Name

Estimating sums

Make an Estimate Round the numbers in the problems and add mentally to estimate the sum. (Round to the that makes sense for each number or problem.)

_71

-72 _-.73 __74

_75

3.96..@ +8.31 ..@

_.76

]r."@

-.77

i-78

-79 _-80

A.

2.04 + 5.75

6.014 + 3.275

10.33 + 17.4

3.49 + 15.52

-..81

-82 _.83 --84

-85 __86

B.

87.43 + 80.40

1.28 + 9.40

61.29 + 59.24

22.14 + 95.52

2.4 + 39.6

c.

5.37 + 3.79

29.34 + 34.56

70.16 + 45.42

256.11

+ 29.93

49.99 + 34.56

24.92 76.38

+ 67.21

74.89 27.36 + 56.03

19.55 4.46 + 20.26

124.95 59.50 + 100.40

9.95 41.45 + 60.88

21.07 39.54 + 60.24

70.88 12.45 + 3.98

26.97 39.51 + 59.94

13.06 26.91 + 5.27

434.15 202.01 + 46.82

--87

-88 -89 _90 -..91

-92

-.93 -.94 ls

-95 -96 -97

-98

--99

_r00

D.

_r01

_102 _103

_r04 _r05

E.

ular t

O Frank Schaffer Publications, lnc.

l

FS-10219 Pre-Algebra

Name

Estimating ditlerences

Rough Estimates Round the numbers in the problems and subtract mentally to estimate the subtraction. (Round to the place that makes sense for each number or problem.)

s7.o6o"@

9.67

5.03

-gs.g8o"@

- 3.81

- 4.21

11.20 - 9.67

19.05

-

32.79 12.19

12.89 - 5.24

-

52.74 13.14

-

46.83 20.91

-

32.78 18.29

-

12.40 10.66

-

69.05 19.55

-l_a.6e

-

55.70 51.42

-

68.30 45.75

-

42.90 19.72

-

18.05 8.68

B.

c.

D.

E.

237.94 - 99.75

@ Frank Schaffer Publications, lnc.

- 4.41

10.71

8.13

45

32.13 - 1.97

47.85 19.99

9.65 5.84

-

481.3

-76.1

9.46 1;78

-

2

-

-

-

7.83 1.96

-

9.36 5.44

84.37 79.66

-

-

7.83 6.10

42.73 10.99

10.039 - 9.876

FS-l0219 Pre-Alg*e

nces

Name

Sum lt Up Find the sums. 6.2 + 1.73

bg

0.525 + 0.139

TE

96

12.36 + 8.75

7.65 + 3.34

0.25 + 0.73

5.9 + 6.057

38.93 + 17.6

0.68 + 0.4

;

72.88 + 14.75

t6

u

,7i iA

I

DO

9.89 + 42.69

c.

4.769 + 3.825

78.9 + 32.6

34.9 + 67.85

1.79 + 3.826

36.29 + 28.75

D.

4.7 8.8 + 0.45

439.6

72.6 123.12 2.4

2.36 3.78 + 2.67

42.83 75.6 + 36.356

B3

l0

+

7.049 12.32

+

13

p. 7.84 65.3 + 238.72

I

,39

179.6

+

4.98 56.43

2.368 3.26 + 0.471

27.6 3.84 + 51.09

j76

O Frank Schalfer Publications, lnc.

)

3

FS-10219 Pre-Algebra

Name

Subtracting decimai

Decimal Differences Find the differences.

A.

265.3 - 121.44 .-ffi i

..1r.

-

-

0.85 0.68

g

c.

-

26.85 15.97

71.35 - 4.661

-

23.9 18.72

-

44.04 28.15

-

56.53 17.6

213.06 4.8

439.3 - 97.42

83.81 7.96

D.

-

52.67 24.7

-

51.04 22.63

-

73.21 56.56

-

57.19 19.88

-

70.00 16.95

-

54.135 27.950

r'-i i-:

5.25

B.

@

'i

3.74 1.88

Frank Schaffer Publications, lnc.

-

1.343 0.975

-

1.04 0.999

-

-

100.1

-

4

83.79

680.3 136.9

-

8.35 2.967

17.31 14.9

143.79 - 88.81

95.41

-

8.72

-

7.342 2.617

4.0

-

2.91

6.01

- 3.07

FS-10219 Pre-Algebra

bimals

Name

Estimating products

Product Estimates

fl

Estimate the products by rounding the numbers and multiplying. (Round to the place that makes sense for each number or problem.)

g.1g..@

)

43.82 x 17.9

8.97 x 56.3

27.87 x 3.56

52.7 x 1.87

19.97 x 4.95

3.7 x 8.3

6.47

8.96

x7.19

71.974 8.6

67.46 x 39.28

319.3 86.76

909.36 6.2

9.15 x 57.8

6.45 x 8.59

7.83 x 0.84

3.62 x 7.8

26.9 x 7.3

43.46 x 37.3

63.40

29.2

73.9 2.03

".@

;

A.

32.9 8.6

x 3.9oo@

i

x

:79

p1 t

x

4.1

.41

,72

x

i.

x

x

3.826 7.4

x

2.26

8.99 x 2.3

808.2 5.8

29.5 x 0.137

57.8

98.4 x 0.5

48.42

x

o 91

x

i

pl 07

x

l

@

4.91

Frank Schafier Publications, lnc.

x 8.71

x

x

6.34

FS-10219 Pre-Algebra

Name

Multiplying decimals

Multiplying Decimals Find the products. A.

3.5 x 6.7

8.09 x 5.7

B.

5.12 x 7.6

c.

D.

12.5 0.74

9.4 x 2.7

12.8 x 3.5

9.12 x 6.8

0.73 x 4.2

5.6 x 8.3

6.9 x 5.4

8.42 x 7.3

7.58 x 4.8

53.7 x 6.9

4.86 x 3.7

6.45 x 7.6

7.25 x 1.89

5.62 x 3.84

3.79

1.23 x 3.7

O FrarTft Scfiaffer Publications, lnc.

x

x

6

1.01

FS-10219 Pre-Algebra

rimals

Name

Estimating quotients

Quotient Estimates Estimate the quotients by rounding the numbers and dividing. (Round to the place that makes sense for each number or problem.) 12.8 3.5

6.9

A.

176.2 + 63 =

B.

301.38 + 5.3 =

c.

11

.93 + 3.2 =

D.

12.398 + 4.1 =

162.58 + 4.4 =

E.

482.04 + 8.32 =

14.948

F.

359.6

G.

64.26 + 8.3 =

12.345

H.

354.64 + 69.3 =

1,615.9 + 4.35 =

l.

413.66 + 5.1 =

279.31

J.

3,112.4 + 5.2 =

363.63 + 3.6 =

K.

409.4 + 48.4 =

123.94

L.

54.43 + 9.32 =

34.594 + 4.8 =

M.

48.14

*

561.84 + 79.3 =

N.

544.82 + 9.1 =

.5.4

*

8.5 =

*

5.1 =

266.7 + 3.1 =

*

3.3 =

8.45

7.6

Filgebra

6.4 =

O Fnnk Schaffer Publications, lnc.

t_

355.39

* 4.1 =

* 3.9 =

*

5.7 =

FS-l0219 Pre-Algebra

Dividing with decimals

Ilecimal Division l.r:.i

0.12 F;99_

o.4T 26

i"; i"j

o.s

lre

0.46 33.12

0.294

o.es) r o

s.+-12s2.

o.67wn

0.8265

o.tfTz+

o.oere

z.r fTo

o.oa)g-68

o.tz@

0.42F.47s

a.+F-

O Frank Schaffer Publications, lnc.

s

FS-10219 Pre-Algebra

Dimals

Name

Problem solving with decimals

Super Shoppers

t.12

A. Sue bought 3

Workspace

B. Sean spent \$5.00 in all. He bought a package of rolls and some salad. How many pounds of salad did he buy?

294

cans of tomato sauce. How much did she spend?

t05

C. Jorge bought a package of rolls and 2 pounds of salad. How much did he spend?

E. Emily spent

F. How many

;4\$

O Frank Schafier Publications, lnc.

S-pound box of spaghetti for \$7.50. How much less expensive is this than buying five 1-pound boxes?

pounds of mushrooms can Judy buy for \$e.00?

Workspace

Name

Exponents

Powers to the Numbers Write in exponent form. Then find the value. You may use a calculator to check your answers.

A.

five squared

\$o\$o\$o\$

nine to the 4th power

B.

15. 15.

ten to the 5th power

seven cubed

C.

one-half cubed

4.4.4.4.4

six to the 3rd power

D.

2.3 . 2.3. 2.3

twelve squared

1.5.1.5.1.5.1.5

E.

twenty cubed

7.7.f of

15

F. 12.3. 12.3

O

Frai( Schaffer Publications,

o-/

of

two to the 6th power

lnc.

10

one to the 12th power

three-fourths squared

FS-10219 Pre-Algebra

hlame

Scientific notation

Scientific Notation Scientific notation is an easy way to represent a hrge number. To write a number in scientific ndation, move the decimal point the number of places necessary to get a number from 1 to g. Then write the number from 1 to 9 with a rnultiplication sign and a power of 10 showing the number of places you moved the decimal point.

A.

5,300 '1_ -:

8,700,000=8.7x106 8.7 is between 1 and 9. You moved the decimal point 6 places.

70,000

260

990,000

1

ii

._.

i

B.

450

8,200

45,300

976,000

c.

416,000

52,000

93,700

4,960

gr

Write the numbers in standard form.

D.

3.5 x

wer

red

.:;.!l

E.

3.4 x

F.

2.46 x

OH<

4.37 x

1O'z

9.7 x 10'

104

1

.315 x

103

:

103

106

Schaffer Publications, lnc.

8.37 x

10u

1

.05 x

10'z

9.876 x

9.21 x

104

3.89 x

106

8.4 x 108

11

104

FS-l0219 Pre-Algebra

Name

Divisibilit

Even Steven A number is divisible by

I@ if it ends in O,2, 4,

6,or8

if the sum of the digils is

divisible by 3

if the last two

if it ends

if it is divisible

digits form a number that is divisible by 4

in0or5

by2and3

if the sum of the digits is

if it ends

in0

divisible by 9

Complete the table. Write Y (yes) or N (no). Divisible by

56,712

67,125

@

Frank Schaffer Publications, lnc.

FS-10219 Pre-Algebr

Itame

Prime and composite numbers

Primo Primes A prime number has only two whole-number factors-itself and A composite number has more than two whole-number factors. Write prime or composite beside each number.

d ndsl

:_l

1.

A.

3

41

B.

18

19

c.

64

39

D.

10

11

15

E.

6

17

25

F.

5

51

36

G.

49

7

91

H.

53

85

13

t-

89

23

93

J.

43

79

47

K

73

75

86

L

67

83

29

M-

31

87

97

N.

94

59

37

o.

61

81

63

@

H<

Scfiaffer Publications, lnc.

13

FS-10219 Pre-Algebra

Name

Factoring numbers

Perfect Products List all of the factors of each number from least to greatest. Then tell whether the number of factors is odd or even.

Number

Factors

Odd or Even Number of Factors

12 16 18

20 25 32

36 40 48 56 60 64 72 81

100 121

144 225 Look at the numbers that have an odd number of factors. The middle factor of each number should be the square root of the number.

@

Frank Schafier Publications, lnc.

14

FS-10219 Pre-Algebra

T

i

numbers

Name

Prime factorization with exponents

Find the Prime Factors Draw a factor tree to find the prime factors. Then write the prime factors using exponents. 75

A.

/\ i'.Lt

1;

::;

!...-

O

B.

FAgebra

I I

i

c.

98

D.

60

(o Frank Schaller Publications, lnc.

50

36

90

120

FS-10219 Pre-Algebra

Name

Greatest common factor

Factors Are Great! On scratch paper, find the factors for each number. Write the greatest common factor (GCF) for each pair of numbers on the line below the pair.

A.

16 and 40

4 8 12 24

10 and 21

GCF=6

B.

24 and 40

36 and 54

48 and 64

C.

18 and 27

12 and 36

21 and28

D.

16 and24

18 and 30

B and 27

E.

45 and 60

28 and 42

48 and72

F.

26 and 51

100 and 130

24 and 72

G.

27 and

18 and 32

42 and 56

H.

90 and 189

91 and 95

84 and 108

136 and 162

121 and 143

l.

@

1

81

44 and 216

Frank Schaffer Publications, lnc.

16

FS-10219 Pre-Algebra

I I I

n

lactor

Name

Least common multiple

Multiples, at Least On scratch paper, find the multiples of each number. Write the least common multiple (LCM) for each pair of numbers on the line below the pair.

A.

5and9

4

6

I

18

16

30 42 48

20 28 32

4 and 18

)

LCM = 12

B.

3and4

6 and 21

18 and 27

C.

4 and 10

8 and 18

9 and 36

D.

2O and25

18 and 30

30 and 70

E.

18 and 60

27 and 36

20 and 24

Rewrite each pair of fractions using the LCM.

>Algebra

F. franofr

!ano]

Ianof

c. Iano]

Ianol

Ianof

H.

Iano\$

\$anof

fanof

r.

SanaI

franoI

]anof

@

Frank Schafler Publications, lnc.

17

FS-i0219 Pre-Algebra

Decimals

9 lessons covering decimals