 18 000 000 + 4 000 + 605 1 804 000 + 605 b Find two 10-digit numbers with the difference between them is one million. 1 800 000two + 410-digit 000 + 605 1 804 605 c Find numbers with the difference between them is one thousand. 18 004 605

1 800 000 + 40 000 + 605

Write the following quantities of money in digits. a 14 milliard pound ............... 1 840 605 b 1 milliard pound ...............

13

1 840 000 + 605

2

c 3 milliard pound ............... 4 3 Complete using suitable numbers. a 56 340 608 < ………………………… < 56 430 608 the following numbers in terms of million. 6 Express b 61 708 425 < ………………………… < 61 807 425 c 500 600 700 < ………………………… < 500 700 600 a 2 milliard . d 43 051 289 < ………………………… < 430 051 278 1 b 3 2 milliard . 4

5

c

10 milliard .

a

Which of the following numbers is the nearest to five hundred million: 500 000 900 , 500 005 000 or 499 999 000?

b

Which of the following numbers is the nearest to one hundred million: 110 000 000 , 100 900 000 or 101 000 000?

a

Find two 9-digit numbers with the difference between them is one million.

b

Find two 9-digit numbers with the difference between them is one thousand.

11

Third: Hundred Millions Complete the following table to find the sum of: 99 999 999 + 1

Lesson 4Ten 3 Hundred Millions

Millions

Operations Milliards (Billions) on Large Numbers Hundred Ten

Millions

Thousands Thousands

Thousands Hundreds

Tens

Units

9 9 9 9 9 9 9 First: Adding Complete the following Large Numbers table to find the sumNumbers of: Adding and Subtracting Large 999 999 999 + 1

9 + 1

Units

Thousands Millions MillionsproducedThousands and sum in the 642 thousand tons . The isnext 100year 000 000, Hundred Ten9-digit Example: Thousands Hundreds Tens Thousands (a) Find the production number and issum read as ‘hundred 9 9of Thousands 9 9in the two 9 years 9. 9 9 (b) Find and the amount increase . on million’, can beofrepresented

Tens

Hundreds

Thousands

Ten Thousands

Thousands

Hundred Thousands

Millions

Ten

Ten Millions

Hundred

Hundred Millions

Drill 1: : A Factory produced fertilizer in year 450 thousand tons Example Ten Add as Hundred the example. Hundreds Tens Units Milliards Millions Units

9 + 1 3 6 9

1

Units

Tens

Hundreds

Thousands

Ten Thousands

Millions

Hundred Thousands

Ten Millions

Hundred Millions

Milliards

5 4 2 7 5 the abacus as in the figure opposite. + 3 5 0 1 2 = 8 9 2 8 7 To read the number 714 326 518, we separate its digits as the solution Milliards Thousands Units shown below Millions 714 4 891 326243 518c a 3a 785 4214 5b 0 000 b 6 4 2 01 0256 0 312 The +sum is 1 000 000 000 which is 210 0 287 +2346 4 2 0+ 0 03 102 315 -‫ــ‬ - 4 5+ 0 08 0341 the smallest 10-digitMillions numberThousands and Units = …………… = 1 0 9 2= 0 0…………… 0 = 1 9= 2 0…………… 00 is as 302 ‘milliard’, be d read 3 265 + 4 313and 491can = …………… represented onleft thetoabacus in million, 326 thousand and 518 it is read from right as: as 417 the figure Drill 2:opposite. Exercise 4 Add as the example.

To wecomplete. separate its digits as 1 read Readthe thenumber following numbers, then Example: 5 2 566408 7 0192 2 357, shown a below 564 +2536601 1 4 2 5…… 8 3 million, …… thousand and …… 408 192…… thousand 357 the and b 901 420 1 1368 369 9 2…… 8 5 million, (read sum)…… c 987 654 321 …… million, …… thousand and …… Milliards Units 123 456 789 bMillions …… million, …… thousand and ……200 a d 4 579 208 9Thousands 302 198 c 2 879 e 600 …… ……380 + 702400 354200 + million, 1 748 …… 327 thousand+ and 1 352 and = read005 from left to right 6 Milliard, 408 million, 192 fit is …………… 809 000 …… million, …… thousand …… = as: …………… = and …………… thousand and 357 10 d 5 208 107 + 9 274 305 = ………………… (read the sum)

14 12

13

2

Circle the number nearest to the correct answer, without performing the usual addition operation.

e f

(3 280 075 + 5 909 138) – 7 657 249 = …………… (4 512 247 + 5 067 753) – (1 200 105 – 2 489 105) = ……………….……………….

6 005 + 3 095 235 to = …………… 25 cCircle the 218 number nearest the correct answer, without Drill 4:

c

270 408 213 is subtracted from it, the result will be 18 200 999.

Third: Multiplying a Whole Number by Another a Multiplying by a 1-digit Number Drill Secan3: d: Dividing a Whole Number by Another InatheDividing 2008-09 by governomental budget and in the context of the a 1-digit Number Drill 1: c 6 005 218 + 3 095 235 = …………… governomental efforts to support basic commodities, 2 milliard Find the product as the example. (9 million , 8 and a half 10 million) pounds were allocated for that perpouse, 405million million ,pounds to maintain the prices of medicines and 750 million pounds to reduce Example: Find the product of: 357 × 4 = …………… 3the Ifinterest the income from the advertisements during African on housing loans. Find the total sum the for the three items Football Cup of Nations ‘Ghana 2008’ for the Egyptian in the governomental expenditure. 357 7 + 21 50 million + 300 and eight hundred357 Channel Two was thousand × pounds, 4 × Sports 4 TV seven hundred thousand × 4 pounds forsolution: Nile 354 Complete the + 200 + 1 200 = 1 428and eight + 50and += 428 and300 Youth Sports Radio Channel hundred x five 4 basic 2 000 000 000 pounds support commodities xthousand pounds. 4 Find the total income acheived the three 16 pricessixteen 405 000 000 pounds maintain ofby medicine a 218 8+ …… + ……… + 200 218tens 1200+200+16 =the ........ destinations from advertisements. + 750 000 000 pounds reduce interest20 of housing loans × ………………………………………………………………………… 7354 x 4 = 1416 × 7 …… 12× hundreds +1200 354 = 300 ……………… governomental expenditure + 50 += 456 +pounds …… + ………x1416 = ……… 4 x 4 sixteen 16 Second: Subtracting Large Exercise 6 Find the product of 9318Numbers x 8 + 200 1200+200+16 = ........ 20 tens b 7346 6 + …… + ……… ……… 354 x 4 = 1416 +1200 12× hundreds × 61: × …… … 9318 Drill 1 Add, then use the calculator to check your answer. 1416 8x = … (+8+....+....+....+) …… + ………x8=....+....+....+....=.... = ……… Subtract as the example. a 8 752 013 b 2 560 000 18 ................. 6 9 12 0 15 Find+the product of 9318 x 8+ 5 981 812 439 815 + =1: 80 Example 7 350 128 Example 2: 9 870 215 = …………… 9318…………… + .............. – 5 040 115 – 7 818 408 + .............. 8x ( 8+....+....+....+)x8=....+....+....+....=.... =1 465 2 310 = 2 051 807 c 789013 ................. 5 984 078 + + 80 a 6 215 108 b 8 167 105 .............. + = …………… – 3 104 007 – 4 056 104 + .............. d =2 107 305 + 5 760 119 = ……………… = …………… …………… ................. e (3 217 907 + 4 814 256) + 5 152 917 = …………… c 7 423 856 d 3 255 202 2 Circle number – the 5 018 739 nearest to the correct answer, – 2 without 028 139 performing the usual addition operation. = ……………… = …………… a 5 260 180 + 7 985 954 = …………… (900 million , milliard , 13 million) e 9 312 000 – 9 211 775 = ……………… 100789 + 2 –600 050558 = …………… fb 8 400 6 505 4 327 = ……………… (11 million , 7 milliard , 6 milliard)

15

16

=

16

17

c

6 352 × 5

= =

(2 + …… + ……… + …………) × 5 10 + …… + ……… + ………… = ……………

Drill4: 2: Drill 4: 3: Drill Drill 4:

If thethe budget allocated to support drinking in two Mostafa bought two kinds of cloth, the the price pricewater of one oneincreased metre of of the the Find product as kinds the examples. Mostafa bought two of cloth, of metre of the Mostafa bought two kinds of cloth, the price of one metre first kindisis is97 97years pounds and the250 price of pounds one metre metre of the the second is consecutive 270 000 to 750 180 2 from 6 and 1 2second 2 000 3 3 4 ﬁrst kind pounds the price of one of is first kind 97 pounds and the price of one metre of the second is 158 pounds. IfMostafa Mostafa bought 4 metres metres of the the2:ﬁrst first kind kind and 679 3 pounds. Find the of increase. Example 1: IfIf 9amount 308bought Example 8 354 158 pounds. 44 of and 3 158 pounds. Mostafa bought metres of the first kind and 3 metres ofthe the×second, second,8how how many many pounds pounds did did Mostafa Mostafa pay? Solution: × 5 metres of pay? metres of the second, how many pounds did Mostafa pay? The amount= of 74 increase …………… 464 = 750 180 000 – …………… = 41 =773 395 Solution: (read the remainder, then write it in words) Solution: Solution: Price ofﬁrst first kind == = …………………………………………… …………………………………………… pounds a 7first 354 b 83 204 c 3 pounds 605 421 Price of kind pounds Price of kind …………………………………………… Price×of ofsecond second kind == = ………………………………………… ………………………………………… pounds Exercise 4 kind × 8 7 × 6 Price pounds Price of second kind ………………………………………… pounds Mostafa paid = ………………………………………………… pounds 1 =Find the== difference in each of the following ……… = ………… = …………… Mostafa paid ………………………………………………… pounds Mostafa paid ………………………………………………… a 2 256 912 b 6 444 382 Use the calculator to check your answers. – 1 145 810 – 4 317 159 b Multiplying Multiplying by a 2-digit Number bb by a 2-digit Number Multiplying by a 2-digit Number= …………… = ……………

Drill 1: 1: Drill Drill 1: c 9 000 100

Findthe the product product as as the the examples. examples. Find as the examples. Find –the product 8 087 089

= …………… Example 1: 27 ×× × 53 53 == = 27 27 ×× × (3 (3 ++ + 50) 50) Example 2: 2: 5 3 3 Example 1: 27 53 27 (3 50) 5 Example 1: 27 Example 2 3 22 33 d 9 887 000 –27 7 ×115 306 …………… = 3 + 27 ×=50 50 × 2 2 7 7 = 27 27 ×× 33 ++ 27 27 ×× 50 × = × e (3 280 075 + 5 909 138) – 7 657 249 = …………… = 81 +067 1 350 350 371 f (4 512== 24781 +5 753) – (1 200 105 – 2 489 105) 3 371 81 350 ++ 11 7 1 = ……………….………………. = 11 1 431 431 + 01 16060 060 431 == + 1+ 0 = 1 431 2 Circle the number nearest to the correct answer, without = = 1 41 431 3 1

19

performing the usual subtraction operation. (Notice that the312 product is the the same same even with with different different methods, methods, (Notice that the product is even a that 7 256 – 7 056 = …………… (Notice the product is the300 same even with different methods, use a a calculator calculator to to check check your answer.) answer.) use your (200 million , 200 thousand , 250 thousand) use a calculator to check your answer.) b 8 205 107 – 3 198 119 = …………… 24 × 43 = = 24 24 × × (……… (……… + + 40) 40) (8 milliard , 6 milliard 43 43 24××43 43 , 5 million) 24 = 24 × (……… + 40) 43 = 24 × 3 + ……… ……… ……… × 24 c == 459 212 200×××=……… …………… 24 ……… × 24 24 ×× 33–++350 ……… × 24 = ……… ……… +ten ……… ………, milliard) (hundred and+ thousand , hundred thousand ……… ……… == ……… + ……… ……… d = 9 575 100 – 4 275 090 = …………… + = ……… + ……… ……… ……… = ……… + ……… (two milliard , 5 million 850 million) = ,……… ……… = = ………

20 20

17

3

Complete. Drill 2: a 3 256 712 + …………… = 7 807 300

Find the product of 4 × 12 × 25 using more than one method. b 9 256 000 – …………… = 5 312 989 c …………… – 7 218 305 = 6 977 455 First Method: Second Method:

4 If the budget allocated to support medicine in two consecutive (4 × 12) × 25 4 × (12 × 25) years increased from 380 million pounds to 405 million pounds = 48 × 25 = 4 × 12 × (5 + 20) to preserve the prices of medicine. Find the amount of the = 48 × (5 + ……) = 4 × (12 × 5 + …… × ……) increase. = …… × …… + …… × …… = 4 × (……… + ………) = …… + …… = …………… = 4 × ……… + 4 × ……… 5 Find the number that if: = ……… + ……… = ……… a subtracted from one milliard, the result is 758 209 312. bDrill added 3:to it 7 812 159, the result will be ten million. cA school 270 408 subtracted from it, the result will be 18 200 999. took213 theisopportunity No. Quantity Unit Price Total Price of the Cairo International Book Third: a Whole by 1 12Another34 Fair andMultiplying sent delegates to buyNumber asome Multiplying by abook 1-digit Number 2 15 42 books for the

3 18 48 library. Using the part of the Drill 4 invoice 1: opposite, answer the Find the product as the example. following questions. Grand Total: ...................... a What is the number of Example: Findcost the34 product of:each 357 × 4 = …………… books that pounds and what is their total price? 7 + 50 + 300 357 b 357 What is the number of books × that 4 cost 42 pounds × 4each and × 4 = 28price? + 200 + 1 200 = 1 428 what is their total c What is the number of books a 218 8 + …… ……… 218 that cost 48 pounds each+and × what 7 is their total × price? 7 × …… d Find the total =amount of money required from =the……… school. 56 + …… + ………

your teacher, discuss the annual Cairo bWith7346 6 + …… + benefits ……… of holding the……… International Book× Fair in Egypt and its annual timing. × 6 …… × … = … + …… + ……… = ……… 21

18

Drill 2:

Exercise Exercise 58

Find the product as the example. 1 the following numbers, then complete. the product for each of the following. 1 FindRead …… …… million, Example: × 57302 324 b = …………… a a1238×719 158 645 2 784milliard, ×8 c 5 467 × 84 …… thousand …… = ×849 × (4 + 20 e + 300 7 000 + 50and 000) d 23 278 475+ 209 × 23 f 3 785 × 17 53932006 475 …… milliard, + 160 + 2 400 + 56 000 +…… 400 million, 000 Usebthe6= calculator to check your answer. …… thousand and …… = 458 592 c 2 163 900 800 ……inmilliard, using a suitable digit each …… . million, 2 Complete …… and …… 4 4 8 a a6 × 4 259 4 5= 6 × b (9 + …… + ……… +c …………) 3thousand 5 d× 5 1807= 070 milliard, …… 54506 + …… ……… = …………… × +…… 8 + ………… × million, 75 =45 5 = …… 7 4 thousand and = …… 1702040 b 9 × 784 = …… × (… ++…… 7+ 0………) 0 + 2 Join the two cards expressing same number. = …… + ………the + ………… ==…………… 7 000 600 900 7 million, 6 thousand and 900 352 = happy (2 + …… + ……… + …………) 5 kilograms one ×of5their occasions, a family bought×18 33c 7In6million, 600 and+900 70 =thousand …… ……… ………… =900 …………… of meet for LE 3510a +kilogram and 16+litres of 600 juice for PT 400 a the family pay? 7litre. 006How 900 many pounds7did milliard, 600 thousand and 900

Drill 3: product astothe examples. for his family. He bought 15 man wanted build 44FindAthe 7 000 000 +a6house 000 + 900

6 1 2 2 3 3 4 tons of building2 steel for LE 7 356 a ton and 48 tons of cement Example 1:475 a ton. 9 308 2: 8 354 679 How much did Example theisman 3 afor LE Which of the following numbers the pay? nearest to one × 8 × 5 milliard? Represent the numbers on the number line. = number 74 464 = 41 773 395 to 990 the correct 55 Choose 1 000the 000 090 , nearest 999 999 or 1 answer, 100 000 without 000 operation. bperforming Which ofthe themultiplication following numbers is the nearest to two a a 25 7 354 b 83 204 c 3 605 421 × 977 × 4 = …………… milliard? × 4 × × 6 (98 000 10 000 110 000) 2 000 000 020 , 299 999 999 or ,1 999 999 ,900 ……… = ………… = …………… b= 40 × 75 × 50 = …………… thousand , with 200 thousand , 500 thousand) 4 a Find two(300 10-digit numbers the difference between Usecthe100 calculator× to check your answers. = …………… them×is99 one 98 milliard. (900 thousand , 800 one million) b Find two 10-digit numbers with thethousand difference, between d them 125 ×is48 = …………… one million. (five thousand , six thousand , seven thousand) c Find two 10-digit numbers with the difference between them is one thousand.

22

13 19

Fourth: Drill 4:

Dividing a Whole Number by Another a Dividing 1-digit Mostafa boughtby twoa kinds ofNumber cloth, the price of one metre of the first kind is 97 pounds and the price of one metre of the second is Example: 568bought ÷ 2 4 metres of the first kind and 3 158 pounds. IfDivide Mostafa metres of the second, how many pounds did Mostafa pay? Solution: We know that 568 = 5 hundreds + 6 tens + 8 units Solution: = 4 hundreds + 16 tens + 8 units Price of first kind = …………………………………………… pounds Price of second kind = ………………………………………… pounds Then, paid 568 ÷ = (400 + 160 + 8) ÷ 2 Mostafa = 2………………………………………………… pounds = (400 ÷ 2) + (160 ÷ 2) + (8 ÷ 2) = 200 + 80 + 4 = 284 b Multiplying by a 2-digit Number

Drill 1: Follow1: the steps of the following example to carry out the division Drill operation: 459as ÷ 3the examples. Find the product

Complete solution: Example 1: the 27 × 53 = 27 × (3 + 50) Example 2: 5 3 2 3 459 = 4 hundreds + 5 tens + …… units = 27 × 3 + 27 × 50 × 2 7 = 3 hundreds + 15 tens + …… units = 81 + 1 350 371 459 ÷ 3 = (300 + 150 + ……) ÷ 3 = 1 431 + 1 060 = (300 ÷ 3) + (……… ÷ 3) + (…… ÷ ……) = ……… + ……… + ……… = ……… = 1 431 Note:that You perform thesame previous write the (Notice thecan product is the evensteps with mentally different and methods, quotient as shown in the following example. use a calculator to directly check your answer.) 742+÷40) 2 24Example: × 43 = 24Divide × (……… 1 = 24 × 3 + ……… × ……… Solution: 7 4 2 + ÷……… 2 = 371 = ……… = ………

20

× + =

43 24 ……… ……… ………

23

Fourth:2: Dividing a Whole Number by Another Drill Drill 2: by a 1-digit Number a Dividing

Find the 4 × 12 for × 25 using more than one method. Write theproduct quotientofdirectly each of the following division operations, then use the÷ calculator to check your answer. Example: Divide 568 2 First Method: Second Method: a 946 ÷ 2 b 486 ÷ 3 Solution: (4 ×847 12) ÷× 725 4 × (12 c d + 655 ÷ 5+×825) We know that 568 = 5 hundreds 6 tens = 48 × 25 = 4 × 12 units × (5 + 20) = 4 hundreds + 16 tens + 8 = 48 × (5and + ……) = 4 × (12 ×units 5 + …… × ……) Dividend Divisor = …… × ……a +number …… × by …… =the4first × (……… ………) When dividing another, number+ is called the Then, 568 ÷ 2 = (400 + 160 + 8) ÷ 2 = …… + and ……the = …………… = 4 × ……… + 4 × ……… dividend second the = (400 ÷ 2) is+ called (160 ÷= 2) +divisor. (8 ÷ 2)+ ……… = ……… ……… = 200 + 80 + 4 = 284 For example, in the division operation 54 ÷ 9, Drill 3: 54 is the dividend and 9 is the divisor. Drill A school1: took the opportunity No. Quantity Unit Price Total Price Follow the of the following of the Cairosteps International Book example to carry out the division operation: 459 ÷ 3 1 12 34 Fair and sent to buy Quotient anddelegates Remainder 2 15 42 some books for the book Complete the solution: 3 18 48 library. Using the part of the 459 = 4 hundreds + 5 tens + …… units invoice opposite, answer the that4need to be distributed equally Example: We have 17 pens = 3 hundreds + 15 tens + …… units following questions. Grand ...................... among 3 children. Find the Total: greatest number of pens a What is that the number of can be given to3every child. 459 books ÷ 3 = (300 + 150 + ……) ÷ that cost 34 pounds each = (300 3) + total (……… ÷ 3) + (…… ÷ ……) and what is÷their price? Solution: Directly is 5 pens and 2 pens are left = ……… + ……… + ……… = ……… b What is because the number books 5 × of 3= 15 and 17 – 15 = 2 that cost 42 pounds each and Note: You can total perform the previous steps mentally and write the what is their price? In this example the quotient is 5 in and the remainder is 2. quotient directly as shown the following example. c What is the number of books that 48 and Then, 17cost = 5Divide × 3pounds + 2742 ÷each Example: 2 what is their total price? 1 d Find the total amount of money required from the school. Solution: 7 4 2 ÷ 2 = 3 7 1 With your teacher, discuss the benefits of holding the annual Cairo International Book Fair in Egypt and its annual timing.

24

21 23

Drill 3: Drill 3:the following table as the example. Complete Drill 4: the following table Exercise 8 Complete as the example. Relation between Mostafa bought two kindsThe of cloth, the one metre of the The division Theprice ofThe Drill 3: The elements of Relation between

division The for The The The of the second is first 1The Find kind the is 97 product pounds and each theof price the following. of oneremainder metre operation dividend divisor quotient division operation Complete the following table as the example. elements of operation dividend divisor quotient remainder operation 158 apounds. 123 ×If15 Mostafa bought b 42 metres 784 × 8of the first kind c division 5and 467 3 × 84 Relation between 78 = 10 ×7+8 78 ÷ 10 78 10 7 8 The The The f pay? metres ddivision of 23the 278second, ×The 49 howThe many e 475 pounds 209 ×did 23 Mostafa 3 785 × 17 elements 78 = 10 × 7 of +8 78 ÷ 10 78 10 7 8 operation dividend divisor quotient remainder division operation Use the calculator to check your answer. 43 ÷ 2 ......... ......... 21 ......... ......... Drill 3: Drill 3:43 ÷ 2 Solution: Complete the ......... Complete the table as the 78 =following 10 × 7 + 8table 78 10 78 10 example. 7 76 5 ......... ......... 77 ÷÷following 5 28 Price 2 76 Complete of using = …………………………………………… a suitable digit in each . pounds ÷ 5first kind Relation between ......... ......... ......... ......... 43of÷÷ second 2 68 4 64 The The division The The= ………………………………………… The The The0division Price kind 4 5 3 5 4 8 The elements 4 of pounds a b c 68 ÷ 4 dividend divis operation dividend divisor quotient remainder operation division operation Mostafa = ………………………………………………… pounds ......... ......... ......... 76 ÷ ×paid 5 ………… 10× 796 8 × 75

………… 96 10 4 5 = The 5 4 =÷= 10 1 ×7 70+2878 040 78remainder 10 78 78 ÷ The 10 68 10 7 7 quotient+ 8 The ÷ =478 dividend divisor x=The

+ by aby 72-digit 0a 02-digit +with remainder Dividing aaWhole Number Number Dividing Whole Number Number 43 ÷2 43 ÷bb 2 ………… 96 10 Multiplying by a 2-digit Number b

10

= Dividing a Whole Number by a 2-digit Number

76 ÷ 5 Drill 4: 0261 Drill 1: Example: Find the quotient of theby division without In one of their happy occasions, family bought 18 kilograms b Dividing a Whole Number a 2-digit Number 4: 68 ÷ 4 68 ÷3Drill 4 Divide as the example. 76 ÷ 5

96

10

25

a is If405 79 × 18000 = 1 pounds 422, then 1 422 ÷ 79 prices = 18. of medicine(( 000 maintain zero. )) 678000 = 52 × 13 + 2, then the remainder ÷ 52loans + b If750 000 pounds reduce interestof of 678 housing equalsusing the remainder 678 13. ( ) ……………… governomental expenditure 2 = Complete apounds suitableofsign <,÷>, or = in each without c When dividing 13, 26, 39, 52, … etc. by 13, the remainder performing the division operation. Fourth: Dividing a Whole Number by Another is zero. ( ) Exercise 6 a Dividing by÷a18 1-digit Number a 2 538 2 538 ÷ 37 b then 780 ÷use 9 the acalculator (78 ÷ 9)sign 10 2 Add, Complete using suitable <, >, your or = answer. in each without 11 to× check Example: Divide 568 ÷ 2 the division operation. c 100 × (287 865 ÷ 24) 282786 aperforming 8 752 013 b 560500 000÷ 24 439 + 375 981 812 a ÷ 18 2 538 ÷ d +2 If 538 1 288 =815 56 × 23, then: Solution: = …………… 2…………… b = 780 ÷ 568 9 divide (78 ÷ 9) We know that = 5 hundreds + 10 6 the tensremainder + 8 units will be when we 12 293 ÷× 56 5 =865 4 hundreds + 16 tens +500 8 units c when 100 × we (287 ÷1 24) 28 786 ÷ 24 2448 24480 divide 283 ÷ 23 the remainder will be 5 c 1 465 789 d + If 15 288 56 × 23, then: 984 =078 Then, 568 ÷ 2 = (400 + 160 +of 8)the ÷ 2following division operations, 23 Find the quotient of each = when …………… we divide 1 293 ÷ 56 the will be 5 = (400 ÷ 2) + (160 ÷ 2) + remainder (8 ÷ 2) without using the calculator. we 1 119 283 23 bthe 18 remainder 5 80 + 4 =÷ ……………… 284 da 2 when +divide 5+ 760 3107 654305 ÷= 3200 905 ÷ 5 will be ec (3350 217714 907÷+74 814 256) + 5 152 917 130 = …………… d 390 ÷ 13 3 Find Drill 1:the quotient of each of the following division operations, without using calculator. 345 Circle Follow thethe steps of the thenearest following example to answer, carry the division Find the quotient and remainder for each ofthe the following. 2 number to the without Find the quotient of 18the 936 ÷ 24correct without usingout calculator, a 654 ÷3 18 905 operation: 459the 2use 312 68 b to 3423 3find 415 ÷ b62 c5 9327 9 of 000 performing the usual addition operation. then3 quotient the quotient of ÷each the÷ 28 714 77 985 130f÷ 13 d 5 350 96 ÷÷+48 e 954 70the ÷d 35390 64 064 ÷ 16 ac 260960 180 =070 …………… following without carrying division operations. Complete the940 solution: (900 million , 13 million) a 18 ÷ 24 b ,18milliard 931 ÷ 24 Find quotient of5 18 ÷…………… 24 units without using the calculator, 459 4the hundreds tens += …… number that if:936 8= 400 100 + 2 +600 050 446 bFind then thebyquotient find ofthe each the 17. 3use hundreds + 15 tens + the …… a =divided 48, theto quotient isquotient 625 remainder (11 million ,units 7and milliard , of 6 milliard) a number ifthe divided by 69 quotient 2358 . following without the division operations. b The divided bythat 69,carrying quotient is, the 2 358 and is the remainder 0.15 The number that multiplied product a 18 940+ ÷150 24 931 ÷ is244158 . 459 ÷b (300 +54, ……) 3 by 54b,isthe c3 = multiplied by the÷product 418158. = (300 ÷ 3) + (……… ÷ 3) + (…… ÷ ……) 26 = ……… + ……… + ……… = ……… 7 The daily production of a Note: You can perform the previous steps mentally and write the factory producing garments 26 from quotient directlyitem as shown one clothing is 732 in the following example. units and from a second item Example: 742box ÷ 2used for is 956 Divide units. The 1 packaging the actory Solution: 7 4 2for÷export 2 = can 371 production hold 18 units of the first kind or 15 units of the second. Find: 23 a The number of boxes consumed by the factory daily. b The daily remainder from each kind produced.

b c

divided by 69, the quotient is 2 358 and the remainder 0. multiplied by 54, the product is 4 158.

57 The2:daily production of a Drill

producing garments Writefactory the quotient directly for each of the following division from one clothing item is 738 732 to check your answer. operations, then use the calculator units and from a second item is 945 956 for 486 ÷ 3 a 946 ÷ 2 units. The box used b packaging the actory c 847 ÷7 d 655 ÷ 5 production for export can hold 18 units of the first Dividend and Divisor or 15aunits of the Whenkind dividing number by another, the first number is called the second. Find: dividend and the second is called the divisor. a The number of boxes consumed by the factory daily. b The remainder eachoperation kind Fordaily example, in thefrom division 54 ÷ 9, produced.54 is the dividend and 9 is the divisor. bought a flat in a housing tower 68 Adel and Quotient Remainder for LE 168 940. He paid LE 100 000 as a down payment and the rest on 18 equal Find theneed value Example: Weinstallments. have 17 pens that to be distributed equally of eachamong installment. 3 children. Find the greatest number of pens that can be given to every child. Solution:

Directly is 5 pens and 2 pens are left because 5 × 3 = 15 and 17 – 15 = 2

In this example the quotient is 5 and the remainder is 2. Then, 17 = 5 × 3 + 2

24

27

Drill 3:

Unit 1 Activities

Complete the following table as the example. Activity 1 Relation between The division The The The The Numerals and Numbers elements of operation dividend divisor quotient remainder division operation a Find the smallest number formed from 10 different digits. b 78Find number different 78digits. = 10 × 7 + 8 ÷ 10the greatest 78 10 formed 7 from 10 8 c Find the smallest even number formed from 10 different digits. 43 ÷ 2 d Find the greatest odd number formed from 10 different digits. ÷ 5 the smallest number formed from 10 different digits and e 76 Find the 68 ÷ 4sum of its units and tens digit numbers equals 3. f Find the greatest number formed from 10 different digits and ………… 96 10 the sum of its units and tens digit numbers equals 9. b Dividing a Whole Number by a 2-digit Number Activity 2 Write Drillthree 4: numbers each is formed from four different digits of 9, 6, 5,as 4 and 0 such that: the first is nearest to 4 000 Divide the example. the second is nearest to 15 2000 0 Example: 1 320 ÷ 11 = 120 the third is nearest 320 11to 61 000 –11 Note: We start with the division 22 Activity 3 operation as shown opposite, – 22 Noticethen andwe deduce write the quotient. 00 In the figure opposite, geometric were drawn 18 2 4 3 0 a 2 430 ÷shapes 18 = ……… to express the number 21 003 005. Deduce the possible numerical value of each the÷ following shapes. 15 3 9 1 5 b 3 of 915 15 = ……… 21 003 005 =

……………

=

……………

= …………… = or …………… (check your answer by using the calculator any other method.)

28

25

Drill 4: General Exercise Exercises9 on Unit 1

Mostafa bought two kinds of cloth, the price of one metre of the first 11 kind (✔) isthe 97 forresult pounds the correct statement the ofand one(✗)metre for the of incorrect the second one is 1 Put Find Find the result for forand each each of ofprice the the following. following. 158 and pounds. If Mostafa the 4 metres of kind and 3 a a correct 87 87 562 562 ++ 55wrong 429 429bought ==statement. ……… ……… b b 39 39the 057 057first –– 14 14 583 583 == ……… ……… metres ac If3379 the ×second, 18 422, how then many1pounds 422 did= 014 Mostafa 18. ÷÷ 77 == pay? ( ) c of 478 478 ×× 99===1……… ……… d d÷ 79 721 721 014 ……… ……… be 678××=18 52==×……… 13 + 2, then theff remainder 678 ÷ 52 e If267 267 18 ……… 62 62 550 550 ÷÷of25 25 == ……… ……… Solution:equals the remainder of 678 ÷ 13. ( ) Price of When first kind dividing = …………………………………………… 13, 26, 39, 52, … etc. by 13, the remainder pounds 2 2 cComplete. Complete. Pricea second zero.the kind = ………………………………………… pounds ( ) aof is Write Write the value value of of the the underlined underlined digit digit in in each each of of the the Mostafa paid = ………………………………………………… pounds following following numbers. numbers. 2 Complete a suitable >, or each without 33 256 256using 812 812 159 159 ,, 958 958sign 214 214<,100 100 ,, =77in100 100 279 279 312 312 performing the division operation. ……………… ……………… ,, ……………… ……………… ,, ……………… ……………… b Multiplying bynumbers a 2-digit2of ab 538 ÷the 18 538 37 b 2Write Write the numbers ofNumber a a in in÷words. words. bc ÷ 9×× 29 (78 ÷ 9)then: × 10 c 780 IfIf 458 458 29 == 13 13 282, 282, then: Drill 1: ii 13 13 282 282 ÷÷ 29 29 == …… …… ii ii

13 13500 282 282÷÷÷24 458 458 == …… …… × (287 ÷ 24) 28 786 Findcthe100 product as 865 the examples. iii iii 13 13 291 291 == …… …… ×× 29 29 ++ …… …… d If 1 288 = 56 × 23, then: Examplewhen 1: we27divide × 53 1 = 293 27 ×÷(356+ 50) Example the remainder will2:be 5 35 3 3 Circle Circle the the number number nearest nearest to to the the correct correct answer. answer. 2 3 = we 27divide ×++311+475 ×987 50 × 2 75 127 283 ÷ 23 the remainder will be a a when 77 815 815 100 100 475 987 == …………… …………… (9 (9 million million ,, milliard milliard ,, 990 990 million) million) = 81 + 1 350 371 3 Find the quotient each000 of the following division operations, b b 9 9 145 145 000 000 –– of 88 142 142 000 == …………… …………… = 1 the 431calculator.(3 1 060 without using (3 000 000 ,, million million ,, 200 200+million) million) ac 3 ×× 125 b 18 905 ÷ 5 c 388654 ×× 66÷958 958 125 == …………… …………… = 1 431 c 350 714 ÷ 7 d 390,, 130 ÷ 13 ,, 55 million) (7 (7 million million 66 million million million) d d (4 (4 000 000 ÷÷ 4) 4) ×× 999 999 == …………… …………… (Notice that the product is the same even with different methods, 4 Find the quotient of 18 936 ÷ 24,, without using the calculator, (one (one million million one one milliard milliard ,, 900 900 thousand) thousand) use a calculator to check your answer.) then use the quotient to find the quotient of each of the without the are division operations. 4 4 following a a IfIf 756 756 pupils pupilscarrying in in aa school school are distributed distributed equally equally among among 18 18 24 × 43 = 24 × (……… + 40) 43 a 18 940 ÷ 24 18 931 ÷ 24class. classes, classes, find find the the number number of ofbpupils pupils in in each each class. = 24 × 3 + ……… × ……… × 24 b b Find Find the the number number that that ifif multiplied multiplied by by 17, 17, the the product product will will be be =11 156. ……… + ……… ……… 156. = ……… + ……… = ………

26 20

29 29

Exercise 5 1

Choose the correct answer. a 7 251 309 + 748 691 = …… (8 milliard , 8 million , 8 thousand) b 5 000 000 – 324 067 = …… (95 324 076 , 91 675 933 , 4 675 933) c 8 × 641 × 125 = ... (641 thousand , 641 hundred , 641 million) Relation Between Two Straight Lines d The number 2 100 is divisible by …… (35 , 11 , 13 , 17) e XYZPolygons is a triangle in which m(∠X) = 40° and m (∠Y) = 30°, Triangle thenThe ∆XYZ is …… triangle. (a right-angled , an obtuse-angled , an acute-angled) Applications f TheUnit L.C.M. of 15 and 35 is …… (15 , 105 , 35 , 5) 2 Activities

2

General on side Unit length 2 Draw the squareExercises XYZL whose 3 cm. Join its diagonals XZ and YL.

3

a b c d e

4

a b

Multiples of 6 are ……, …… and …… Prime factors of 350 are ……, …… and …… The perimeter of a rectangle whose dimensions are 7 cm and 11 cm = ………………………… = …… cm The H.C.F. of 18 and 30 is …… 1 4 of a day = …… hours = …… minutes. Calculate 2 106 425 + 894 075 – 3 000 500. Find the number that if subtracted from 256 412 307, then the remainder will be 255 million.

27 93

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quare.

96 28 1 3

31 to 90˚ not equal (acute or obtuse), thenand thenot twoperpendicular. straight lines are intersecting lines are intersecting and not perpendicular.

31

the two perpendicular straight lines make an angle with measure ………˚.

- ……………………………… - ……………………………… - ………………………………

Drawing Triangle of Given the Measure Angles If thea measure the angle between of twoTwo straight linesand is the of obtuse), One Side not equal to 90˚Length (acute or then the two straight lines are intersecting and not perpendicular.

Drill 6:

Draw ∆ABC in which BC = 4 cm, A Drill =2:30˚ and m(∠C) = 80˚. m(∠B) Join each figure to the suitable statement. Notice and draw.

C

80˚

30˚ 4 cm

31

B

The Sum of Measures of the Angles of the Triangle

Drill 7:

TwoDraw straight intersecting a anylines, triangle on a piece of Two straight lines, intersecting andcardboard not perpendicular and perpendicular. paper. . b theyour angles of the triangle at (youColour can use geometric instruments.) its vertices in red, green and yellow as shown Drill 3: in the figure opposite. c scissors cut the three a Use Drawthe two straighttolines Write the greatest number of examples of parallel angles and fix them on a piece on two lines of your lines that of you can see arround you. paper as shown in the figure. copybook, as shown in the figure below. Notice: The three angles together formed a straight angle and we know that the measure of the straight angle is 180˚. Then, we deduce that: - The lines of the copy-book.

The Do sum of expect measures of the- interior angles of any triangle = 180˚. b you these The two edges of the ruler. straight lines to - ………………………………………………………… intersect if they were - ………………………………………………………… Drill 8: from both - ………………………………………………………… extended Drawsides? the triangle ABC in which ∠B is a right angle, m(∠C) = 60˚ - ………………………………………………………… and BC = 4 cm. Measure ∠A, then check that the sum of - ………………………………………………………… measures ( yes of, angles no ) of a triangle is 180˚. Note: 29 45 You can draw two parallel lines These two straight lines are called parallel lines. using the two edges of your ruler, as shown in the

Two straight lines, intersecting and not perpendicular .

Two straight lines, intersecting and perpendicular.

(you can use your geometric instruments.) c What Drill 3:is the type of the ∆DEF according to its: ………… measures? ………… a side Drawlengths? two straight lines Write the angles greatest number of examples of parallel d What is the type of the ∆NKM according to its: on two lines of your lines that you can see arround you. side lengths? ………… angles measures? ………… copybook, as shown in the figure below. Drawing a Triangle given the Length of two Sides and the Measure of the Included Angle

Drill 5:

- The lines of the copy-book.

Draw in which AB = 5- cm, b Do∆ABC you expect these The two edges of the ruler. BC =straight 4 cm and m(∠B) = 60˚. lines to - ………………………………………………………… A intersect if they were B C - ………………………………………………………… extended from both - ………………………………………………………… 4 cm sides? - ………………………………………………………… ( yes

, noA

)

- ………………………………………………………… B Note: 60˚ B You can draw twoA parallel5 cm lines

Notice and straight draw. lines These two are called parallel lines. using the two edges of your ruler, as shown Exercies 1 in the opposite. Draw ∆XYZ in which XY = 7figure cm, YZ = 5 cm and m(∠Y) = 40˚.

32

Drill 4:

Join each figure to the suitable statement, Exercies 2 use your geometric instruments to which be sure. Draw ∆DEF in ∠D is right, DE = 3 cm and EF = 4 cm.

Measure the length of DF, then answer the following questions. a Calculate the perimeter of ∆DEF, given that the perimeter of any polygon = the sum of its side lengths. b What is the type of the triangle, according to the measures of its angles? …………… 1 2 3 4 (acute-angled , obtuse-angled or right-angled) c What is the type of the triangle, according to the length of its Twosides? parallel …………… lines Two lines, intersecting Two lines, intersecting and not perpendicular and perpendicular (isosceles , equilateral or scalene)

30 30 44

Drill 5:

How to draw a perpendicular to a straight line from a point on it.

Two parallel lines

Two lines, intersecting and not perpendicular

Two lines, intersecting and perpendicular

Drawing Drill 5:a Triangle Given the Measure of Two Angles and the Length One Side How to draw a perpendicular toof a straight line from a point on it.

Drill A6:

A

A 0 0

Draw ∆ABC in which BC = 4 cm, m(∠B) = 30˚ and m(∠C) = 80˚. 1

1

2

2

A

3 4 5

3

4

5

6 7 8

Notice Notice and and draw. draw.

C

80˚

30˚ 4 cm

B

DrillThe 6: Sum of Measures of the Angles of the Triangle

How to draw a perpendicular to a straight line from a point outside it.

Drill 7:

B

a

Draw any triangle on a piece of cardboard paper. b Colour the angles of the triangle at its vertices inAred, green and yellow A as shown in the figure opposite. c Useand thedraw. scissors to cut the three Notice angles them on⊥aBC. piece of In this case,and wefix write AB paper as shown in the figure.

B

0 0

C

1

2

3

1

2

3

4

5

4

5

A

6

7

8

Notice:

33

The three angles together formed a straight angle and we know that the measure of the straight angle is 180˚. Then, we deduce that:

The sum of measures of the interior angles of any triangle = 180˚.

Drill 8:

Draw the triangle ABC in which ∠B is a right angle, m(∠C) = 60˚ and BC = 4 cm. Measure ∠A, then check that the sum of measures of angles of a triangle is 180˚.

31 45

cDrill What7: is the type of the ∆DEF according to its: lengths? ………… measures? ………… Howside to draw a straight line parallel angles to a given straight line from a dpoint What is the outside it. type of the ∆NKM according to its: A side lengths? A ………… angles measures? ………… D 8

Drawing a Triangle given the Length of two Sides and the C B MeasureCof the IncludedBAngle 7

6

8

5

7

4

6

3

Drill 5:

5

2 4

1 00

1

3

Draw ∆ABC in which AB = 5 cm, BC = 4 cm and m(∠B) = 60˚. 2

3

2

4

5

1

00

A

B

1

2

3

4

5

C 4 cm

Notice and draw. In this case, we write AB // CD. A

B

Exercise 1

60˚

A B 5 cm Notice and draw. 11 Write the relation between each two straight lines under each Exercies 1 figure. Draw ∆XYZ in which XY = 7 cm, YZ = 5 cm and m(∠Y) = 40˚.

Exercies 2

Draw ∆DEF in which ∠D is right, DE2 = 3 cm andFigure EF = 43 cm. Figure 1 Figure Measure the length of DF, then answer the following questions. ………………… ………………… ………………… a Calculate the perimeter of ∆DEF, given that the perimeter of A polygon = the sum ofCE itson side lengths. 22 any Draw the perpendicular b What is thestraight type ofline theAB. triangle, according to the measures of C the given its angles? …………… Then, complete. (acute-angled , obtuse-angled or right-angled) m(∠BCE) m(∠………) = ………˚. c What is the=type of the triangle, according to the length ofB its sides? …………… (isosceles , equilateral or scalene)

34 32 44

3 Drawing Triangle Given from thethe Measure point X of onTwo Angles and the 3 Draw a perpendicular Y Length of One Side the given straight line YZ, then complete. X

Drill If O6: is the point of intersection of the

Drawdrawn ∆ABCperpendicular in which BC and = 4 cm, the straight line A m(∠B) = 30˚ and m(∠C) = 80˚. YZ, then m(∠XOY) = m(∠………) = ……˚. Notice and draw.

C

80˚

Z 30˚

4 cm

B

44 Draw a straight line parallel to the given N The Sum of Measures of the Angles of the Triangle straight line L and passing through the point N.

Drill 7: a

Draw any triangle on a piece of cardboard paper. b the figure anglesopposite, of the triangle at 55 Colour Notice the then complete. A its vertices in red, green and yellow a shown AB ……… (⊥ or //) as in theBC figure opposite. b AB YZto cut the three (⊥ or //) c Use the……… scissors angles fix them of //) c XY and ……… BC on a piece (⊥ or paper shown inwith the BZ figure. d AYasintersects at the point

L

……… X Y Notice: The three angles together formed a straight angle and e YC we intersects withthe BXmeasure at the point know that of the straight angle is ……… 180˚. Then, we deduce that: B Z C The sum of measures of the interior angles of any triangle = 180˚.

Drill 8:

Draw the triangle ABC in which ∠B is a right angle, m(∠C) = 60˚ and BC = 4 cm. Measure ∠A, then check that the sum of measures of angles of a triangle is 180˚.

33 45 35

Lesson 2

Polygons

Drill 1:

Notice the following polygons, then complete.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

The number of

The number of

The number of

Sides

aertices

angles

1

…………

…………

…………

2

…………

…………

…………

3

…………

…………

…………

4

…………

…………

…………

5

…………

…………

…………

6

…………

…………

…………

Figure number

What do you notice? The relation between the number of sides of a polygon with respect to the number of its vertices and the number of its angles. Notice that, for any polygon: Number of sides …… Number of vertices …… Number of angles

34 36

Drill 2:

A

Complete drawing the square ABCD, then answer the following (consider the unit of length = 1 cm). a b c

d

AB = BC = …… = …… = …… cm m(∠B) = m(∠…) = m(∠…) = m(∠…) = …˚.B

C

Notice that m(∠B) can be written instead of measure (∠B) for simplicity.

From all the above, it can be said that the square is a ……… (pentagon , quadrilateral , hexagon) that has ……… sides that are ……… in length and ……… angles that are ……… in measure and the measure of each is ………˚ (check by drawing other squares on graph paper). Using your geometric instruments, check that AC = BD and for other squares that you drew on graph paper, you will find that the diagonals of the square are always equal in length.

Notice:

In any quadrilateral, the diagonal is the line segment joining two non-consecutive vertices.

From the above, we deduce that the diagonals of the square are equal in length. e

Using the set-square, or the protractor, check that AC ⊥ BD and similarly for other squares that you drew on graph paper. From the above, we deduce that the diagonals of the square are perpendicular.

f

If M is the point of intersection of AC and BD, use the geometric instruments to check that MA = MB = MC = MD and similarly for other squares that you drew on graph paper. From the above, we deduce that the diagonals of the square bisect each other.

35 37

Drill 3:

A

Complete drawing the rectangle ABCD, then answer the following (consider the unit of length = 1 cm).

B

a

C

AB = …… = …… = …… cm and BC = …… = …… = …… cm i.e. In the rectangle, every two opposite sides are ……… in length.

b

m(∠B) = m(∠…) = m(∠…) = m(∠…) = …˚. i.e. In the rectangle, all angles are ……… in measure and the measure of each is ……˚.

c

From all the above, it can be said that the rectangle is a ……… that has ……… sides and every two opposite sides are ……… in length and ……… angles that are ……… in measure and the measure of each is ………˚ (check by drawing other rectangles on graph paper).

d

Use the geometric instruments to identify the relation between AC and BD and similarly for other rectangles that you drew on graph paper. i.e. In the rectangle, the diagonals are ……… in length.

e

Using the set-square, or the protractor, check that AC and BD are not perpendicular and similarly for other rectangles (not squares) that you drew on graph paper. i.e. The diagonals of the rectangle are not perpendicular.

f

36 38

If N is the point of intersection of AC and BD, use the geometric instruments to check that NA = NC and NB = ND and similarly for other rectangles that you drew on graph paper. i.e. The diagonals of the rectangle bisect each other.

Drill 4:

Without using graph paper or squared paper, can you draw a square, given its side length? Required: Draw the square ABCD whose side length 3 cm long.

A

B

8

8

7

7

6

6

5

5

4

4

3

3

2

C

2

1 0 0

D

1 1

2

3

4

5

0 0

1

2

3

4

5

A

3 cm

B

Notice and draw.

Drill 5:

Without using graph paper or squared paper, can you draw a D C rectangle, given its dimentions? Draw the rectangle ABCD in which AB = 5 cm and BC = 4 cm. A

4 cm

B

4 cm

A

Notice and draw.

B

5 cm

Drill 6:

L D

A Figure 1 B

C

E

F

Figure 2 Figure 3

Z Y

N

M

37 39

a

Is figure 1 a rhombus? ……… Why? ……………………… Because AB ≠ ……………

b

In figure 1, AB // ……… and AD // ……… i.e. Each two opposite sides are ………………………………… • The figure is called a parallelogram.

c

Is figure 2 a parallelogram? ……… Why? ……………………… Because XY // ……, but XL is not parallel to …… • This figure is called a trapezium.

d

Is figure 3 a parallelogram? ……… Why? ……………………… Because MN // …… and MF // ……

e

In figure 3, MN = NE = …… = …… i.e. Figure 3 is a quadrilateral and its sides are ……… in length. • This figure whose four sides are equal in length is called a rhombus.

Drill 7:

Join each figure to the suitable name.

Rectangle

Rhombus

Parallelogram

Trapezium

Square Triangle

Exercise 2 1

Join each figure to the suitable name.

Rectangle

38 40

Trapezium

Triangle

Rhombus

Square

Parallelogram

2

Put (✔) for the correct statement and (✗) for the incorrect one and correct the wrong statement. a The angles of a rectangle are right. ( ) b The sides of a square are equal in length. ( ) c The opposite sides of a parallelogram are parallel. ( ) d The measure of any angle of the square = 45˚. ( ) e Any of the four angles formed from the intersection of two straight lines is a right angle. ( ) f Any angle of the four angles formed from the intersection of two perpendicular straight lines is a right angle. ( ) g Two parallel straight lines are two non-intersecting straight lines. ( ) h Two perpendicular straight lines on the same straight line are intersecting straight lines. ( ) i The two diagonals of the square are perpendicular. ( )

3

Draw the square ABCD with side length 4 cm, then complete. a AB = …… = …… = …… = …… cm. b AB // …… and BC // …… c AB ⊥ ……, CD ⊥ …… and BD ⊥ ……

4

Draw the rectangle XYZL in which its two dimensions are 5 cm and 2 cm, then complete. a XY = …… = …… cm and YZ = …… = …… cm. b XY // …… and XY ⊥ …… c YZ // …… and YZ ⊥ ……

5

Complete the following. In the quadrilateral: a Each two opposite sides are parallel in ………, ………, ……… and ……… b Each two opposite sides are equal in length in ………, ………, ……… and ……… c The four sides are equal in length in ……… and ……… d The four angles are right in ……… and ……… e The two diagonals in ……… and ……… are equal and bisect ……….

39 41

Lesson 3

The Triangle

Drill 1:

A Notice the figure opposite, then complete. a The sides of the triangle ABC are C AB, …… and …… b The vertices of the triangle are A, … and … B c The angles of the triangle ABC are ∠A, ∠… and ∠… d The triangle is ……… (a polygon , an open curve), it has … sides and … angles.

Identifying the Type of the Triangle According to the Measure of its Angles

Drill 2:

Notice the following triangles, then complete. D

A

B

C Figure 1

a

E

F Figure 2

X

Z

Y Figure 3

In ∆ABC, ∠……… is a right angle, for that the triangle is called a right-angled triangle.

Question: Can you draw a triangle with two right angles? b

In ∆DEF, its three angles are ………, for that the triangle is called an acute-angled triangle.

c

In ∆XYZ, ∠……… is an obtuse angle, for that the triangle is called an obtuse-angled triangle.

Question: Can you draw a triangle with two obtuse angles?

40 42

Identifying the Type of the Triangle According to the Length of its Sides

Drill 3:

Notice the following triangles, then complete. A

D

E

F

X

B

C

Figure 1

Y

Z

Figure 2

Figure 3

a

In figure 1, use the compasses to check that DE = DF. This triangle is called an isosceles triangle.

b

In figure 2, use the compasses to check that AB = BC = CA. i.e. the three sides of the triangle are ……… in length. This triangle is called an equilateral triangle.

Questions c

Is the equilateral triangle Isosceles? …………… Is the isosceles triangle equilateral? ……………

In figure 3, use the compasses to check that the three sides of the triangle are different in length. This triangle is called a scalene triangle.

Drill 4:

Notice the following triangles, then complete. X

A C

a b

B

Z

Y

F

N

D

E

K

What is the type of the ∆ABC according to its: side lengths? ………… angles measures? ………… What is the type of the ∆XYZ according to its: side lengths? ………… angles measures? …………

M

41 43

c d

What is the type of the ∆DEF according to its: side lengths? ………… angles measures? ………… What is the type of the ∆NKM according to its: side lengths? ………… angles measures? ………… Drawing a Triangle given the Length of two Sides and the Measure of the Included Angle

Drill 5:

Draw ∆ABC in which AB = 5 cm, BC = 4 cm and m(∠B) = 60˚. A

B

C 4 cm

A

B A

Notice and draw.

5 cm

60˚

Exercies 1

Draw ∆XYZ in which XY = 7 cm, YZ = 5 cm and m(∠Y) = 40˚.

Exercies 2

Draw ∆DEF in which ∠D is right, DE = 3 cm and EF = 4 cm. Measure the length of DF, then answer the following questions. a Calculate the perimeter of ∆DEF, given that the perimeter of any polygon = the sum of its side lengths. b What is the type of the triangle, according to the measures of its angles? …………… (acute-angled , obtuse-angled or right-angled) c What is the type of the triangle, according to the length of its sides? …………… (isosceles , equilateral or scalene)

42 44

B

Drawing a Triangle Given the Measure of Two Angles and the Length of One Side

Drill 6:

Draw ∆ABC in which BC = 4 cm, m(∠B) = 30˚ and m(∠C) = 80˚. Notice and draw.

A

C

80˚

30˚ 4 cm

B

The Sum of Measures of the Angles of the Triangle

Drill 7: a b c

Draw any triangle on a piece of cardboard paper. Colour the angles of the triangle at its vertices in red, green and yellow as shown in the figure opposite. Use the scissors to cut the three angles and fix them on a piece of paper as shown in the figure.

Notice:

The three angles together formed a straight angle and we know that the measure of the straight angle is 180˚. Then, we deduce that:

The sum of measures of the interior angles of any triangle = 180˚.

Drill 8:

Draw the triangle ABC in which ∠B is a right angle, m(∠C) = 60˚ and BC = 4 cm. Measure ∠A, then check that the sum of measures of angles of a triangle is 180˚.

43 45

Drill 9:

Draw ∆XYZ in which = XY = 7cm, m(∠X) = 100˚, and m(∠Y) = 50˚. Measure (∠Z), then answer: a What is the sum of the measures of angles of ∆XYZ? ………˚ b What is the type of the triangle XYZ according to the measures of its angles? ………

Drill 10:

Use the two set-squares in your geometric instruments box to draw two triangles as shown in the figure opposite, then answer: C

a

b c

B

Z

X

Y A

Measure the angles of each triangle, then complete. i The sum of the measures of angles of ∆ABC equals ………˚ + ………˚ + ………˚ = ………˚ ii The sum of the measures of angles of ∆XYZ equals ………˚ + ………˚ + ………˚ = ………˚ What is the type of ∆ABC according to its side lengths? ……… (scalene , equilateral , isosceles) What is the type of ∆XYZ according to its side lengths? ……… (scalene , equilateral , isosceles)

Exercies 3 1

44 46

Put (✔) for the correct statement and (✗) for the incorrect one and correct the wrong statement. a There can be two right angles in one triangle. ( ) b There can be three acute angles in one triangle. ( ) c There can be a right angle and an obtuse angle in one triangle. ( ) d The measure of the straight angle = the sum of the measures of the angles of a triangle. ( )

2

Draw ∆LMN in which MN = 6 cm, m(∠M) = 40˚ and m(∠N) = 70˚. a Without using the protractor, find m (∠L). b What is the type of the triangle according to the measures of its angles? c What is the type of the triangle according to its side lengths? (measure the lengths of the sides)

3

Draw ∆XYZ in which XY = 5 cm, m(∠X) = m(∠Y) = 45˚. a Without using the protractor find m(∠Z). b What is the type of the triangle according to the measures of its angles? c What is the type of the triangle according to its side lengths? (measure the lengths of its sides)

4

Draw ∆ABC in which AC = 7 cm, m(∠A) = 45˚, and m(∠C) = 75˚. a Calculate, mentally, m(∠B), then check your answer using the protractor. b What is the type of the triangle according to the measures of its angles? c What is the type of the triangle according to its side lengths? (measure the lengths of the sides)

5

Draw ∆DEF in which DE = 5 cm, EF = 6 cm and m(∠B) = 80˚. a What is the sum of the measures of the two angles ∠FDE and ∠DFE? b use the protractor to find m(∠DFE). c Calculate m(∠FDE). (without measuring) d What is the type of ∆DEF according to the measures of its angles and its side lengths?

45 47

Lesson 4

Applications

Question How to make a solid using cardboard paper?

Drill 1:

You can make a cube-shaped box without a lid as follows. a Draw a square of (choose a proper side length, for example 30 cm, on cardboard paper. b Divide the large square into 9 small squares, as in the figure. c Use the scissors to cut the four blue squares in the four corners of your drawing. d Fold the remaining figure on the dotted lines e Glue the edges, to get the solid opposite (a cube-shaped box without a lid).

Drill 2:

You can make a cuboid-shaped box with a lid by drawing a figure with suitable dimensions (as in the figure opposite) on cardboard paper, fold on the dotted lines then glue the edges to get the resulted solid as in the figure below.

46 48

Drill 3:

You can make a pyramid with square-shaped base by drawing a figure with suitable dimensions as in the figure on cardboard paper, fold on the dotted lines then glue the edges and you will get the solid opposite.

Exercies 4

1

a b c d e f g

A On the lattice, draw the square ABCD whose side length is 4 cm. Draw AC and BD. Into how many triangles was the square ABCD divided? Are these triangles congruent? Divide each of these triangles into B two congruent triangles. Colour the resulted triangles in two different colours consecutively to get an ornamental nice figure. With the aid of your teacher, use the â&#x20AC;&#x2DC;Paintâ&#x20AC;&#x2122; program in your computer to do the final figure.

2

The figure opposite represents a rectangular-shaped hall. Its two dimensions are 6 m and 8 m. Two types of tiles were used to tile the hall as shown in the figure. Complete tiling in the same pattern, then answer the questions. a How many squared tiles are needed? b How many rectangular tiles are needed?

3

A square-shaped room of side length 4 metres. On squared paper, design a pattern of your choice where you use 2 or 3 different kinds of tiles to cover its floor.

47 49

Unit 2 Activities Activity 1 In the multimedia lab in your school and with the aid of your teacher, use the computer to draw the following geometric figures. a Rectangle b Square c Triangle d Other ornamental figures Activity 2 In the figure opposite, three straight lines intersect at three points. a What is the greatest number of intersection points can you get using four straight lines? b What is the greatest number of intersection points can you get using six straight lines? c What is the greatest number of intersection points can you get using six straight lines, if four of them are parallel? d What is the greatest number of intersection points can you get using ten straight lines, if seven of them are parallel?

48 50

General Exercises on Unit 2 1

Put (✔) for the correct statement and (✗) for the incorrect one and correct the wrong statement. a If ABC is a triangle in which m(∠B) = 98˚, then it is possible to be a right-angled triangle. ( ) b If XYZ is a triangle in which m(∠X) = 100˚ and m(∠Y) = 58˚, then m(∠Z) = 30˚. ( ) c The rhombus is a quadrilateral in which all sides are equal in length. ( ) d It is possible to draw a triangle given the measures of each of its angles. ( )

2

Join each figure to the suitable name.

Parallelogram

Rhombus

Rectangle

Square

Trapezium

3

Write only one difference between each of the following. a The square and the rectangle. b The triangle and the circle. c The rhombus and the parallelogram. d The square and the cube.

4

Draw The triangle ABC in which AB = 3 cm, BC = 4 cm and m(∠B) = 90˚. Measure the length of AC, then complete the rectangle ABCD and answer. a Calculate the perimeter of each of the rectangle ABCD and the triangle ABC. b What is the type of the triangle ABC according to: i its side lengths. ii the measure of its angles.

49 51

b c d

The triangle and the circle. The rhombus and the parallelogram. The square and the cube.

Unit Draw The triangle ABC2in Activities which AB = 3 cm, BC = 4 cm and m(∠B) = 90˚. Measure the length of AC, then complete Activitythe 1 rectangle ABCD and answer. In theamultimedia your school and with therectangle aid of your Calculatelab theinperimeter of each of the ABCD and teacher, use the computer the triangle ABC. to draw the following geometric figures. a Rectangle Square b What is the type of thebtriangle ABC according to: c Triangle ornamental i its side lengths. d Other ii the measure figures of its angles. 4

5 In the 2opposite figure ABCD is a parallelogram complete Activity 51 D figure E ⊥ ........ In the opposite, three straight 7 cm D A linesAintersect B ⁄⁄ ........at three points. a What is the ABED greatest number of 5 cm The shape is ......... intersection points can you get the perimeter of ABED is ......... using four straight lines? the perimeter of DEC is ....... b What is the greatest number of C B 4 cm E intersection points can you get using six straight lines? c What is the greatest number of intersection points can you get using six straight lines, if four of them are parallel? d What is the greatest number of intersection points can you get using ten straight lines, if seven of them are parallel?

50 50

Multiples Divisibility Factors and Prime Numbers Common Factors (H.C.F.) Common Multiples (L.C.M.) Unit 3 Activities General Exercises on Unit 3

Lesson 3 1 Factors and Prime Numbers Multiples Lesson 1 Multiples

9 10

First: Factors of the Number Drill We know1: that we can write a number in the form of the product of a or Complete the following table. two, more, numbers. •

With respect 0 1to the 2 number 3 4 56, we 6 can 7 write 8 9it as: 10 ×2 6 = 1 × 6 or 6 = 2 × 3, then the numbers 1, 2, 3 and 6 are 0 2 4 called the factors of the number 6.

3 •b 4 9 10 11

With theofnumber 35, we can write it as: 5 6respect Opposite is atoset consecutive 0 1 2 3 7 and 4 5 6 35 = 1 × 35 or 35 = 5 × 7, then the numbers 1, 5, 35 numbers arranged in a table. 12 13 7 8 9 10 11 12 13 are called factorsusing of thethe number 35. Completethe colouring 5 16 17 18 19 20 Complete. With respect to the number 12, 14we15can 16write 17 it18as:19 20 same pattern. 12 = 1 × ……, 12 = 2 × …… or 12 = 3 × ……, then the factors of the 12 are ………………………… c number Complete. es are 0, 2, 4, …… TheThe numbers written in thethe coloured are 0, Note: process of writing numbersquares in the form of 2, the4, …… y …… andproduct they are of numbers multiplication by …… of the tworesults or more is called factorization 2

of the number 2 of the number into factors. These numbers are called the multiples of the number 2

Drill mbers is 0, 2, 4, 61: Note: The unitseach digitofofthe each of these numbers is 0, 2, 4, 6 Complete1factorizing following numbers into factors 8. and write theor factors of each. s that you studied 2 Multiples of 2 are the even numbers that you studied a 18 = 1 × before. … = 2 × … = 3 × …, then the factors of the number 18 are ………

b Generally: 42 = 1 × …… = 2 × …… = 3 × …… = 6 × ……, then the uct is a multiple of of the 42by are Iffactors a number is number multiplied 2,…………… then the product is a multiple of c 24 = 1 × …… = 2 × …… =the 3 ×number …… = 24 × ……, then the factors of the number 24 are ……………

of the number 2 = 1 × …… = 2 × …… = 3 × …… = 4 × …… = 5 × …… = d 120 Example: 17 × 2 = 34, hence 34 is a multiple of the number 2 10 × ……, then the factors of the number 120 are ……………

52 62

53

53

3: Drill 2:

a Complete Complete the the following following table. table. a 5 ×3

0

1

0

5 3

2

3

4

5

6

b Opposite Opposite is is aa set set of of consecutive consecutive b numbers arranged arranged in in aa table. table. numbers Complete colouring colouring using using the the Complete same pattern. pattern. same

7

8

9 10

00 11 22 33 44 55 66 10 11 11 12 12 13 13 77 88 99 10 14 15 15 16 16 17 17 18 18 19 19 20 20 14 21 22 22 23 23 24 24 25 25 26 26 27 27 21 28 29 30 31 32 33 34

c Complete. c The Complete. numbers written in the coloured squares are 0, 3, 6, …… The they numbers written in the coloured squares are 0, 5, 10, …… and are the results of multiplication by …… and they are the results of multiplication by …… These numbers are called the multiples of the number 3 These numbers are called the multiples of the number 5 Generally: Generally: If Ifa anumber numberisismultiplied multipliedbyby5,3,then thenthe theproduct productisisa amultiple multipleofofthe thenumber number5 3 Example: Example:

32 ×× 35 == 63, 160,hence hence63160 a multiple of the number 21 is aismultiple of the number 3 5

Note: For the multiples of the number 5, the units digit of each of c Complete. d numbers 0 or 5 of 3 because 30 = …… × 3 The these number 30 is a is multiple The number 24 is a multiple of … because 24 = …… × 3 c Complete. 17 × 5 = …, then the number … is a multiple of the number 5 42 × 5 = …, then the number … is a multiple of the number 5

54

53 55

Drill2: 3: Drill

Completethe thefollowing followingtable. table. aa Complete ××35

10 00 11 22 33 44 55 66 77 88 99 10 00 35

Oppositeisisaaset setofofconsecutive consecutive bb Opposite numbersarranged arrangedininaatable. table. numbers Completecolouring colouringusing usingthe the Complete samepattern. pattern. same

00 11 22 33 44 55 66 10 11 11 12 12 13 13 77 88 99 10 14 15 15 16 16 17 17 18 18 19 19 20 20 14 21 22 22 23 23 24 24 25 25 26 26 27 27 21 28 29 30 31 32 33 34

c Complete. c The Complete. numbers written in the coloured squares are 0, 3, 6, …… Thethey numbers written in of themultiplication coloured squares are 0, 5, 10, …… and are the results by …… and they are the results of multiplication by …… These numbers are called the multiples of the number 3 These numbers are called the multiples of the number 5 Generally: Generally: IfIfaanumber numberisismultiplied multipliedby by5, 3,then thenthe theproduct productisisaamultiple multipleof ofthe thenumber number53 Example: 21 32××35==63, 160, hence a multiple of the number Example: hence 63160 is aismultiple of the number 3 5 For the multiples of the number 5, the units digit of each of cNote: Complete. these numbers is 0 or 5of 3 because 30 = …… × 3 The number 30 is a multiple The number 24 is a multiple of … because 24 = …… × 3 c Complete. d 17 × 5 = …, then the number … is a multiple of the number 5 42 × 5 = …, then the number … is a multiple of the number 5

54 54

55

Drill Drill4: 3:

The belowthe contains numbers a table Complete following table. from 0 to 49. ×0 5 10

10 1 2 2 3 3 4 45 0 512 11 13 14

65 7 68

97 10 8

9

15

16

17

18

19

20

21

25

26

27

28

29

22

23

24

0 137 2 38 3 439 5 6 30 31 is a32 34 35 36 Opposite set of33consecutive numbers in a table. 7 847 9 48 10 114912 13 40 41 arranged 42 43 44 45 46 Complete colouring using the 14 15 16 17 18 19 20 a Put a yellow point in the cells having a multiple of the number 2. same pattern. 21 22 of23the24number 25 263.27 Put a red point in the cells having a multiple Put a blue point in the cells having a multiple 28 29 of 30the 31number 32 33 5.34 b Complete. The numbers in the cells having yellow and red are …………………………………………………………… c points Complete. each of these numbers a multiple …… and the…… The numbers written inisthe colouredofsquares are…… 0, 5,at10, same timeare andthe is also considered a multiple of …… and they results of multiplication by …… c Complete. The numbers in the cells having yellow points only areThese …………………………………………………………………… numbers are called the multiples of the number 5 each of these numbers is a multiple of …… and it is not a multiple of …… or …… Generally: d If aComplete. numbers cells and blue number isThe multiplied by in 5,the then the having productyellow is a multiple of the points are …………………………………………………………… number 5 each of these numbers is a multiple of …… and …… at the same time a multiple of of …… Example: 32and × 5 is = also 160, considered hence 160 is a multiple the number 5 e Complete. The numbers in the cells having blue points only are ……………………………………………………………………… Note: For the multiples of the number 5, the units digit of each of eachthese of these numbers numbers is 0isora 5multiple of …… and is not a multiple of …… or …… c Complete. 17 × 5 = …, then the number … is a multiple of the number 5 42 × 5 = …, then the number … is a multiple of the number 5 b

56

55

Drill 2: a

Exercise 1

Complete the following table. 1 1 Underline Underline each each number number of of the the following following that that is is a a multiple multiple of of the the number 0 2: 5 ,, 64 10 number 2: 1 2 17 173 ,, 5 54 ,, 26 26 4 ,, 713 13 8,, 2 2 9,, 20 20 × 3 0 3 2 Underline 2 Underline each each number number 3: 3:

following following that that is is a a multiple multiple of of the the 3 3 ,, 10 10 ,, 12 12 ,, 22 22 0 1 2 3 4 5 6 b 3 Opposite is a set of consecutive 3 Underline Underline each each number number of of the the following following that that is is a a multiple multiple of of the the numbers arranged in a table. 7 8 9 10 11 12 13 number 23 number 5: 5: 23 ,, 15 15 ,, 40 40 ,, 51 51 ,, 5 5 ,, 8 8 ,, 20 20 Complete colouring using the 14 15 16 17 18 19 20 same pattern. 4 3 10 20. 4 Write Write all all the the multiples multiples of of the the number number21 3 between between 10 and and 20. 27 22 23 24 25 26

c

number number of of the the 4 4 ,, 15 15 ,, 21 21 ,,

5 5 Write Write all all the the multiples multiples of of the the number number 5 5 between between 14 14 and and 44. 44. Complete. numbers in of thethe coloured areless 0, 3,than 6, …… 6 The Write all the the written multiples numbersquares 2 that that are are 10. 6 Write all multiples of the number 2 less than 10. and they are the results of multiplication by …… 7 Write all the the multiples multiples of of the the number number 3 3 that that are are less less than than 20. 20. 7 Write all These numbers are called the multiples of the number 3 8 8 Write Write all all the the multiples multiples of of the the number number 5 5 that that are are less less than than 30. 30.

Generally: 9 9 Complete. Complete. If a12 number is multiplied by 3, then the12 product is a multiple of 12 = =3 3× × …… …… hence hence the the number number 12 is is a a multiple multiple of of …… …… the number 3 a multiple of …… and and also also considered considered a multiple of …… 28 28 = =7 7× × …… …… hence hence the the number number 28 28 is is a a multiple multiple of of …… …… Example: 21 × 3 = 63, hence 63 is a multiple of the number 3 and and also also considered considered a a multiple multiple of of …… …… 45 45 = =5 5× × …… …… hence hence the the number number 45 45 is is a a multiple multiple of of …… …… c Complete. and and also also considered considered a a multiple multiple of of …… …… The number 30 is a multiple of 3 because 30 = …… × 3 The number 24 is a multiple of … because 24 =that …… × less 3 10 10 Write Write the the multiples multiples of of the the two two numbers numbers 2 2 and and 5 5 that are are less than than 50. 50.

56 54

11 11 Write Write the the multiples multiples of of the the two two numbers numbers 2 2 and and 3 3 that that are are less less than than 30. 30.

57

12 Join3: each number to its multiples. 12 Drill a

2 3 following table. 5 Complete the

0 1 2 3 4 5 6 ×5 7, 8, 0 11 ,5 12 , 15 , 21 , 30

7

8

9 10

13 a 13

Write a number greater than 20 that is a multiple of the two numbers and and also a multiple 0 of 1 their 2 product 3 4 8. 5 6 b Opposite is a2set of 4consecutive b Write arranged a numberingreater than 20 that of the numbers a table. 7 is8a multiple 9 10 11 12 two 13 numbers 2 and 4 and not a multiple of their product 8. Complete colouring using the 14 15 16 17 18 19 20 same pattern. 14 Complete with the multiples of the number as 24 the 25 example. 14 21 221023 26 27 Example: 50 < 57 < 60 28 29 30 31 32 33 34 a …… < 24 < …… b …… < 11 < …… …… < 43 < …… d …… < 76 < …… c c Complete. e < 69 written < …… in the coloured f …… < 95 are < …… The…… numbers squares 0, 5, 10, …… and they are the results of multiplication by …… 15 Complete with the multiples of the number 5 as the example. 15 Example: 20 < 23 25 These numbers are< called the multiples of the number 5 a …… < 17 < …… b …… < 8 < …… c …… < 32 < …… d …… < 66 < …… Generally: …… < < …… by 5, then fthe …… < 94 If aenumber is 81 multiplied product is <a …… multiple of the number 5 16 If the number of pupils in a class is a multiple of the two 16 numbers32 2× and that is included between 30 and 40.number How 5 Example: 5 =3 160, hence 160 is a multiple of the many pupils are there in the class?

Note: For the multiples of the number 5, the units digit of each of 17 ringsisregularly 17 An alarm these clock numbers 0 or 5 every two hours, while another one rings every 3 hours. If the two alarms ring together at 12 at what time will they ring together after that? c o’clock, Complete. 17 × 5 = …, then the number … is a multiple of the number 5 42 × 5 = …, then the number … is a multiple of the number 5

58

57 55

Drill 2: Lesson 2 theDivisibility a Complete following table. 1 2 of 3 Divisibility 4 5 6 7 8 9 10 First:× 3The0Meaning Alaa and Yasmine 0 3 baught a bag of sweets to distribute it equally among them. Complete. • If the bag contains 5 pieces of sweets, then every one will take 2 pieces, and …… piece will be left. 0 1 2 3 4 5 6 b Opposite is a set of consecutive • If the bag contains 6 pieces of sweets, then every one will take numbers arranged in a table. 7 8 9 10 11 12 13 …… pieces, and nothing will be left in the bag. Complete colouring using the 17 18 19 i.e. When dividing 5 ÷ 2, the quotient is 214 and15the16remainder is 120 same pattern. When dividing 6 ÷ 2, the quotient is 321 and22the23remainder is zero 24 25 26 27 It is said that: in the first case, the number 5 is not divisible by 2. in the second case, the number 6 is divisible by 2. c Complete. Generally: The number that is divisibe by another, The numbers written in the coloured squares are 0, if3,the 6, …… division operation and they areremainder the resultsofofthe multiplication by ……is zero.

DrillThese 1: numbers are called the multiples of the number 3

Complete. a In dividing 7 ÷ 3, the quotient is …… and the remainder is ……, hence 7 is …………… by 3. Generally: b In dividing 20 ÷ 4, the quotient is …… and the remainder is If a number is multiplied by 3, then the product is a multiple of ……, hence 20 is …………… by 4. the number 3 Second: Multiples and divisibilty Example: 21 × 3 = 63, hence 63 is a multiple of the number 3 We know that 35 is a multiple of the number 5, because if we multilpy 7 by 5 the product will be 35 (5 × 7 = 35). To express this c Complete. meaning in another way that 35 is considered a multiple of the The number 30 is a multiple of 3 because 30 = …… × 3 number 5 because if we divide 35 ÷ 5 the quotient will be a whole The number 24 is a multiple of … because 24 = …… × 3 number 7 and the remainder will be zero. So, it is said that multiples of the number 5 are divisible by 5 and multiples of the number 7 are divisible by 7. Generally: All multiples of a number are divisible by this number.

58 54 60

Drill 2:

Complete as in the example. Example: a b c

3 × 4 = 12, then 12 is a multiple of each of the two numbers 3 and 4 and 12 is divisible by each of 3 and 4.

7 × 9 = ……, then …… is the multiple of each of …… and …… and …… is divisible by each of …… and …… 5 × 11 = ……, then …… is the multiple of each of … and …… and …… is divisible by each of …… and …… 3 × 7 = ……, then …… is the multiple of each of …… and …… and …… is divisible by each of …… and ……

Drill 3:

Complete as in the example. Example:

15 is not divisible by 2 because when we divide 15 ÷ 2, the remainder is 1, hence 15 is not a multiple of the number 2.

a

35 is not divisible by 3 because when we divide 35 ÷ ……, the remainder is ……, hence 35 is not a multiple of ……

b

28 is not divisible by 8 because when we divide …… ÷ 8, the remainder is ……, hence 28 is …………… of 8.

c

72 is …………… by 9 because when we divide …… ÷ ……, the remainder is ……, hence 72 is …………… of 9.

59

Generally: Drill 2:

A number divisible bytable. 2, if its units digit is 0 or any other even a 1Complete theisfollowing number.

0

1

0

3

2

3

4

5

6

7

8

9 10

2×3 A number is divisible by 5, if its units digit is 0 or 5. 3

A number is divisible by 3, if the sum of its digits is divisible by 3.

0 1 2 3 4 5 6 Opposite is a set of consecutive 2 8 9 10 11 12 13 numbers arranged in aExercise table. 7 Complete colouring using the 14 15 16 17 18 19 20 1 same Complete. pattern. a 35 ÷ 6 = ……… and the remainder ……… 21 22is23 24 25 26 27 b A number is divisible by 2 if its units digit is …………… c A number is divisible by 5 if its units digit is …………… c Complete. d numbers 34 ÷ 3written = ……… andcoloured the remainder is ………, 34 is The in the squares are 0, 3,then 6, …… by 3.of multiplication by …… and they…………… are the results b

2

Circle the numbers arethe divisible by 2. These numbers are that called multiples of the number 3 15 , 18 , 102 , 5224 , 6143

3 Circle the numbers that are divisible by 5. Generally: , 3123 , 1460 , by 2327 , 4265 If a125 number is multiplied 3, then the product is a multiple of the number 3 4 Circle the numbers that are divisible by 3. 33 , 1256 410hence , 1278 Example: 21 ×, 373 = 63, 63 is a multiple of the number 3 Write three numbers that are divisible by 2 and 5. c5 Complete. The number 30 is a multiple of 3 because 30 = …… × 3 6 The Write three 24 numbers that are by 3 and number is a multiple of divisible … because 24 =5.…… × 3 7

60 54

Write three numbers that are divisible by 2, 3 and 5.

61

Lesson 3 Lesson 3 Factors and Prime Numbers n 3 Factors and Prime Numbers

First: Factors of the Number Factors of thethat Number We know we can write a number in the form of the product of w that weor can writenumbers. a number in the form of the product of two, more, more, numbers. • With respect to the number 6, we can write it as: respect6to=the write as: 1 ×number 6 or 6 6, = 2we × can 3, then theit numbers 1, 2, 3 and 6 are 1 × 6 or called 6 = 2 the × 3,factors then the numbers 1, 6. 2, 3 and 6 are of the number ed the factors of the number 6. • With respect to the number 35, we can write it as: respect35 to = the number as:numbers 1, 5, 7 and 35 1× 35 or 35, 35 we = 5 can × 7,write then itthe 1 × 35 are or 35 = 5 the × 7,factors then the 1, 5, called of numbers the number 35.7 and 35 called the factors of the number 35. Complete. With respect to the number 12, we can write it as: e. With to 12 the=number it as: 12 = respect 1 × ……, 2 × ……12,orwe12can = 3write × ……, then the factors of ……, = 2 × …… or………………………… 12 = 3 × ……, then the factors of the12number 12 are ber 12 are ………………………… Note: The process of writing the number in the form of the The processproduct of writing the formisofcalled the factorization of the twonumber or moreinnumbers product of two numbers is called factorization of or themore number into factors. of the number into factors.

1:

Drill 1:

Complete factorizing each of the following numbers into factors e factorizing of the following and writeeach the factors of each. numbers into factors e the factors of each. a 18 = 1 × … = 2 × … = 3 × …, then the factors of the number 1 × … =182 are × ………… = 3 × …, then the factors of the number re ……… b 42 = 1 × …… = 2 × …… = 3 × …… = 6 × ……, then the 1 × ……factors = 2 × of …… 3 × ……42= are 6 × …………… ……, then the the=number ors of the number 42 are …………… c 24 = 1 × …… = 2 × …… = 3 × …… = 4 × ……, then the 1 × ……factors = 2 × of …… 3 × ……24= are 4 × …………… ……, then the the=number ors of the number 24 are …………… d 120 = 1 × …… = 2 × …… = 3 × …… = 4 × …… = 5 × …… = = 1 × …… × …… = the 3 × factors …… = 4of×the …… = 5 × 120 ……are = …………… 10 =× 2 ……, then number ……, 62 then the factors of the number 120 are …………… 61

Second: Drill 2: Prime Numbers a Complete the following table. Drill 2:

0 1 2 3 4 5 6 7 8 9 10 , 11 , 15 , 17. Find ×the 3 factors of each of the numbers: 4 , 7 , Complete the 0 solution. 3 a

4 = 1 × … = 2 × …, then the factors of the number 4 are ……

b 7 = 1 × …, then the factors of the number 7 are …… 0 1 2 3 4 5 6 bc Opposite is a set of consecutive 10 = 1 × … = 2 × …, then the factors of the number 10 are … numbers arranged in a table. 7 8 9 10 11 12 13 d Complete 11 = 1 × ……, then the factors of the number 11 are ………… colouring using the 14 15 16 17 18 19 20 e same 15 = 1 × … = 3 × …, then the factors of the number 15 are … pattern. 22 231724 26 27 f 17 = 1 × ……, then the factors of the21 number are25……… cFrom Complete. the above, the numbers 4, 10 and 15 have more than two The while numbers written in 7, the11coloured squares 0,factors 3, 6, …… factors the numbers and 17 have onlyare two (one are the of multiplication …… andand thethey number) andresults they are called Primebynumbers. These numbers are called the multiples of the number 3 Generally: The number that has only two factors is called a prime number. Generally: i.e. The prime number is divisible by itself and the whole one. If a number is multiplied by 3, then the product is a multiple of number 3 Note: The whole one is notthe a prime number. Example: Drill 3: 21 × 3 = 63, hence 63 is a multiple of the number 3 Discuss, which of the following numbers is considered a prime cnumber Complete. and which is not: 27, 5, 22, 13 and 19 , then complete. a multiple of 3 because 30 = …… × 3 a The Withnumber respect30 tois27: The a multiple … because 24 then = …… 3 It is number possible24 to iswrite 27 = 1 of × …… = 3 × ……, 27×has other factors than 1 and 27. So, it is not considered a ………

62 54

63

b

With respect to the number 5: Drill 2: It is impossible to write it in the form of the product of two

Complete as in the example. numbers except in the form of 5 = 1 × … or 5 = 5 × …, then the factors of the number 5 are only … and … So, it is a ……… Example: 3 × 4 = 12, then 12 is a multiple of each of the two c With respect to the3 number 22:12 is divisible by each of 3 and 4. numbers and 4 and It is possible to write 22 = 1 × …… = 2 × ……, then the number it has …………… a 22 7 ×is9a=…………… ……, then because …… is the multiple of each of …… and ……

and …… is divisible by each d With respect to the number 13:of …… and …… b It5is× impossible 11 = ……, then …… the multiple each of … andis…… to find twoisnumbers, the of product which 13 and …… is divisible by…………… each of …… and …… except … and …, then 3 × 7respect = ……,tothen ec With 19: …… is the multiple of each of …… and …… and …… is divisible by each of …… and …… ………………………………………………………………………… ………………………………………………………………………… Drill 3: ………………………………………………………………………… Complete as in the example.

Third: Factorizing the Number (non-prime) to its Prime Factors Example: is not divisible by 2tobecause we means divide 15 ÷ 2, We saw that 15 factorizing a number its primewhen factors, writing thethe remainder 1, hence a multiple of the this number in form of aisproduct of 15 twoisornot more numbers. number 2. Example: For example:Factorize the number 315 to its prime Factors .

Solution aa To a number 28 intowhen factors, is possible to write 35 factorize is not divisible by 3like because we itdivide 35 ÷ ……, the divide theaprime 28 = 4 ×we 7. is But 4 isthe notnumber a prime number, because it has3 more remainder ……, hence 35 isbynot multiple of …… 315 factors. factorize the number into105 its prime 2,3,5,7,..... according b than 28 istwo notnumbers divisibleSo, by to 8 because when we divide …… ÷38, the factors, we write 28 hence = 2 ×of228 × is 7,number because to the divisibility this byeach 352 and 5 7 is remainder is ……, …………… of 8.of 2, a prime factor. these prime . when we divide …… 7 ÷7……, c 72 is …………… by numbers 9 because b Also, to factorize the number 24 to its prime factors, we write the remainder is ……, hence 72 is …………… of 9.1 first 24 = 3 × 8. But 8 is not a prime number. So, we complete 315 = 3 × 3 × 5 × 7 the factorization, then 24 = 3 × 2 × 2 × 2.

Drill 4:

Factorize each of the following numbers to its prime factors. 15 , 12 , 9 , 26 and 36

64

63 59

Drill 2:

Exercise 2

a Complete the following table. 1 Find the factors of each of the following numbers. 0, 1 143 , 38 26 ,2 753 4 5 6 7 8 9 10 × 0 3 2 Complete. a A prime number has two factors that are …… and …… 0 1then 2 the 3 factors 4 5 of 6the b 16 =is1 a× set …… 2 × …… = 4 × ……, b Opposite of =consecutive number 16 arein………………………… numbers arranged a table. 7 8 9 10 11 12 13 c 1 is not considered prime number because ……………… Complete colouring usingathe 14 15 16 17 18 20 d 3pattern. is considered a factor of the numbers ……… and19 ……… same 21 22 23 24 25 26 27 3 State which of the following is a prime number. 2 , 7 , 25 , 29 , 34 , 57 c Complete. The numbers written in the coloured squares are 0, 3, 6, …… 4 and Factorise each the following numbersbyto…… its prime factors. they are the of results of multiplication 12 , 18 , 23 , 36 These numbers are called the multiples of the number 3 5 Find the number whose prime numbers are 2, 2 and 3. 6 Find the number whose prime numbers are 2, 5 and 7. Generally: If a number is multiplied by 3, then the product is a multiple of the number 3 Example: c

64 54

21 × 3 = 63, hence 63 is a multiple of the number 3

Complete. The number 30 is a multiple of 3 because 30 = …… × 3 The number 24 is a multiple of … because 24 = …… × 3

65

Common Factors for Two or Common Factors for Two or Factors for TwoLesson or Lesson 4 Common 4 4 Lesson more Numbers and Highest 4 more Numbers more Numbers and Highest and Highest Common Factor (H.C.F.) Common Common Factor (H.C.F.) Factor (H.C.F.) Drill 1: Drill 1: Complete.

Complete. Factors 30 of the number 303 are 16,, 210 , ,3 … , 5, , … 6 , 10 , … , … e number are 1 , 2 , , 5 , Factors of number 30 11 ,, 22 ,, 34 ,, 55for ,, 68 ,, Two 10 ,, … Common Factors Factors 40 of the the number 404are are 10 ,, … …or … e number are 1 , 2 , , 5 , 8 , 10 , … , … Factors ofthat the number 40 of arethe 1number , 2 , 430 , and 5 , 8at, the 10 same , … , time … Lesson 4the Numbers are factors more Numbers and Highest at are factors of number 30 and at the same time Numbers are factors of the and at the same time factors 40 of that the number 40 are 1, ,number …… , 30 …… , …… e number are 1 , …… , …… …… Common (H.C.F.) factors of the number 40 are 1 ,Factor ……factors , …… , for …… These numbers are called common the two numbers. ersThese are called common factors for the two numbers. numbers are called common The highest of these common factorsfactors is …… for the two numbers. of The these common factors is …… of these common factorscommon is …… factor for the two Drill So,10ithighest is1: saidhighest that 10 is the highest that is the common factor for the factor two So, it is said that 40 10 and is the highest common for the two Complete. numbers 30 and is symbolized as H.C.F. and 40 and is symbolized as H.C.F. numbersof30 and 40 and symbolized Factors the number 30isare 1 , 2 , as 3 ,H.C.F. 5 , 6 , 10 , … , … Factors of the number 40 are 1 , 2 , 4 , 5 , 8 , 10 , … , … Generally: Generally: Numbers that are factorsfactor of the(H.C.F.) numberfor 30aand at numbers the same istime The highest common set of the st common factor (H.C.F.) for a set of numbers is the The highest common factor a set of numbers factors of the number 40that areall 1(H.C.F.) , …… ,for…… , …… highest number the numbers are divisible by.is the est numberhighest that allnumber the numbers are divisible by. thatcommon all the numbers arefor divisible These numbers are called factors the twoby. numbers. Example (1)of: these Find the H. C. Ffactors for theisnumbers 30 , 40 The highest common …… Drill 2: Solution Drill So, it the is 2: said thatfor 10the is the highest common factor forthem the two Find H.C.F. numbers 30 and 40them by factorizing to C.F.Find for the numbers 30 and 40 by factorizing to 30 2 40 2 the H.C.F. 30 andas40H.C.F. by factorizing them to numbers 30factors. andfor 40the andnumbers iscomplete. symbolized theirThen, prime Then, actors. complete. 15 factors. 3 20 2 their prime Then, complete. 30 = 2 × 3 × …… 3 ×30…… 5 10 2 = 22 ×× 532 ×× …… Generally: 30 = 2 × 3 × 5 40 = 2 × …… 2 ×402 = × …… 12 common 5 (H.C.F.) 540 = 2 × 2 × × 2 × ……factor The highest for a=set numbers 40 2= ×of × 5 × 2 is×the 2 H.C.F. for the numbers 30 and …… …… e numbers 30 and 40 = 2 × …… = …… H.C.F. for the numbers 30 and 2 × …… 140 = highest number that all the numbers divisible H.C.F. = are 2=×…… 5 = 10 by. Example: Find thenumbers H.C.F. for the numbers 9 , 12 and 15. Find the H.C.F. for the 9 , 12 and 15. Example: the H.C.F. for the numbers 9 , 12 and 15. Drill 2:theFind Complete solution. e solution. Find the H.C.F. for the numbers 30 and 40 by factorizing them to Complete the solution. 9 =prime 3 ×factors. …… Then, complete. their …… 9 = 3 × …… 12 ×==…… × …… 30 23 ×× 3…… × …… …… 12 = 3 × …… × …… 15 == 23 ×× 2…… 40 × 2 × …… …… 15 = 3 × H.C.F. …… for the numbers 9 , 12 and 15 = ……… H.C.F. numbers ,3012and 40 15 = 2= × …… = …… H.C.F. for for thethe numbers and ……… H.C.F. for9the numbers 9 , 12 and 15 = ………

66 66 Example:

Find the H.C.F. for the numbers 9 , 12 and 15.

Complete the solution.

65

Exercise 4

Drill 2:

a Complete the following table. 1 Find three common factors for 8 and 16. 0 1 2 3 4 5 6 7 8 9 10 ×3 0 3common factors for 12 and 28. 2 Find three 3 Facorize each of the two numbers 6 and 15 to their prime factors, then findofthe H.C.F. for them.0 1 2 3 4 5 6 b Opposite is a set consecutive numbers arranged in a table. 7 8 9 10 11 12 13 4 Complete Completecolouring the following usingtable the as the example. 14 15 16 17 18 19 20 same pattern. Division Quotient Remainder 21 22 23 Divisibility 24 25 26 27 operation

c

Example

65 ÷ 4

16

1

65 is not divisible by 4

Complete.57 ÷ 7 The numbers in the coloured squares are 0, 3, 6, …… 21 ÷ written 3 and they are the results of multiplication by …… 75 ÷ 9

These numbers are called the multiples of the number 3 a Find all the factors for each of the numbers 16 and 20. b Find the common factors for the numbers 16 and 20. c Find the H.C.F. for the numbers 16 and 20. Generally: 5

If a number is multiplied by 3, then the product is a multiple of 6 Find the H.C.F. for eachthe of the following sets of numbers. number 3 a 20 and 30 b 35 and 49 c 12 21 and× 16 24, 40 of and Example: 3 = 63, hence 63 is d a multiple the56number 3 e 15, 18 and 21 f 6, 7 and 8 c Complete. 7 If the H.C.F. for two numbers is 7, then what are the two The number 30 is a multiple of 3 because 30 = …… × 3 numbers? Give three possible answers. The number 24 is a multiple of … because 24 = …… × 3

66 54

67

or 5 CommonCommon MultiplesMultiples for Two for or Two Lesson n 5Lesson more Numbers and Lowest more5Numbers and Lowest CommonCommon MultiplesMultiples (L.C.M.) (L.C.M.)

know thatnumbers each of the numbers 18, … is for a multiple for thatWe each of the 6, 12, 18, … 6, is a12, multiple numbers and 3. that So, iteach is said that each of these bersboth 2 and 3. So, it2 is said of these numbers is numbers is common for the numbers 2 and 3. on amultiple formultiple the numbers 2 and 3. theisnumber 15 for is aboth multiple for both numbers 3 and 5. the Similarly, number 15 a multiple numbers 3 and 5. So, it is a common multiple for the numbers and45, 5. Also 30, 45, common multiple for the numbers 3 and 5. Also330, 60, … are common multiples for the numbers 3 and 5. common multiples for the numbers 3 and 5.

: Drill 1:

reach70. the number 70. leteatill Complete you reach till theyou number multiples 5 (up to …………, 70) are 0, 70 5, …………, 70 multiplesThe of the numberof5the (upnumber to 70) are 0, 5, multiples 7 (up to …………, 70) are 0, 70 7, …………, 70 multiplesThe of the numberof7the (upnumber to 70) are 0, 7, common multiples for the numbers 5 and 7. rlinebtheUnderline common the multiples for the numbers 5 and 7. c Are all these common multiples for the product l these common multiples alsomultiples multiplesalso for the product of 5 × 7 (i.e. multiples for35)? the number 35)? 7 (i.e. multiples for the number

: Drill 2:

reach24. the number 24. leteatill Complete you reach till theyou number multiples 2 (up to …………, 24) are 0, 24 2, …………, 24 multiplesThe of the numberof2the (upnumber to 24) are 0, 2, multiples 4 (up to …………, 24) are 0, 24 4, …………, 24 multiplesThe of the numberof4the (upnumber to 24) are 0, 4, common multiples for the numbers 2 and 4. rlinebtheUnderline common the multiples for the numbers 2 and 4. c Are all these common multiples for the product l these common multiples alsomultiples multiplesalso for the product of 2 × 4 (i.e. multiples for8)? the number 8)? 4 (i.e. multiples for the number

: Drill 3:

reach60. the number 60. leteatill Complete you reach till theyou number multiples 2 (up to …………… 60) are 0, 2, …………… multiplesThe of the numberof2the (upnumber to 60) are 0, 2, multiples 3 (up to …………… 60) are 0, 3, …………… multiplesThe of the numberof3the (upnumber to 60) are 0, 3, multiples 5 (up to …………… 60) are 0, 5, …………… multiplesThe of the numberof5the (upnumber to 60) are 0, 5, btheUnderline common multiples for the rlineb common the multiples for the numbers 2, 3numbers and 5. 2, 3 and 5.

68

67

c What is the smallest common multiple (other than zero) for the Drill 2: numbers 2, 3 and 5? (This number is called the lowest a

Complete the following table. common multiple for the numbers 2, 3 and 5) 0 1 2 3 4 5 6 7 8 9 10 ×3 The lowest common multiple for a set of numbers is the 0 3 smallest number (other than zero) that is divisible by each of these numbers, then it is a multiple for each of these numbers individually and is abbriviated 0 as1 L.C.M. 2 3 4 5 6 b Opposite is a set of consecutive numbers arranged in a table. 7 8 9 10 11 12 13 Complete colouring using the Example: Find the L.C.M. for 4 , 12 and 14 15. 15 16 17 18 19 20 same pattern. Complete the solution. 21 22 23 24 25 26 27 Multiples for the number 4 are 0, 4, 8, ……………………………… Multiples for the number 12 are 0, 12, ……………………………… c Complete. Multiples for the number 15 are 0, 15, ……………………………… The numbers written in the coloured squares are 0, 3, 6, …… The lowest common multiple for the numbers 4 , 12 and 15 and they are the results of multiplication by …… (other than zero) is …… Then, the L.C.M. for the numbers 4 , 12 and 15 is ……… These numbers are called the multiples of the number 3 Another solution using factorization to the prime factors. 4 = 2 × 2 Generally: 12 = 2 × 2 × 3 If a number is multiplied by 3, then the product is a multiple of 15 = 3 × 5 the number 3 L.C.M. Example:

2 × 2 × 3 × 5 = 60 21 × 3 = 63, hence 63 is a multiple of the number 3

Then, L.C.M. for the numbers 4 , 12 and 15 is 60. c Complete. The number 30 is a multiple of 3 because 30 = …… × 3 The number 24 is a multiple of … because 24 = …… × 3

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Drill 2:

Exercise 5

Complete as in the example. 11 Write three multiples for the number 7. Example: 3 × 4 = 12, then 12 is a multiple of each of the two 2 common multiples numbersby6 each and 10. 2 Write three numbers 3 and 4 andfor 12 the is divisible of 3 and 4.

33a 4

Write three common multiples for the numbers 2, 7 and 10. 7 × 9 = ……, then …… is the multiple of each of …… and …… Find theiscommon between 50 …… and 100 for the and all …… divisible multiples by each of …… and b numbers: 5 × 11 = ……, then …… is the multiple of each of … and …… aand3 …… and 5is divisibleb by4each and 6 c …… 2, 7 and 8 of …… and 3 × 7 = ……, then …… is the multiple of each of …… and …… 5c aand Write the multiples for the number 3 up to 63. …… is divisible by each of …… and …… b Write the multiples for the number 7 up to 63. c Write all the common multiples for the numbers 3 and 7 Drill 3: up to 63. Complete as in the example. d Write the L.C.M. for the numbers 3 and 7.

not divisible by 2number because when we divide 15 ÷ 2, a Write15 theismultiples for the 2 up to 60. 66Example: is 1, hence 15 is nottoa 30. multiple of the b Writethe theremainder multiples for the number 3 up 2. c Writenumber the multiples for the number 5 up to 30. d Write all the common multiples for the numbers 2, 3 and 5 to 30. a 35 up is not divisible by 3 because when we divide 35 ÷ ……, the eremainder Write theis L.C.M. for the35 numbers 3 and 5. ……, hence is not a 2, multiple of ……

b a28 Factorize is not divisible 8 because we18divide 8, the 7 each by of the numberswhen 8 and to its …… prime÷factors. ……, hence is …………… of 8. bremainder Find theisL.C.M. for the 28 numbers 8 and 18. c 72 is …………… by 9 because when we divide …… ÷ ……, 8 Find the L.C.M. for each of the following sets of numbers. the remainder is ……, hence 72 is …………… of 9. a 2, 3 and 4 b 3, 4 and 5 c 2, 6 and 7 d 3, 6 and 7 9 If you know that the lowest common multiple for two numbers is 24, what are the two numbers (give more than one answer). 10 Find the L.C.M. for the numbers (5 × 7 × 13) and (2 × 5 × 11). 11 Find the L.C.M. for the numbers (2 × 3 × 5 × 7) and (3 × 3 × 7).

70

69 59

d e

Write all the common multiples for the numbers 2, 3 and 5 up to 30. Write the L.C.M. for the numbers 2, 3 and 5.

Drill Factorize each ofExercise the numbers 8 5 and 18 to its prime factors. 7 7 a 2: a 1 8 8 2

Complete theL.C.M. following table. b Find the for the numbers 8 and 18. Write three multiples for the number 7. 0 1 2 3 4 5 6 7 8 9 10 Find × 3 the L.C.M. for each of the following sets of numbers. Write common a 2, three 3 0and3 4 b 3,multiples 4 and 5 for c the 2,numbers 6 and 7 6dand3,10. 6 and 7

3 multiples for themultiple numbers 7 and 10. 9 If you three know common that the lowest common for2,two numbers 9 Write is 24, what are the two numbers (give more than one answer). 0 501 and 2 100 3 for 4 the 5 6 4 Find all the multiples between b Opposite is common a set of consecutive 10 Find the L.C.M. for in thea numbers (5 × 77 × 13) (2 ×115 ×1211). 10 numbers: numbers arranged table. 8 and 9 10 13 a 3 and colouring 5 b 4 and c 2, 7 and 8 using the 6 17 (3 18× 19 11 Find the L.C.M. for the numbers (2 × 14 3 × 15 5 × 16 7) and 3 × 20 7). 11 Complete same pattern. to 63. 22 23 24 25 26 27 705 a Write the multiples for the number213 up b Write the multiples for the number 7 up to 63. c Write all the common multiples for the numbers 3 and 7 c Complete. up to 63. The numbers written for in the d Write the L.C.M. the coloured numberssquares 3 and 7.are 0, 3, 6, …… and they are the results of multiplication by …… 6 a Write the multiples for the number 2 up to 60. bThese Writenumbers the multiples are called for the thenumber multiples 3 up of to the30. number 3 c Write the multiples for the number 5 up to 30. d Write all the common multiples for the numbers 2, 3 and 5 Generally: up to 30. If ea number Write the is multiplied L.C.M. forby the 3,numbers then the 2, product 3 and is5.a multiple of the number 3 7 a Factorize each of the numbers 8 and 18 to its prime factors. b Find21 the× L.C.M. the numbers 8 and 18. Example: 3 = 63,for hence 63 is a multiple of the number 3 8 Find the L.C.M. for each of the following sets of numbers. c Complete. a 2, 3 and 4 b 3, 4 and 5 c 2, 6 and 7 d 3, 6 and 7 The number 30 is a multiple of 3 because 30 = …… × 3 9 The If younumber know that lowest common multiple 24 for =two numbers 24 isthe a multiple of … because …… ×3 is 24, what are the two numbers (give more than one answer). 10 Find the L.C.M. for the numbers (5 × 7 × 13) and (2 × 5 × 11). 11 Find the L.C.M. for the numbers (2 × 3 × 5 × 7) and (3 × 3 × 7).

70 70 54

Unit 3 Activities Activity 1 Find: a the common multiple of all numbers. b the common factor of all numbers. Activity 2 First: Complete the following table. 1

2

3

4

5

2

4

6

8

10

3

6

9

12

4

8

12

5

10

6

7

8

9

10

11

12

6 7 8 9 10 11 12 Second: Using the table above, complete the following. a The number 108 is divisible by …… and …… b The number …… is divisible by 11 and 12. c The number 54 is considered a common multiple for the two numbers …… and …… d Multiples of the number 12 that are less than 150 are ……… e The number 11 is considered one of the factors of the numbers ……………

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General Exercises on Unit 3 1

Join each number from group a with the suitable phrase from group b. a 15 24 28 39

b

divisible by 7

divisible by 3

divisible by 13

divisible by 5

2

Put (✔) for the correct statement and (✗) for the incorrect one and correct the wrong statement. a The number 63 is divisible by 6. ( ) b The number 17 is a prime number. ( ) c 0 and 7 are multiples of the number 7. ( ) d The H.C.F. for the two numbers 8 and 24 is 4. ( ) e The L.C.M. for the two numbers 8 and 24 is 8. ( )

3

Complete. a The multiples of the number 6 which are between 20 and 40 are ……… b The factors of the number 35 are ………

4

Find: a the H.C.F. for the numbers 24 and 36. b the L.C.M. for the numbers 7 and 9.

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The Length The Area Unit 4 Activities General Exercises on Unit 4

Lesson 1

The Length

You know that the centimetre (cm) and metre (m) are units used for measuring length. The metre (m) = 100 centimetres (cm)

Drill 1:

Complete. a The metre …… the centimetre b 3 metres = …… centimetres c 4 metres = …… centimetres d …… metres = 700 centimetres e …… metres = 300 centimetres

(< , > or =) 1 cm

The centimetre (cm) = 10 millimetres (mm)

Drill 2:

complete. a 3 centimetres = …… mm b 2 cm = …… mm c …… cm = 40 mm d …… cm = 60 mm e …… m = 400 cm = …… mm f Arrange the units of length ascendingly (cm , m , mm) …… , …… , ……

Drill 3:

Choose the suitable unit to measure each a Thickness of an electric wire. (mm , b Length of the classroom. (mm , c Length of the playground. (mm , d The height of a lamppost. (mm ,

74

of the following. cm , m) cm , m) cm , m) cm , m)

Figure number

Figure name

Side length

Sum of side lengths (Perimeter)

1

Square

1 cm

1 + 1 + 1 + 1 = 1 × 4 = 4 cm

2

…………

… cm

… + … + … + … = … × … = … cm

3

…………

… cm

… + … + … + … = … × … = … cm

4

…………

… cm

… + … + … + … = … × … = … cm

From the previous we deduce that: perimeter of a square = side length × ……

Drill 7:

Use the relation between the perimeter of the square and its side length to complete. a Perimeter of a square of side length 9 cm = … × … = …… cm b Perimeter of a square-shaped piece of land of side length 10 m = …………… = ……… c Perimeter of a square-shaped piece of paper of side length 2 dm = …………… = …… dm = …… cm

Drill 8:

Notice the following rectangles, then complete ( consider the unit of length = 1 cm).

1

76

2

3

4

Rectangle Length Width number

Sum of side lengths (Perimeter)

1

5

4

5 + 5 + 4 + 4 = 5 × 2 + 4 × 2 = (5 + 4) × 2 =18 cm

2

4

…………

4 + 4 + … + … = 4 × 2 + … × 2 = (4 + …) × 2 =… cm

3

…………

2

… + … + 2 + 2 = … × 2 + 2 × 2 = (… + 2) × 2 =… cm

4

………… ………… … + … + … + … = … × 2 + … × 2 = (… + …) × 2 =… cm

From the previous we deduce that: The perimeter of a rectangle = (……… + width) × ……

Drill 9:

Complete. a The perimeter of a rectangle whose length is 7 cm and width 3 cm = (…… + ……) × …… = …… cm b The perimeter of a rectangle whose dimensions 6 m and 3 m = (…… + ……) × …… = …… metre Example: Calculate the perimeter of a rectangle of dimensions 3 dm and 50 cm. Solution: 3 dm = 30 cm, then the perimeter of the rectangle equals (30 + ……) × …… = …… cm Note: To calculate the perimeter of a figure whose dimensions are in different units, you have to make the dimensions in the same unit.

Drill 10: The kilometre (km) = 1000 meters (m) Complete. a 3 km = …… m c 8 km = …… m = …… dm

b d

9000 m = …… km 4 km = …… m = …… cm

Drill 11:

A rectangular-shaped piece of land with dimensions 3 km and 2 km, it is needed to be surrounded by a wire fence. The cost of one metre of wire fence equals 8 pounds what is the total cost of the fence? Solution: Perimeter of land = (… + …) × 2 = …… km = …… m Cost of fence = …… × …… = …… pounds

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Exercise 1 1

Put (✔) for the correct statement and (✗) for the incorrect one and correct the wrong statement. a The perimeter of the square = side length + 4. ( ) b The perimeter of a rectangle = (length + width) + 2. ( ) c The decimetre > the metre. ( ) d The millimetre < the centimetre. ( ) e If the dimensions of a rectangle are 3 cm and 5 cm, then half its perimeter equals 8 cm. ( )

2

Arrange the units of length in ascending order. centimetre , decimetre , millimetre , kilometre , metre

3

Choose the suitable unit to measure each of the following. a The distance between Cairo and Alexandria. (mm, dm, km) b The height of a building. (mm, dm, m) c The height of a man. (km, cm, mm) d The length of an ant. (km, mm, m)

4

Choose the closest answer. a The length of a taxi = ……… (2 km, 20 m, 200 cm) b The length of my pen = ……… ( 12 km, 15 dm, 15 cm) c The height of my brother = ……… (3 m, 160 cm, 160 mm) d My mother bought a piece of cloth of length = ……… (3 km, 3 m, 3 cm, 3 mm) e In my house, there is a squared room of side length = …… (5 m, 5 cm, 5 mm, 5 km)

5

Calculate the perimeter of each of the following. a A square of side length 3 dm. b A rectangle whose length is 12 cm and width 5 cm. c A rectangle whose length is 3 dm and width 25 cm. d A rectangle whose dimensions are 2 m and 150 cm.

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6 Calculate, in centimetres, the side length of a square whose perimeter is 4 dm. 7 The perimeter of a rectangle is 86 cm, and its length is 23 cm. Find its width: a in centimetres. b indecimetres. 8 The sum of the perimeters of two squares is 100 dm. If the side length of one of them is 8 dm, find the side length of the other square. a in decimetres b in centimetres 9 It is wanted to make a frame to a rectangle-shaped picture whose dimensions are 400 cm and 500 cm. If the cost of one metre of the frame is 3 pounds, what is the cost of the frame? 1

10 The width of a rectangle-shaped piece of land equals 3 of its length. Calculate its perimeter if its width equals 15 metres. 11 Calculate the perimeter of each of the following. a A rectangle-shaped room whose dimensions are 4 m and 3 m. b A rectangle-shaped picture frame whose dimensions are 5 dm and 20 cm. c A rectangle-shaped bed sheet whose dimensions are 2 m and 150 cm. d A rectangle-shaped room door whose length is 18 dm, and width 1 metre. e A square-shaped window of side length 15 dm. 12 Notice the drawn figure, imagine that you cut the red part, calculate the perimeter of the remaining part (consider that the side length of the small square is 1m). 13

The figure represents a rectangular piece of land, its dimensions are 70 m and 50 m and a squared playground, its side is 30 m long is constructed inside it. If the shaded part is surrounded by a wire from inside and outside, find the length of the wire in each case.

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Lesson 2

The Area Preface

Areas of the figures like squares, rectangles, triangles, … etc, are measured by units of area, In this lesson, you will know some of these units.

Drill 1:

Notice the following figures, each figure is divided into equal parts, units of area.

Figure 1 Figure 2 Complete the following table:

Figure 3

Figure number

Number of equal parts (area of figure)

1

……………

2

……………

3

……………

Question Can you determine, which of the previous figures is greater in area? why? To compare the areas of some figures, you have to calculate the area of each using the same unit. So, we are in need of standard units, One of these units is the square centimetre and its symbol is cm2. Then, what is the square centimetre?

80

Drill 2:

Notice the shaded figure opposite to recognize the square centimetre cm2, then complete. cm2 is the area of a square of side length ……

Drill 3:

Notice the following squares and count the square centimetres which form each square (number of small squares), then complete as the example.

cm2

1

2

3

Square Number of small Side length of number squares (cm2) square Example 1 4 cm2 2 cm

Notes 4=2×2

2 3

Given that the area of the square = Number of the small squares (cm2), then complete: a Area of square 1 = 4 cm2 = 2 cm × 2 cm b Area of square 2 = … cm2 = … cm × … cm c Area of square 3 = ……… = … cm × … cm From the previous, we deduce that: Area of the square = side length × ……

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Drill 4:

Using the previous relations, complete. a Area of square of side length 9 cm = …… × …… = …… cm2 b Area of square of side length 2 cm = …… × …… = ……… c Perimeter of a square is 24 cm Side length of the square = …… ÷ 4 = …… cm (Why?) Area of the square = …… × …… = ……………

Drill 5:

Notice the following rectangles and calculate the number of square centimetres (small squares) in each figure, then complete.

cm2

1 Rectangle number Example

2 Number of square centimetres (area)

3 Rectangle Rectangle length

width

length × width

1

6 cm2

3 cm

2 cm

3 cmx × 2 cm = 6 cm2

2

……

……

……

…… × …… = ……

3

……

……

……

…… × …… = ……

From the previous, we deduce that:

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Area of the rectangle = ……… × ………

Drill 6:

Use the previous relation between the area of the rectangle and its dimensions, then complete. a Area of rectangle whose length is 9 cm and width 6 cm equals …… cm × …… cm = …… cm2. b Area of rectangle whose dimensions are 3 cm and 8 cm equals …… × …… = …………… c The perimeter of a rectangle is 18 cm and its width 3 cm 1 length + width = 2 perimeter = …… cm We know that width = 3 cm, then length = … – … = …… cm Then, area of rectangle = …… × …… = …………… d The length of a rectangle is 12 cm, which is twice its width. 1 width of rectangle = 2 length = …… cm Then, area of the rectangle = …… × …… = …… cm

Drill 7:

The figure opposite represents a rectangle whose dimensions are 10 cm and 6 cm with a square of side length 5 cm inside it. Calculate: 1 the area of the shaded part. 2 the perimeter of the shaded part.

6 cm

5 cm

10 cm

Drill 8:

We knew that the square centimetre (cm2) is the area of a square of side length 1 cm. Use the same pattern to write mathematical statements to show the meaning of the following units of area. a the square metre (m2) is the area of a square of side length ……… (m2 = 1 m × 1 m) b The square kilometre (km2) is the area of …… whose side length …… (km2 = ……… × ………) c The square decimetre (dm2) is …… (dm2 = ……… × ………)

83

Drill 9:

Use the relations you got in the previous drill, and complete. a m2 = 1 m × 1 m = 100 cm × 100 cm = 10 000 cm2 b km2 = …… km × …… km = …… m × …… m = …… m2 c dm2 = …… dm × …… dm = …… cm × …… cm = …… cm2 From the previous, we deduce that: The square decimetre = 100 cm2 The square metre = 100 dm2 = 10 000 cm2 the square kilometre = 1 000 000 m2

Drill 10:

Choose the suitable unit to measure each of the following. a Area of the floor of the room. (km2 , dm2 , cm2 , m2) b Area of the agricultural land in Egypt. (km2 , dm2 , cm2 , m2) c Area of the surface of a book page. (km2 , cm2 , m2) d Area of the playground of your school. (km2 , cm2 , m2 , dm2) e Area of the eastern desert. (km2 , cm2 , dm2)

Drill 11:

Choose the closest answer. a Area of the flat which I live in is …… (75 km2 , 75 cm2 , 75 m2 , 75 dm2) b Area of the classroom in our school is …… (24 m2 , 24 cm2 , 24 km2) c A pupil in Primary 4 used his geometric instruments to draw a rectangle whose area is …… (12 m2 , 12 dm2 , 12 cm2) d Area of the tile used in tilling our house is …… (25 dm2 , 25 cm2 , 25 m2)

84

Exercise 2 1

Put (✔) for the correct statement and (✗) for the incorrect one and correct the wrong statement. a The square metre (m2) is a unit of measurement used to measure the perimeters of figures. ( ) b The decimeter (dm) is a unit of measurement used to measure the areas of the figures. ( ) c The millimetres (mm) is a unit of measurement used to measure the lengths of the things. ( ) d Area of square = side length × 4 ( ) e Area of rectangle whose length is 2 dm and width 5 cm is ( ) 100 cm2. f Area of a square-shaped piece of land of side length 3 km is 9 million m2. ( )

2

Complete.

3

a

3 cm = …… mm

b

5 dm = …… cm

c

2 km = …… m

d

2 m = …… cm

e

50 mm = …… cm

f

850 cm = …… dm

g

4 200 mm = …… dm

h

8 000 cm = …… m

i

6 000 m = …… km

j

3 km = …… m

b

7 m2 = …… cm2

d

2 700 dm2 = …… m2

f

6 000 000 m2 = …… km2

Complete. a c e

3 m2 = …… dm2 1 2

km2 = …… m2

90 000 cm2 = …… m2

85

4

Complete using a suitable sign <, >, or = in each

.

a

3 km

c

5 000 mm

e

Area of square of side length 8 cm Area of rectangle whose dimensions are 9 cm and 8 cm.

f

Area of rectangle whose dimensions are 3 dm and 7 cm Area of square of side length half a metre.

300 m 5 metres

b

8 dm

80 cm

d

7 km

75 000 cm

5

The figure opposite is a rectangle whose dimensions are 9 cm and 6 cm. A square of side length 4 cm is cut from it. Calculate:

6 cm

9 cm

4 cm 2 cm

3 cm

a

the area of the remaining part by two different methods.

b

the perimeter of the remaining part.

6

The length of a rectangle is three times its width. If its perimeter is 64 cm, find its area in cm2.

7

The perimeter of a square is 28 cm, find its area.

8

If the sum of the perimeters of two squares is 48 cm, and the side length of one of them is 7 cm. Find: a the side length of the second square. b the sum of their areas.

9

A rectangle-shaped hall whose dimensions are 8 m and 6 m. How many tiles are needed to tile this hall, given that the side length of the required square-shaped tiles is 20 cm?

86

Unit 4 Activities Activity 1 1 cm In the figure opposite, 15 dots are arranged in the form of a lattice such 1 cm that the horizontal and vertical distances between every two adjacent dots, vertically or horizontally, are equal. Consider that the distance between every two adjacent points is 1 cm, then answer the following questions. a How many squares can be drawn such that the vertices of each coinside with these dots, and its area equals: ii 2 cm2 iii 4 cm2 i 1 cm2 b How many rectangles can be drawn such that the vertices of each coinside with these dots, and its perimeter equals: i 6 cm ii 8 cm iii 10 cm Activity 2 Notice and deduce. a Find the area of the coloured part and also its perimeter (consider that the side length of the small square is 1 cm). b If the previous figure is drawn three times, you will get the figure below. What is the area of this new figure? What is its perimeter?

c

If you imagine that we drew the original figure 20 times using the same previous way (on a large paper), what is the area of the resulted figure? What is its perimeter?

87

General Exercises on Unit 4 1

Complete using a suitable sign <, >, or = in each a c

2

6 metres 1 2

km2

650 cm 25 000 m2

.

b

10 dm

1 metre

d

81dm2

6 400 cm2

Choose the suitable unit of measurement for each of the following life situations. a

Measuring the heights of the pupils. (square centimetre , millimetre , centimetre , kilometre)

b

Calculating areas of the walls in a house. (m , cm2 , km2 , m2)

c

Calculating the perimeter of a piece of land allocated for building a new city in facing the problem of over-population. (m , km2 , km , cm2)

d 3

4

88

Calculating the distance between the earth and the moon. (cm , m , km , km2) Complete. a

The condition of congruency of two squares is ……

b

Area of rectangle = ………………………… and perimeter of square = …………………………

c

If the dimensions of a rectangle are 8 cm and 5 cm, then its area = …………………………

d

If the perimeter of a square = 24 cm, then its area = ………

The dimensions of a rectangle are 90 cm and 40 cm. If the area of the rectangle equals the area of a square find the perimeter of the square in decimeters.

General Exercises Exercise 1 1

Find the result of the following. a 587 692 + 401 203 = …………… b 9 806 735 – 8 805 524 = …………… c 35 867 d 9 000 000 + 8 954 – 278 456 ………… ……………

2

Complete using a suitable sign <, >, or = in each . a 3 × 15 90 ÷ 2 b 4 × 13 3 × 17 c Measure of the acute angle Measure of the right angle. d Measure of the straight angle Measure of the obtuse angle. e Area of the rectangle whose dimensions are 4 cm and 15 cm Area of the square of side length 8 cm.

3

a

Join each figure to the suitable name.

Rhombus

b

Trapezium

Parallelogram

Rectangle

Square

Find the H.C.F. and L.C.M. for the numbers 6 and 8.

4

Draw the triangle ABC in which BC = 4 cm, m(∠B) = 70˚ and m(∠C) = 50˚, then answer. a Without using the protractor, calculate m(∠A). b What is the type of ∆ABC with respect to the measures of its angles.

5

Hesham has LE 20 000, he bought a bedroom suite for LE 8 750 and a reception suite for LE 6 250. Find the remainder.

89

Exercise 2 1

Put ( ) for the correct statement and ( ) for the incorrect one and correct the wrong statement. a 549 467 + one hundred thousand = 559 467 ( ) b 8 256 344 – three thousand = 8 256 044 ( ) c 906 ÷ 3 = 302 ( ) d 65 × 8 = 800 ( ) e The sum of measures of angles of a triangle = 180˚( ) f The L.C.M. for the two numbers 12 and 30 is 60. ( )

2

Complete using a suitable sign <, >, or = in each . a 4 × 16 100 ÷ 2 b 3 milliard 965 752 812 c Area of the square of side length 3 dm Area of the rectangle whose dimensions are 90 cm and 10 cm. d Perimeter of a square of side length 5 cm Perimeter of an equilateral triangle of side length 7 cm. e Measure of the straight angle Sum of the measures of the angles of a triangle.

3

Find:

4

Draw the triangle ABC, right-angled at B where BC = 8 cm and AB = 6 cm. Determine the mid-point M of AC.

5

Join each ﬁgure to the suitable name.

a b

Rhombus

90

the L.C.M. for the two numbers 6 and 8. the H.C.F. for the two numbers 45 and 60.

Parallelogram

Trapezium

Exercise 3 1

Complete. a 65 348 475 – three hundred thousand = ……… b The value of the digit 4 in the number 546 789 = ……… c The L.C.M. for the numbers 4 and 8 is ……… d The H.C.F. for the numbers 6 and 30 is ……… e The side length of a square whose perimeter is 36 cm = ..... ………

2

Complete using a suitable sign <, >, or = in each . a 3 407 805 + 92 716 3 500 521 – 1 b 256 × 4 256 × 5 c 9 600 ÷ 5 9 600 ÷ 4 d Perimeter of a square of side length 2 m Perimeter of a rectangle whose dimensions are 24 dm and 16 dm.

3

Draw the rectangle ABCD in which BC = 4 cm and AB = 3 cm. Draw AC and BD where M is their point of intersection.

4

Factorize each of the two numbers 24 and 30 to its prime factors, then find: a the L.C.M. for 24 and 30. b the H.C.F. for 24 and 30.

91

Exercise 4 1

Complete. a 3 287 500 + 713 250 – 3 000 750 = ……… b If 13 × 45 = 585, then 585 ÷ 45 = …… and 587 = 45 × …… + …… c The value of the digit 3 in the number 3 721 014 is …… d 4 × 765 × 25 = …… e (25 × 8) – 150 = ……

2

Put (✔) for the correct statement and (✗) for the incorrect one and correct the wrong statement. a If ABC is a triangle in which m(∠A) = 70° and m(∠B) = 20°, then it is an acute-angled triangle. ( ) b The square is a quadrilateral in which all angles are right and all sides are equal in length. ( ) c The rectangle is a quadrilateral in which all angles are right. ( ) d In a parallelogram, every two opposite sides are not parallel. ( )

3

Complete: a The number 105 is divisible by ... and also divisible by... b The H.C.F. of 16 and 24 = …… c The L.C.M. of 14 and 10 = …… d The factors of 45 are …… e 14 a day = …… hours

92

Exercise 5 1

Choose the correct answer. a 7 251 309 + 748 691 = …… (8 milliard , 8 million , 8 thousand) b 5 000 000 – 324 067 = …… (95 324 076 , 91 675 933 , 4 675 933) c 8 × 641 × 125 = ... (641 thousand , 641 hundred , 641 million) d The number 2 100 is divisible by …… (35 , 11 , 13 , 17) e XYZ is a triangle in which m(∠X) = 40° and m (∠Y) = 30°, then ∆XYZ is …… triangle. (a right-angled , an obtuse-angled , an acute-angled) f The L.C.M. of 15 and 35 is …… (15 , 105 , 35 , 5)

2

Draw the square XYZL whose side length 3 cm. Join its diagonals XZ and YL.

3

a b c d e

4

a b

Multiples of 6 are ……, …… and …… Prime factors of 350 are ……, …… and …… The perimeter of a rectangle whose dimensions are 7 cm and 11 cm = ………………………… = …… cm The H.C.F. of 18 and 30 is …… 1 4 of a day = …… hours = …… minutes. Calculate 2 106 425 + 894 075 – 3 000 500. Find the number that if subtracted from 256 412 307, then the remainder will be 255 million.

93

General revision on the Mathematics syllabus for Fourth form Primary - for the first term 1 Complete each of the following :

1. The Smallest 7-digit number is ............

2. The Smallest different 6-digit number is ............ 3. The greatest 7-digit number is ............

4. The greatest 5-digit number is ............

5. The million is the smallest number formed from ............ digits.

6. Without repeating digits , the greatest number formed from the digits : 0 , 3 , 2 , 5 , 1 , 6 is ............ 7. Ten million is the smallest number formed from ............ digits. 8. 49 Ă&#x2014; 830 = ............

In the Exercises (9 â&#x2020;&#x2019; 15) , the place value of the digit 9. 6 in the number 2641 ............

10. 4 in the number 54678 ............

11. 2 in the number 762618 ............

12. 8 in the number 73985241 ............ 13. 7 in the number 54365724 ............

14. 5 in the number 135649728 ............ 15. 3 in the number 2834571 ............

16. Rewrite the following numbers using the digits : (a) 2 million , 37 thousand , 9 (b) 24 million , 35 thousand , 47 (c) 4 million , 7 thousand , 706 (d) 5 million , one thousand (e) 4 million , five hundred and thirty eight. (f) 45 million , 30 thousand , 99 (g) 32 million , 8 thousand , 15 (h) 6 million , 727 thousand , 704 (j) 71 million , 354 thousand , 12 17. 350 tens = ............ hundreds.

18. 15 0000 = ............ hundreds.

19. 3092000 = ............ million , ............ thousand. 20. 342 million = ............ thousand.

21. 240 thousand = ............ hundreds = ............

22. L.C.M of the numbers 36 , 24 and 12 is ............

94

23. H.C.F of the numbers 35 , 42 and 28 is ............

Exercise 5

1

2 3

4

24. The greatest number formed from the digits 5 , 8 , 4 , and 9 is ............

25. The place of the answer. digit 3 in the number 8 376 542 is ............ Choose thevalue correct prime numbers that are included between 2 , 30 is ............ a 26.7The 251 309 + 748 691 = …… 27. The prime numbers that lie between and 10 is ............ (86 milliard , 8 million , 8 thousand) number prime067 factors 2 , 3 and 5 is ............ b 28.5The 000 000whose – 324 = are …… , 552324 , 175076 , 577 ,, 546 29. From the numbers 865 , 570(95 91 675 933 , 4 675 933) Complete the following : c 8 × 641 × 125 = ... (a) Numbers that are divisible by 2 are ............ (641 thousand , 641 hundred , 641 million) (b) Numbers that are divisible 5 are ............ d The number 2 100 is by divisible by …… (35 , 11 , 13 , 17) (c) Numbers that are divisible 10 are ............ e2 XYZ is a triangle in which m(∠X) = 40° and m (∠Y) = 30°, Choose the correct answer : ∆XYZ issmallest …… number triangle. 1.then The million is the formed from ............ digits. a. 3 (a right-angled , an b. 7 obtuse-angled , anc.acute-angled) 4 f 2.The L.C.M. of 15 and 35inisthe…… (15is ............ , 105 , 35 , 5) The digit which represents million number 46835714 a. 6

b. 8

c. 3

Draw XYZL whose side length 3 cm. Join its 3. 50the × 40 square = ............ hundreds. a. 2 b. 200 c. 2000 diagonals XZ and YL. 4. 805 × 100 = ............ × 10 a. 85 8050 Multiples of 6 are ……,b.……

c. 250 and …… ............ 28 hundreds. 5.Prime 280 tens factors of 350 are ……, …… and …… a. > b. < c. = The perimeter of a rectangle whose dimensions are 7 cm 6. The value of the digit 8 in the number 587627 is ............ and 11 cm = ………………………… = …… cm a. 80 000 b. 800 000 c. 8000 d 7.The H.C.F. of 18 and 30 is …… 150 thousands = ............ 1 e 4a. 150 of a =thousands …… minutes. c. 1500 hundreds tensday = …… hours b. 15

a b c

a b

8. Three millions , three thousands and three is ............ Calculate 2 106 425 b.+ 30 894 a. 300 3003 300 075 – 3

000 500. c. 3030 ............256 412 307, then 9.Find The value the digit 7 inthat the number 40735126 isfrom theofnumber if subtracted a. 7 million b. 70 million. thousand c. 700 thousand the remainder will be 255

10. 71 million , 354 thousand and 12 a. 71354120 b. 7135412 11. 365274 ............ 359876 a. >

12. 30 × 40 ............ 20 × 60 a. < 13. 6934 + 3359 = ............

c. 71354012

b. <

c. =

b. >

c. =

95 93

a. 12093

14. 5 million ............ 500 000 a. <

b. 10293

c. 20193

b. >

c. =

15. The value of the digit 8 in the number 1096835 is ............ a. 8 b. 800 16. ............ is one of the factors of the number 8 a. 16 b. 4 17. 70 × 20 = 14 × ............ a. 10

18. 40 × 500 ............ 20 × 10 a. >

c. 8000 c. 20

b. 100

c. 1000

b. =

c. <

19. The numbers 1 , 5 , 7 are ............ a. even b. odd

20. 54 is a number that is divisible by ............ a. 4 b. 6 21. The number ............ is divisible by 5 a. 495 b. 594

c. prime c. 7 c. 54

3 Find the result of each of the following : a. 879156 + 498068 = ............ b. 608467 - 129585 = ............ c. 2525 ÷ 25 = ............

d. 4803 × 67 = ............

e. 471564 + 126469 = ............ f. 738594 – 153037 = ............

4 Solve the following problems :

1. Factorize the number 120 to its prime factors. 2. Underline the numbers that are divisible by 2 and 3 , 1926 – 3431 – 3330 – 2112 – 1064 3. In a certain year the profit of one factory was L.E. 7316 , if the profit is distributed equally among 31 workers , find the share of each worker 4. Find the result of 502 × 6 , 502 × 90 , then deduce the product of 502 × 96 5. Find a prime number lies between 11 and 37 6. Find L.C.M , H.C.F for the numbers 12 and 15 7. A hotel contains 204 rooms divided equally by a number of floors , each floor contains 17 rooms. How many floors are there in this hotel ? 8. Draw D ABC right at B , where BC = 4 cm. , AB = 3 cm. , Write the type of this triangle according to its side lengths. 9. Using the geometric instruments - Draw D XYZ in which XY = 7 cm. , YZ = 5 cm.

96

,m(

2 3

5 Put the suitable relation (< , > or =) :

............ 652 × 5 1. 652 × 4 square Draw the XYZL whose side length 3 cm. Join its 2. The area of a square of side length 6 ............ the area of rectangle whose dimensions diagonals XZ , and YL.

a b c d e

4

4 cm

5 cm

1

Exercise 5

XYZ) = 40° 10. If the sum of two perimeters of two squares is 88 cm. and if the side length of one of , then find : the two squares is 12 cm. Choose the correct answer. (a) The side length of the other square. a 7(b)251 309 + 748 691 = …… The difference between the areas of the two squares. , 8 thousand) , ( milliard 11. Draw D ABC in which AB = 5 cm.(8 B) = 90° ,,BC8=million 5 cm. , then complete : ............ b 5(a)000 000 – 324 067 = …… AC = cm. (b) The perimeter of D ABC(95 = ............ 324cm. 076 , 91 675 933 , 4 675 933) type×of125 the D = ABC c 8(c)×The 641 ... according to its side lengths is ............ (d) The type of the D ABC according to the measures of its angles is ............ (641 thousand , 641 hundred , 641 million) 12. Draw the square ABCD of side length 4 cm. , Join its diagonals AC , BD to intersect d The 2 of 100 is divisible , 17) at M ,number Find the area the square ABCD by …… (35 , 11 , 613 cm e 13.XYZ is a triangle in which m(∠X) = 40° and m (∠Y) = 30°, The opposite figure : Shows∆XYZ a rectangle another one. then is drawn ……inside triangle. (a) Find area of the shaded (atheright-angled , part. an obtuse-angled , an acute-angled) (b) Find the difference between the perimeters of the two rectangles f The L.C.M. of 15 and 35 is …… (15 , 105 ,5 cm 35 , 5)

are 4 cm. 6 cm. 3. 12 500 ÷ 5 ............ 10 × 25 Multiples of 6 are ……, …… and …… 4. 678345 ............ 578344 + 100 000 factors of 350angle are............ ……, ……of the angle of a 5.Prime The measure of the straight the…… sum ofand the measure triangle. The perimeter of a rectangle whose dimensions are 7 cm 6.and The measure the………………………… right angle ............ the measure of=the…… obtusecm angle. 11 cmof = ............ 7. 2 0000 ÷ 4 2 000 ÷ 4 The H.C.F. of 18 and 30 is …… ............ The perimeter of an 8. The 1 perimeter of a square of side length 6 cm. of a day = …… = …… minutes. triangle of side hours length 7 cm. 4equilateral 9. 4 milliard ............ 40 × 1000 000

a 10.Calculate 425 + 894 075 – 3 000 500. 6 × 15 ............ 902÷ 106 2 ............ 40 that 6 × 4 milliard × 1000if000 b 11. Find the number subtracted from 256 412 307, then 12. 6 × 70 × 10 ............ 5 tens × 100 the remainder will be 255 million. ............ 13. 200 – 120 160 ÷ 2 2 14. 800 dm . ............ 8 m2. 15. 3 meters , 5 centimeters ............ 350 cm. 16. The value of the digit 4 in the number 94876 ............ the value of the digit 8 in the number 94876.

6 Choose the correct answer : 1. The numbers 2

, 3 , 5 , 7 are called ............ numbers.

( prime – odd – even )

97 93

( 45 – 90 – 150 )

2. The measure of any angle of a square equals ............

3. The two perpendicular straight lines form 4 ............ angles. 4. The number of the factors of the prime number is 5. The number ............ is a prime number.

( a cute – right – obtuse )

............

( one – two – three )

( 15 – 17 – 21 )

6. Number of sides of any polygon does not equal number of its ............

( diagonals – angles – vertices )

7. If the perimeter of an equilateral triangle is 12 cm. , then its side length is ............ cm. ( 3 – 36 – 4 ) 8. 3

1 km. = ............ m. 2

( 35 – 3500 – 350 )

9. L.C.M for the numbers 8 , 12 is ............

( 24 – 48 – 4 )

10. The value of the digit 3 in the number 736542 is ............ ( thousands – ten thousands – hundred thousands – millions ) 11. The number

............

is divisible by each of 2 and 5.

12. The prime number after the number 399 is

............

( 72 – 25 – 100 )

( 400 – 401 – 403 )

13. The diagonals of the square are ............ ( equal in length and not perpendicular – perpendicular but not equal in length – equal in length and perpendicular)

98

Exercise Model (1) 5

1

2 3

1 Complete each of the following :

, 45 million , 473 thousand is written in digits as ............ 1. The number 3 milliardanswer. Choose the correct prime number whose sum = of its factors 6 is ............ a 2.7The 251 309 + 748 691 …… 3. The prime number has only ............ (8factors. milliard , 8 million , 8 thousand) 1 m2. ............ . 5. of a day = ............ hour. b 4.53 000 000 dm – 2324 067 = …… 3 (95 324 076 , 91 675 933 , 4 675 933) dimension of a=door c 6.8If×the641 × 125 ... in the form of a rectangle are 180 cm. , 10 dm. , then its perimeter = ............ cm. (641 thousand , 641 hundred , 641 million) d2 Choose The the number 2 100: is divisible by …… (35 , 11 , 13 , 17) correct answer ............ The number is a common multiple m(∠X) for the two=numbers e 1.XYZ is a 15 triangle in which 40° and m (∠Y) = 30°, a. 2,5 b. 3,4 c. 5,3 then ∆XYZ is …… triangle. 2. The diagonals are equal in length in ............ (a right-angled , an obtuse-angled , an acute-angled) a. square and rectangle b. parallelogram and rectangle f The L.C.M. 15 and 35 is (15 , 105 , 35 , 5) c. rectangle and of rhombus d. square and…… rhombus 3. The value of the digit 5 in the number 5612816 is ............ Drawa.the square XYZLb.whose thousand million side length c. tens 3 diagonals XZthousands and YL. d. hundred

a b c d 3 e

4

a 4 b

4. ............ is a common multiple for all numbers Multiples of 6 are ……, a. zero b. 1 …… and c.…… 10

cm. Join its d. 100

............ 5.Prime The milliard is the smallest formed from factors of 350number are ……, …… anddigits. …… a. 7 perimeter of a b. 8 c. 9 dimensions d. 10 The rectangle whose

36 cm2. is ............

are 7 cm

6.and The perimeter square whose area 11 cmof=a ………………………… = …… cm a. 24 cm. b. 144 cm. c. 1296 cm. d. 72 cm.

The H.C.F. of 18 and 30 is ……

1 the result of each of the following : Find of a day = …… hours = …… minutes. (a)48752013 + 439815 = ............ (b) 7256312 – 7056300 = ............ (c) 436 × 59 = ............ (d) 15408 ÷ 36 = ............

Calculate

2 106 425 + 894 075 – 3 000 500.

(a) Factorize the two numbers 24 , 30 to their prime factors , then find Find the number that if subtracted from 256 412 307, 1. H.C.F 2. L.C.M the remainder willABbe= 6255 (b) Draw D ABC in which cm. ,million. m ( B) = 60° , BC = 4 cm. , then 1. By using the ruler find the length of AC 2. State the type of D ABC according to its side lengths.

then

5 (a) Find the greatest and the smallest number formed from 6 digits using the following digits : 7 , 0 , 2 , 5 , 9 , 4 then Calculate the difference between them. (b) Eman bought 24 meters of cloth for L.E. 648 find the price of one metere.

99 93

1 Complete each of the following :

Model (2)

1. The smallest number formed from 7 digits from the digits 5 , 8 , 4 , 7 , 0 , 2 , 3 is ............ 2. The area of the square whose side length 5 cm. is ............

3. The value of the digit 3 in the number 3721014 is ............ 4. The value of the digit 3 in the number 3721014 is ............ 5. The two diagonals are equal in length in ............

, ............

6. If the dimension of a door in the form of a rectangle are 180 cm. , 10 dm. , then its perimeter = ............ cm.

2 Choose the correct answer :

1. L.C.M for the numbers 20 and 12 is ............ ( 2 or 4 or 30 or 60 ) ............ 2. The smallest prime number is ( 1 or 2 or 3 or 5 ) ............ 3. 7251309 + 7489691 = ( 8 milliards or 8 millions or 8 thousands or 8 hundreds ) , 4. If 45 × 13 = 585 then 589 = 45 × 13 + ............ ( 2 or 4 or 30 or 60 ) , 5. If the perimeter of a square is 28 cm. then its side length is ............ ( 7 or 14 or 4 or 12 ) , , 6. A rectangle its dimensions are 3 cm. 7 cm. then its perimeter = ............ ( 7 or 17 or 20 or 40 )

3 Complete using (< , > or =) : 1. 4 cm2. ............ 400 cm2. 3. 5 km. ............ 500 m. 5. 3 × 14 ............ 90 ÷ 2

2. 8 dm. ............ 80 cm. 4. 300 ............ 3 milliard 6.

1 of a day ............ 12 hours. 6

4 (a) Draw D ABC in which AB = 7 cm. , m ( A) = 45° , m ( C) = 75° ,

Find the area of the shaded part

(b) In a school if 756 pupils are distributed equally on 18 classes. Find number of pupils in each class

100

8 cm

5 (a) In the opposite figure :

6 cm

Find m ( B). Write the type of the triangle according to the measure of its angles. (b) Find H.C.F , L.C.M for 24 and 30

6 cm 9 cm

1

1 Choose the correct answer :

Exercise Model (3) 5

, fivecorrect 1. Ten million hundred seventy two thousand = ............ Choose the answer. 10507200 or 10510072 or 105721 or 10572000 ) a 7 251 309 + 748 691( = …… 2. The triangle whose length of its sides 3 cm. , 7 cm. , and 5 cm. is ............ (8 milliard , 8 million , 8 thousand) ( scalene triangle or equilateral triangle or isosceles triangle ) b The5number 000 ............ 000 –is324 067 =multiples …… of all numbers. ( 0 or 2 or 3 or 1 ) 3. the common ............ (95sides 324 076 , 91is675 , 4 675 933) 4. The geometric figure which its four equal in length called933 ( trapezium or parallelogram or rhombus ) c 8 × 641 × 125 = ... ............ 5. The number is divisible 3 28 or 13 or, 17 or million) 24 ) (641bythousand , 641 (hundred 641 ............ 6. L.C.M of 16 and 20 is ( 80 or 40 or 20 or 10 )

d The number 2 100 is divisible by …… (35 , 11 , 13 , 17) e XYZ is a triangle in which m(∠X) = 40° and m (∠Y) = 30°, 1. The million is the smallest number formed from ............ digits. then ∆XYZ is …… triangle. 2. 11 , 16 , 21 , 26 ............, ............, ............, complete in same pattern. (a right-angled an obtuse-angled 3. The value of the digit 4 in the, number 5467813 is ............ , an acute-angled) f 4.The L.C.M.each of two 15opposite and 35 isare …… (15 , 105 , 35 , 5) ............ in length. In a rectangle sides

2 Complete the following :

2

5. The rectangle whose dimensions are 8 cm , 6 cm , its perimeter = ............

Draw the square XYZL whose side length 3 cm. Join its 6. H.C.F of two numbers 12 and 16 equals ............ diagonals XZ and YL. 3 (a) Put the suitable sign (> , < or =) :

3

4

1. 3 milliard 475956432 Multiples of 6 are ……, …… and …… 2. 7423856 – 5018738 ............ 2415117 Prime of m.350 are ……, …… and …… ............ 3000 3. 3 km. factors The perimeter of a rectangle whose dimensions are 7 cm (b) Put (✓) in front of the correct statement or (✗) in front of the incorrect one : and 11 cm = ………………………… = …… cm 1. 345962 + 154048 = 50000 ( ) d The H.C.F. of 18 and 30 is …… 2. The two parallel lines never intersect each other. ( ) 13. L.C.M of 12 , 30 is 60 ( ) e 4 of a day = …… hours = …… minutes.

a b c

............

4 1. The perimeter of a square is 32 cm. , find its area.

a b5

2.Calculate Calculate 487 × 25 2 106

425 + 894 075 – 3 000 500. , m ( A) = 40°from , m ( 256 number that subtracted 307, then (a)Find Draw the D ABC in which AC = 6ifcm. C) = 412 65° , determine the typeremainder of this triangle will according to the measures the be 255 million.of its angles. (b) Hazem bought 26 books from the book fair of series animal world , if the price of one book is P.T 725. Find out the money that Hazem Paid.

101 93

Model (4) 1 Complete the following :

1. The smallest number formed from 8 digits is ............ 2. The value of the digit 8 in the number 147385 is ............ 3. 59 million , 42 thousand , 63 = ............ 4. The H.C.F for 12 , 30 is ............

5. The sum of the measures of the interior angles of a triangle is ............

6. The multiples of the number 6 that included between 30 , 45 is ............

2 Put the suitable relation (< , > or =) : 1. 360 cm. ............ 6 m 3. 7200 ÷ 3 ............ 60 × 40 5. 3 milliard ............ 965752812

2. 356705 + 3622195 ............ 8 million. 4. 75 thousand ............ 750 hundred 6. 83 dm2. ............ 840 cm2.

3 Complete the following :

1. 50 × 600 = ............ tens. 2. The factors of the number 8 is ............ 3. The triangle whose side lengths are different is called ............ 4. L.C.M of the two numbers 24 and 18 is ............ 5. The diagonals of the rectangle are ............ , ............ 6. Number of vertices in the hexagon is ............

4 (a) Draw D ABC , where AB = AC , m ( B) = 60° , then find :

1. Length of AC 2. Perimeter of D ABC 3. Type of this triangle according to the lengths of its sides.

(b) In a school if 798 pupils are distributed equally among 19 classes. Find the number of pupils in each class

5 (a) Find the result of :

1. 17620 + 5356 = ............

2. 267 × 18 = ............

(b) Reda bought a T.V. set by L.E 4420 , he paid L.E 500 in cash , then he paid the rest in 28 equal installments. Find the value of each installment.

102

Model (5) 5 Exercise

1

2 3

4

1 Complete the following :

1. The rectangle is a parallelogram Choose the correct answer.in which its angles ............ 2= ............ m2. dm309 a 2.75600 251 + 748 691 = …… ............ 3. is the common multiple for(8allmilliard numbers. , 8 million , 8 thousand) perimeter square = ............ × ............ b 4.5The 000 000 of – the 324 067 = …… 5. The number 3 million , 132(95 thousand in digits is ............ 324, 81 076 , 91 675 933 , 4 675 933) ............ digit=3 ... in the number 21538006 is c 6.8The × value 641 of× the 125 2 Choose the correct answer (641 : thousand , 641 hundred , 641 million) ............ is divisible by 2 , 3 10 or ) d 1.The number 2 100 is divisible by …… (35 , ( 11 , 18 13or, 21 17) 32605108 ............ 23511998 > or < or = ) e 2.XYZ is a triangle in which m(∠X) = 40° and m( (∠Y) = 30°, ............ 3. All the are divisible by 2 ( odd or even or prime ) then ∆XYZnumbers is …… triangle. , ............ 4. The H.C.F of 8 12 is ( 2 or 4 or 8 ) (a right-angled , an obtuse-angled , an acute-angled) ............ 5. 25 × 7 × 4 = is divisible by 3 ( 36 or 700 or 179 ) f 6.The L.C.M. of 15 and 35 is …… (15 , 105 , 35 , 5) ............ The triangle whose side lengths 6 cm. is ( scalene triangle or equilateral triangle or isoscles triangle )

Draw the square XYZL whose side length 3 cm. Join its 3 Complete the following : diagonals XZofand YL. of the prime number is ............ 1. The number the factors a b c

2. The diagonals of the parallelogram ............ each other.

…… and …… factors of angles 350 of are ……,are…… and …… , then 4.Prime If the measures of two a triangle 62° , 81° this triangle is ............ angledperimeter triangle. The of a rectangle whose dimensions are 7 cm 5.and 2418011 ÷ 60cm = ............ = ………………………… = …… cm d4 (1)The FindH.C.F. the result of of :18 and 30 is …… 1 ............ = …… minutes. e 4(a)of5034567 a day+ 3203456 = ……= hours a b

ofmillion 6 are= ............ ……, 3.Multiples 2565178 – one

(b) 893756 – 431877 = ............ (c) 235 × 85 = ............ Calculate 2 106 425 + 894 075 – 3 000 500. (2) A hotel contains 192 rooms divided equally by a number of floors , each floor Find the number that if subtracted from 256 412 307, then contains 16 room How many floors are there in this hotel ?

the remainder will be 255 million.

5 1. Find H.C.F , L.C.M of the numbers 28 and 42

2. Rectangle its dimensions are 9 cm. , 12 cm. Find : (a) Its area (b) Its perimerter.

103 93

Model (6) 1 Find the result of each of the following : (a) 70070 ÷ 35 = ............ (c) 123 × 15 = ............

2 Choose the correct answer :

(b) 35859 + 7936 = ............ (d) 90000 – 78456 = ............

1. Hundred thousand and three hundred seventy five is ............ ( 10315 or 100375 or 1375 ) 2. The greatest number formed from the digits 4 , 1 , 5 , 3 , 2 and 9 is ............ ( 45321 or 123459 or 954321 ) 3. The smallest prime number is ............ ( 1 or 0 or 2 ) 4. The value of the digit 4 in the number 546789 is ............ ( 40000 or 4000 or 400000 )

5. The perimeter of square whose side length 3 cm. = ............ ( 9 cm. or 6 cm. or 12 cm. )

6. 105 is divisible by ............

3 (a) Complete the following :

( 2 , 3 or 5 , 2 or 5 , 3 )

1. The number which has only two factors is called ............ 2. The diagonals of the rectangle ............ in length. 3. 5 dm. = ............ cm.

(b) A number if it is divided by 11 the quotient is 488 and remainder 4 , what is this number ?

4 Complete the following :

1. H.C.F for the two numbers 18 , 30 is ............ 2. L.C.M. for the two numbers 7 , 3 is ............ 3. The polygon of 5 sides is called ............ 4. The measure of the right angle = ............ ° 5. 4 × 25 ............ 100 ÷ 2 (by using > , < or =) 6. 5348475 – 3 hundred thousand

5 (a) Draw D XYZ in which XY = 5 cm. , m ( X) = m ( Y) = 45° , find 1. Measure Z 2. What is the type of D XYZ according to the measures of its angles.

(b) In the opposite figure :

the outer shape is a square of side length 4 cm and the inner shape is a rectangle of dimensions 3 cm. , 2 cm.

104

3 cm 2 cm

Find the area of the shaded part ,

5 cm

Model (7)5 Exercise

1

2 3

1 Complete the following :

, 35 thousand , 15 = ............ 1. 94 million Choose the correct answer. The value of the digit 3 in the number 3721014 = ............ a 72. 251 309 + 748 691 = …… 3. The H.C.F of the two numbers 16 and 24 = ............ (8 milliard , 8 million , 8 thousand) 4. The L.C.M of t he two numbers 14 , 10 = ............ b 55. 000 – hundred 324 067 = …… 465276000 + three thousand = ............ (95square 324whose 076perimeter , 91 675 , 4 675 933) 6. The length of the side of the 36 cm933 =............ c 2 8Choose × 641 125answer = ... : the × correct , 641ormillion) ............thousand , 641( hundred 1. 950000 – 324067 =(641 324076 or 625933 675933 ) 2. Thenumber number 2100 divisible by ............ by …… (35 , 11 ( 7, or13 11 ,or17) 13 ) d The 2 is100 is divisible 3. D XYZ in which m ( in X) =which 40° , m m(∠X) ( Y) = 30°=, 40° then Dand XYZ is e XYZ is a triangle m............ (∠Y) = 30°, ( acute angled triangle or right angled triangle or obtuse angled triangle ) then ∆XYZ is …… triangle. 4. The number 108 is divisible by the two prime numbers 3 , ............ ( 5 or 7 or 2 ) right-angled , number an obtuse-angled , an acute-angled) ............ is prime 5. The (a number . ( 6 or 8 or 2 ) f The 15 and 35 is …… (15hundred , 105or, 641 35million , 5) ) 6. 8 × L.C.M. 641 × 125 of = ............ ( 641 thousand or 641 3 Put (✓) in front of the correct statement or (✗) in front of the incorrect one :

Draw1. the 4816 square ÷ 4 = 124 XYZL whose side length 3 cm. Join its , if mYL. 2. In the XZ D ABC ( B) = 105° , then it is possible to be an obtuse angled diagonals and a b c d e

4

a b

triangle. 3. The squareof metre (m2.) is……, used for measuring perimeters of the shapes. Multiples 6 are …… andthe …… 4. The two parallel straight lines never intersect each other Prime factors of 350 are ……, …… and …… 5. The area of the square = side × side The of sides a rectangle whose dimensions are 6. In aperimeter rhombus , all the are equal in length

11 cm = ………………………… 4 and 1. Find the quotient of 19836 ÷ 6 5

7

(

)

( ( ( ( cm (

) ) ) ) )

= …… cm (without using the calculator)

The 30(5is× 4…… 2. FindH.C.F. L.C.M ofof the18 two and numbers × 11) , (5 × 6 × 11) 1 of atheday = …… hours = BC …… minutes. , AB = 3 cm. 1. rectangle ABCD in which = 4 cm. 4 Draw

draw AC intersects BD at M , its+width , Calculate its perimeter Calculate 2 106 425 894equals 075half – 3its000 2. A rectangular piece of land length500. if itsthe width = 24 metre. Find number that if subtracted from 256 412 307, then

the remainder will be 255 million.

105 93

1 Complete the following :

Model (8)

1. 7288316 – 6 million = ............ 2. The value of the digit 4 in the number 354267198 = ............ 3. The L.C.M for two numbers 12 , 16 is ............ 4. 4 × 765 × 25 = ............ 5. In D ABC , m ( A) = 60° , m ( B) = 70° , m ( C) = ............ °

2 Put the suitable relation (> , < or =) :

1. 3407805 + 3592195 = ............ 7 hundred thousand. 2. 3 m2. ............ 30000 cm2. 3. 9200 ÷ 4 ............ 60 × 40 4. The perimeter of a square whose side length 4 cm. ............ the perimeter of a rectangle whose dimensions 35 dm. , 45 dm.

3 1. Find the H.C.F for the two numbers 54,72

2. Arrange the following numbers in an ascending order : 41328 , 43182 , 42138 , 42138 , 42183

4 1. Find the smallest number divisible by 2 , 3 , and 5

2. Which is greater ? The area of the square of side length 6 cm. or the area of the rectangle whose dimensions are 5 cm. , 7 cm.

5 1. Draw D ABC in which AB = BC = 4 cm. , m ( B) = 60° , then find : (a) The length of AC (b) The type of the triangle according to the measures of its angles.

2. Sally bought 26 metres of cloth for L.E 286 , find the price of 8 metres of the same kind.

106

Model (9)5 Exercise

1

2 3

1 Choose the correct answer :

1. Thethe smallest prime number is ............ ( 0 or 1 or 2 ) Choose correct answer. 45 tens = ............ ( 45 or 450 or 4500 ) a 72. 251 309 + 748 691 = …… 3. ............ is the smallest number divisible by each of 2 and 5 ( 5 or 10 or 20 ) (8 milliard , 8 million , 8 thousand) 4. All the sides are equal in length in the ............ b 5 000 000 – 324 067 = …… ( square or rectangle or parallelogram ) (95 324 076 are , 91 675 4 675 933) 5. The area of the rectangle whose dimensions 3 cm. and 5933 cm. is, ............ ( 16 cm. or 15 cm. or 8 cm. ) c 8 × 641 × 125 = ... 6. The value of the digit 8 in the number 437839562 ( 800 ,or 641 80 ormillion) 800000 ) (641 thousand , 641 ............ hundred , < divisible Put thenumber suitable relation or =) : d 2 The 2 100(> is by …… (35 , 11 , 13 , 17) ............ 50 thousand 1. 44302 e XYZ is+a5698 triangle in which m(∠X) = 40° and m (∠Y) = 30°, 2. 4 metre ............ 40000 cm. then ∆XYZ is …… triangle. 3. 999 ............ 50 × 20 right-angled , an............ obtuse-angled , right an angle. acute-angled) 4. The (a measure of the acute angle the measure of the f The of 15100 and is …… (15 , 105 , 35 , 5) 5. 100L.C.M. thousand ............ ten 35 thousand. 6. 580 600 718 ............ 580 600 708.

Draw the square XYZL whose side length 3 cm. Join its 3 Complete the following : diagonals and 1. H.C.F XZ for the two YL. numbers 20 and 30 is ............ a b c d e

4

a b

4

2. The prime even numbers is ............ 3. 300 × 500 = ............ , 250 = ............ 4. 5 million , of 75 thousand Multiples 6 are ……, …… and …… 5. The factors of theof number are ............ Prime factors 35015are ……, …… and …… 6. In the rectangle all angles are ............

The perimeter of a rectangle whose dimensions are 7 cm (a) Find the result of each of the following : and 11 cm = ………………………… = …… cm 1. 62491 + 251542 = ............ The H.C.F. of 18 and 30 is …… 2. 93642 – 32161 = ............ 3. 9180 ÷ 45 = ............ 1 of abought day = hours (b) 25 …… metres of cloth , = the…… price ofminutes. one mere P.T. 475 , How much 4 Nada money did Nada pay ?

Calculate 2 106 425 + 894 075 – 3 000 500. Find the number that if7 cm. subtracted rectangle whose dimensions and 6 cm. ? from 256 412 307, then the remainder will AB be =255 , BC = 4 cm. , m ( B) = 90° , then find the (2) Draw D ABC in which 3 cm.million.

5 (1) Which is greater : the area of the square whose side length 6 cm. or the area of the length of AC

107 93

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‫‪116‬‬ ‫‪116‬‬

‫رقم االيداع ‪2012 / 9099‬‬

‫‪2012‬‬ ‫‪/9099‬‬ ‫االيداع‪9099‬‬ ‫رقمااليداع‬ ‫رقم‬ ‫‪2012‬‬ ‫‪9099‬‬ ‫‪2012‬‬ ‫االيداع‬ ‫رقم‬ ‫‪2012‬‬ ‫‪///9099‬‬ ‫االيداع‬ ‫رقم‬

Math book grade 4 first term

math