Decimals

Name Estimating sums

c.

_71

-72_-.73

__74

_75_.76

-.77i-78

-79_-80

-..81

-82_.83

--84

-85__86

--87-88

-89_90-..91

-92-.93-.94ls

-95-96-97

A. 6.014+ 3.275

10.33+ 17.4

22.14+ 95.52

256.11

+ 29.93

124.9559.50

+ 100.40

13.0626.91

+ 5.27

3.49+ 15.52

2.4+ 39.6

49.99+ 34.56

9.9541.45

+ 60.88

434.15202.01

+ 46.82

B. 87.43+ 80.40

5.37+ 3.79

24.9276.38

+ 67.21

21.0739.54

+ 60.24

61.29+ 59.24

70.16+ 45.42

19.554.46

+ 20.26

26.9739.51

+ 59.94

-98--99_r00_r01_102_103_r04_r05

D.

E.

ulart

Make an EstimateRound the numbers in the problems and add mentally to estimate the sum. (Round to the

that makes sense for each number or problem.)

2.04+ 5.75

1.28+ 9.40

29.34+ 34.56

74.8927.36

+ 56.03

70.8812.45

+ 3.98

3.96..@+8.31 ..@]r."@

l

O Frank Schaffer Publications, lnc. FS-10219 Pre-Algebra

Name Estimating ditlerences

7.83

- 1.96

9.36

- 5.44

84.37

- 79.66

7.83

- 6.10

42.73

- 10.99

10.039

- 9.876

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

B.

c.

D.

E.

12.40

- 10.66

69.05

- 19.55

55.70

- 51.42

42.90

- 19.72

237.94

- 99.75

9.67

- 3.81

19.05

- 4.41

10.71

-l_a.6e

68.30

- 45.75

18.05

- 8.68

481.3

-76.1

5.03

- 4.21

32.79

- 12.19

52.74

- 13.14

8.13

45

9.46

- 1;78

47.85

- 19.99

11.20

- 9.67

12.89

- 5.24

46.83

- 20.91

32.78

- 18.29

32.13

- 1.97

9.65

- 5.84

2

s7.o6o"@-gs.g8o"@

@ Frank Schaffer Publications, lnc. FS-l0219 Pre-Alg*e

nces Name Adding decimals

Sum lt Up

bg

96

;

t6u

Find the sums.

6.2+ 1.73TE

72.88+ 14.75

c. 4.769+ 3.825

4.78.8

+ 0.45

7.8465.3

+ 238.72

O Frank Schalfer Publications, lnc.

0.525+ 0.139

9.89+ 42.69

439.67.049

+ 12.32

179.64.98

+ 56.43

0.25+ 0.73

12.36+ 8.75

7.65+ 3.34

5.9+ 6.057

1.79+ 3.826

2.3683.26

+ 0.471

2.363.78

+ 2.67

27.63.84

+ 51.09

0.68+ 0.4

38.93+ 17.6

36.29+ 28.75

42.8375.6

+ 36.356

,7iIiA

DO

B3

l0

13

p.

I

,39j76

78.9+ 32.6

34.9+ 67.85

72.6123.12

+ 2.4

D.

3

)

FS-10219 Pre-Algebra

Name

B.

Find the differences.

A. 265.3

- 121.44.-ffii 'i ..1r. r'-i i-:

5.25g

c. 26.85

- 15.97

23.9

- 18.72

56.53

- 17.6

439.3

- 97.42

52.67

- 24.7

51.04

- 22.63

73.21

- 56.56

1.343

- 0.975

1.04

- 0.999

100.1

- 83.79

57.19

- 19.88

70.00

- 16.95

54.135

- 27.950

Subtracting decimai

143.79

- 88.81

95.41

- 8.72

7.342

- 2.617

4.0

- 2.91

6.01

- 3.07

D. 44.04

- 28.15

213.064.8

83.817.96

680.3

- 136.9

17.31

- 14.9

8.35

- 2.967

4

Decimal Differences

3.74

- 1.88

0.85

- 0.68

71.35

- 4.661

@ Frank Schaffer Publications, lnc. FS-10219 Pre-Algebra

Name

3.7x 8.3

bimals

fl)i;

:79p1t

.41

,72i.

Estimating products

Product EstimatesEstimate the products by rounding the numbers and multiplying. (Round to the place thatmakes sense for each number or problem.)

g.1g..@x 3.9oo@

".@

98.4x 0.5

26.9x 7.3

o91

i

pl07l

52.7x 1.87

71.974x 8.6

9.15x 57.8

3.62x 7.8

63.40x 4.91

A. 32.9x 8.6

19.97x 4.95

67.46x 39.28

6.45x 8.59

29.2x 8.71

43.82x 17.9

319.3x 86.76

7.83x 0.84

43.46x 37.3

73.9x 2.03

8.97x 56.3

6.47x7.19

909.36x 6.2

48.42x 2.26

808.2x 5.8

57.8x 6.34

27.87x 3.56

8.96x 4.1

3.826x 7.4

8.99x 2.3

29.5x 0.137

@ Frank Schafier Publications, lnc. FS-10219 Pre-Algebra

Name Multiplying decimals

A.

Find the products.

3.5x 6.7

5.12x 7.6

8.42x 7.3

7.25x 1.89

12.5x 0.74

0.73x 4.2

53.7x 6.9

3.79x 1.01

9.4x 2.7

5.6x 8.3

4.86x 3.7

1.23x 3.7

12.8x 3.5

6.9x 5.4

6.45x 7.6

B.

c.

D.

6

Multiplying Decimals

8.09x 5.7

9.12x 6.8

7.58x 4.8

5.62x 3.84

O FrarTft Scfiaffer Publications, lnc. FS-10219 Pre-Algebra

rimals Name Estimating quotients

12.8

3.5

6.9.5.4

8.45

7.6

Quotient EstimatesEstimate the quotients by rounding the numbers and dividing. (Round to the place thatmakes sense for each number or problem.)

176.2 + 63 =

301.38 + 5.3 =

11 .93 + 3.2 =

162.58 + 4.4 =D. 12.398 + 4.1 =

E. 482.04 + 8.32 =

F. 359.6 * 8.5 =

G. 64.26 + 8.3 =

H. 354.64 + 69.3 =

l. 413.66 + 5.1 =

J. 3,112.4 + 5.2 =

K. 409.4 + 48.4 =

L. 54.43 + 9.32 =

M. 48.14 * 6.4 =

N. 544.82 + 9.1 =

14.948 * 5.1 =

266.7 + 3.1 =

12.345 * 3.3 =

1,615.9 + 4.35 =

279.31 * 4.1 =

363.63 + 3.6 =

123.94 * 3.9 =

34.594 + 4.8 =

561.84 + 79.3 =

355.39 * 5.7 =

Filgebra O Fnnk Schaffer Publications, lnc.

A.

B.

c.

t_

FS-l0219 Pre-Algebra

Dividing with decimals

l.r:.i

0.12 F;99_i"; i"j

Ilecimal Division

o.4T 26 o.s lre 0.46

o.es) r o s.+-12s2. o.67wn

o.tfTz+ o.oere

o.oa)g-68 o.tz@ 0.42F.47s

z.r fTo s

a.+F-

33.12

0.294

0.8265

O Frank Schaffer Publications, lnc. FS-10219 Pre-Algebra

Dimals

t.12

294

t05

;4$

Name Problem solving with decimals

Super Shoppers

Solve the problems. Circle your answers.

A. Sue bought 3cans of tomatosauce. Howmuch did shespend?

Workspace B. Sean spent $5.00in all. He boughta package of rollsand some salad.How manypounds of saladdid he buy?

Workspace

C. Jorge bought apackage of rollsand 2 pounds ofsalad. How muchdid he spend?

D. Patrick can buy aS-pound box ofspaghetti for$7.50. How muchless expensive isthis than buyingfive 1-poundboxes?

E. Emily spent$8.75 at thesalad bar. Howmuch salad didshe buy?

F. How manypounds ofmushrooms canJudy buy for$e.00?

O Frank Schafier Publications, lnc.

Name Exponents

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

A. five squared $o$o$o$

B. 15. 15. 15 ten to the 5th power

C. one-half cubed 4.4.4.4.4

D. 2.3 . 2.3. 2.3 twelve squared

E. twenty cubed 7.7.f of o-/ of

F. 12.3. 12.3 two to the 6th power

nine to the 4th power

seven cubed

six to the 3rd power

1.5.1.5.1.5.1.5

one to the 12th power

three-fourths squared

O Frai( Schaffer Publications, lnc. 10 FS-10219 Pre-Algebra

hlame Scientific notation

gr

Scientific notation is an easy way to represent ahrge number. To write a number in scientificndation, move the decimal point the number ofplaces necessary to get a number from 1 to g.

Then write the number from 1 to 9 with arnultiplication sign and a power of 10 showing thenumber of places you moved the decimal point.

A. 5,300 70,000

1

'1_ -: ._. ii i

B. 450 8,200

c. 416,000 52,000

Write the numbers in standard form.

D. 3.5 x 1O'z 4.37 x 104

.:;.!l :

E. 3.4 x 103 8.37 x 10u

F. 2.46 x 106

Scientific Notation

260

45,300

93,700

9.7 x 10'

1 .05 x 10'z

990,000

976,000

4,960

1 .315 x 103

9.876 x 104

8.4 x 108

wer

8,700,000=8.7x106

8.7 is between 1 and 9.You moved the decimal

point 6 places.

red

OH< Schaffer Publications, lnc.

9.21 x 104

11

3.89 x 106

FS-l0219 Pre-Algebra

Name Divisibilit

Even StevenA number is divisible by

if it endsin O,2, 4,6,or8

if the sum ofthe digils is

divisible by 3

if the last twodigits form a

number that isdivisible by 4

if it endsin0or5

if it is divisibleby2and3

if the sum ofthe digits is

divisible by 9

I @if it ends

in0

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

Divisible by

56,712

67,125

@ Frank Schaffer Publications, lnc. FS-10219 Pre-Algebr

Itame

Primo PrimesA prime number has only two whole-number factors-itself and 1.

A composite number has more than two whole-number factors.Write prime or composite beside each number.

Prime and composite numbers

25

36

29

97

37

dndsl

:_l

A.

B.

c.

D.

E.

F.

G.

H.

t-

J.

K

L

M-

N.

o.

3

18

64

10

6

5

49

53

89

43

73

67

31

94

61

41

19

39

11

17

51

7

85

23

79

75

83

87

59

81

15

91

13

93

86

47

@ H< Scfiaffer Publications, lnc. 13

63


Name Factoring numbers

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

Number FactorsOdd 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 numbershould be the square root of the number.

@ Frank Schafier Publications, lnc. 14 FS-10219 Pre-Algebra

T

i

numbers Name

Find the Prime FactorsDraw a factor tree to find the prime factors. Then write the prime factors using exponents.

Prime factorization with exponents

120

A.

98

60

FAgebra I (o Frank Schaller Publications, lnc.I

i

75

/\i'.Lt

1; ::;

!...- O

B. 50 36

c. 90

D.


Name Greatest common factor

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

A. 16 and 40 10 and 21

B. 24 and 40 36 and 54

C. 18 and 27 12 and 36

D. 16 and24 18 and 30

E. 45 and 60 28 and 42

F. 26 and 51 100 and 130

G. 27 and 81 18 and 32

H. 90 and 189 91 and 95

l. 1 44 and 216 136 and 162

481224

GCF=6

48 and 64

21 and28

B and 27

48 and72

24 and 72

42 and 56

84 and 108

121 and 143

@ Frank Schaffer Publications, lnc. 16 FS-10219 Pre-Algebra

II

I

n lactor Name Least common multiple

)

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

A. 5and9 4 and 18

B. 3and4 6 and 21

C. 4 and 10 8 and 18

D. 2O and25 18 and 30

E. 18 and 60 27 and 36

Rewrite each pair of fractions using the LCM.

F. franofr !ano]

Multiples, at Least

Ianol

18 and 27

9 and 36

30 and 70

20 and 24

Ianof

c. Iano] Ianof

H. Iano$ fanof$anof

r. SanaI ]anof

4I

16202832

618304248

LCM = 12

>Algebra @ Frank Schafler Publications, lnc.

franoI

17 FS-i0219 Pre-Algebra

Decimals

Documents

Transcript of Decimals