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88MAMATHTHWWOORRKKBBOOOOKK

LCM = 60

112 43

3.141622%

.625

A=hb

30x + 22y

6.25mm=

X118 3

>32x - 14y

34.66

GCF = 812 = 2 x 2 x 3

I = P x R x T

831-256

=<6.25mm <

=LCM = 60A=hb 32x - 1

4y

.625

30x + 22y

>

34.66

22%

GCF = 812 = 2 x 2 x 33.1416

I = P x R x T

831-256 112 43

=18 X

13

EMP4055i

MathWORKBOOK

AuthorBeverly Nance

Project ManagerE. Rohne Rudder

TypesettingPagecrafters, Inc.

Cover ArtE. Rohne Rudder

Managing EditorKathleen Hilmes

Copyright © 1993Milliken Publishing Company

All rights reserved.

8Finally, a new workbook for eighth grade math!

Basic skills are reviewed and expanded as students work through 58pages of activities. Each page gives an example and step–by–stepsolution of the problem presented. Some of the many skills coveredinclude a review of addition, subtraction, multiplication, and division,plus challenges in decimal fractions, exponential and scientificnotation, primes, probability, percents, and basic geometric principles.Six answer pages are provided.

The purchase of this book entitles the individual purchaser to reproducecopies by duplicating master or by any photocopy process for single class-room use. The reproduction of any part of this book for commercial resale orfor use by an entire school or school system is strictly prohibited. Storage ofany part of this book in any type of electronic retrieval system is prohibitedunless purchaser receives written authorization from the publisher.

Find each sum.

46 + 54 + 62 + 38 =

85 + 15 + 37 + 13 =

127 + 43 + 130 + 30 =

17 + 23 + 35 + 25 =

250 + 350 + 25 + 175 =

© Milliken Publishing Company 1 MP4055

Addition and subtraction of whole numbers

194055281

324+ 1820043, 210

827 724 8245 4537 6331365 599 3605 2009 5224

+ 942 + 307 + 2913 + 5432 + 8445

1234 246 13579 20406 15795678 802 79135 1030 2631

+ 9012 + 468 + 35793 + 99999 + 4682

21300– 895512,345

Find each difference.

4829 2056 8000 7248 5040– 3718 –1264 – 4654 – 3585 – 3999

6213 4000 8219 2467 3579– 5876 – 805 – 7878 – 908 – 2468

12345 9876 50604 7000 48113– 6789 – 6789 – 3080 – 4778 – 36251

Find each quotient.

Find each product.


17 561) 29 899) 35 875) 48 960)

246 135× 82 × 791

1350 2863 1792 8921× 405 × 823 × 544 × 345

5628 5701 9287 8040× 500 × 803 × 123 × 506

358 17542) 256 82176) 987 42441)

Multiplication and division of wholenumbers

358× 493222

143217542

17 R 2432 568) 32

248

224

24

Simplify each expression.

2 + 8 ÷ 4 – 2 =

8 – 5 ÷ 5 + 5 =

Find each sum.

6 x 3 + 2 ÷ 2= 9 ÷ 3 + 6 – 1 = 17 + 2 x 5 ÷ 5 = 24 ÷ 8 + 3 – 2 =


41 – 6 ÷ 6 + 5 = 36 ÷ 12 + 8 – 4 = 52 ÷ 4 x 2 + 1 = 12 x 3 – 4 + 5 =

2 + 3 (5 – 2) = 6 + 4 (8 + 2) = 5 (3 – 2) + 1 = 6 (8 ÷ 8) + 7 =

7 – 2 (5 – 5) = 18 + 3 (4 – 2) = 24 ÷ 2 (1 – 0) = 16 – 3 (8 ÷ 4) =

8 + 12 ÷ 2 – 4 x 3 + 1 =

8 + 6 –12 + 1 =

14 – 12 + 1 =

2 + 1 =

3

18 – 5 x 3 + 6 = 17 + 5 x 2 – 2 = 8 + 8 ÷ 8 – 8 = 25 – 6 ÷ 3 + 3 =

Order of operations (multiplicationand division)


5 + 4 [3 + 4(8 – 6)] =


21 + 4[8 x 3 – 16] = 58 – 5 [6 + 8 ÷ 4] = 6 [5 + 3 x 2] – 12 =

2 + 3 [5 + 8 (6 – 2)] = 78 – 2 [24 – 2(8 – 5)] =

28 + 7[16 – 2 (4 + 3)] = 146 – 5 [8 (6 – 4) – 12] =

16 – 2 [5 + 3 ÷ 3] = 18 + 7 [6 – 4 ÷ 4] = 37 – 3 [4 x 2 – 5] =

More order of operations (inside out)

2 + 3 [5 + 2 (8 – 5)] =

2 + 3 [5 + 2 (3)] =

2 + 3 [5 + 6] =

2 + 3 [11] =

2 + 33 = 35

Find the difference.

20.4 16.23 8.4 12.25 2.803– 8.6 – 4.5 – 2.39 – 6.47 – 1.04

42.56 6.984 8 8.35 2.45– 13.24 – 4.279 – 4.35 – 4 – 1.46

Find each sum.

2 + 4.8 + .2 + 3 =

3.4 + 2.6 + 5 + 2.4 =

6.5 + 8.2 + 2.3 + .5 =

9 + .4 + 8 + .3 + 2.3 =

2.85 + .05 + 2.1 + 4 =


Addition and subtraction of decimals

23.5

.4+ 6.0211.92

8.40– 2.35

6.05

0.456 23.4 2.35 10.2 7.21.234 7.25 4 1.35 5.68

+ 2.345 + 18.07 + 5.6 + .4 + 4


21.4 – (3.2 + 8.4) 18.4 + (6.35 – 2.42)

17.56 + (18.42 – 6) 29.35 – (4.38 + 2.9)

(8.2 + 3.5) – (4.6 + 2.5) + 2.1

Find each product.

3 x 1.5 =

5 x .25 =

2 x .37 =

10 x .04 =

8 x 1.11 =


Multiplication and division of decimals

3.45x 1.2

690345

4.140

2.8 .45 1.23 .456 24.3x .7 x .6 x .9 x .2 x .3

2.9 .47 2.31 .123 12.04x .17 x 2.6 x .12 x .04 x .05

Find the quotient.

.4 16.8) 4 16.8) .04 16.8) .004 .168)

2.5 6.25) .25 6.25) 25 6.25) .025 6.25)

1.2 9.6) .15 7.5) .11 .099) 8 .048)

3.2 960) .21 8.4) 14 1.96) .35 70)

.123 2.46) 2.04 .612) 311 6.22) .481 .962)

12.06.4 4.824)


Round to nearest whole number.

7.4 ≈ 8.6 ≈ 17.11 ≈ 21.51 ≈

1.45 ≈ .09 ≈ 2.145 ≈ .96 ≈

Round to nearest hundreth.

2.456 ≈ .045 ≈ 1.181 ≈ 2.009 ≈

Round to nearest thousandth.

.0456 ≈ .1234 ≈ .2345 ≈ .0604 ≈

Round to nearest tenth.

.24 ≈ .17 ≈ 2.43 ≈ .48 ≈

Write <, >, or = to make a true statement.

2.005 2.5

3.14 3.41

8 7.895

2.115 2.151

4.92 4.29

12.46 14.2 6.35 5.63 3.405 3.045

8.002 8.02 .88 .8 .119 .1109

3.801 3.108 .707 .7 .003 .02

16.16 17 18.05 15.88 2.3 .32

Comparing decimals

2.45 < 2.5

3 > 2.999

Rounding decimals

6.23 ≈ 6.2 6.28 ≈ 6.3

Write in exponential notation.

3 • 3 • 3 =

5 • 5 • 5 • 5=

1 • 1 • 1 • 1 • 1 =

2 • 2 • 2 =

(2.4) (2.4) (2.4) =

10 • 10 • 10 • 10 = 9 • 9 • 9 = 7 • 7 • 7 • 7 • 7 =

(3.2) ( 3.2) = 8 • 8 • 8 • 8 = 6 • 6 • 6 • 6 • 6 • 6 =

Evaluate each expression.

22 = 5

2= 7

2= 1

2= 9

2=

33= 4

3= 2

3= 8

3= 5

3=

44= 2

4= 1

4= 3

4= 5

4=

102= 10

4= 10

1= 10

0= 10

3=

35= 2

6= 1

10= 4

2= 5

5=

Write the missing exponent.

23

• 24= 2 ■■ 8

2• 8

5= 8 ■■ 7

4• 7

5= 7 ■■

53

• 5 ■■ = 54

4■■ • 43= 4

56

8• 6

3= 6 ■■

35

• 37= 3 ■■ 9

1• 9 ■■ = 9

810

3• 10

4= 10 ■■

(2.5) (2.5) (2.5) (2.5)(2.5) (2.5) = (2.5) ■■


Using exponents

2 • 2 • 2 • 2 • 2 = 25

32= 3 • 3 = 9

42

• 43 = (4 • 4) (4 • 4 • 4) = 4

5


Evaluate.

2.4 x 102=

3.71 x 103=

5.06 x 101=

8.371 x 103=

7.008 x 102=

9.23 x 103= 8.405 x 10

1=

6.204 x 104= 2.3 x 10

5=

1.49 x 106= 3.755 x 10

3=

5 x 106= 8.1 x 10

5=

7.42 x 104= 9 x 10

8=

Write in scientific notation.

405 = 8400 =

2468 = 700,000 =

8,040,000 = 42,000 =

1005 = 27 =

550,000 = 4,000,000 =

80,808 = 1450 =

9000 = 6002 =

50,000 = 12345 =

18 = 246 =

908 = 325,000 =

5.23 x 103= 5230

24,680 = 2.468 x 104

Scientific notation

Complete the Prime Factor Treesto find each GCF.


GCF = 6

12 18

2 96 3

2 33 2

2• 2•3 2•3 •3

Use Prime Factor Trees to find GCF

81

3

54

3

GCF =

GCF =

120

2

48

3

120

2

48

3

GCF =

220

2

340

2

GCF =

GCF =

8

2

20

2

175

5

225

5

GCF =

72

2

90

2

GCF =

GCF =

170

2

130

2

The following word problemsrequire you to find a least commonmultiple (LCM). Use either method(A) or method (B).

1. What is the length of the side of the smallest possible square formed byplacing rectangles side by side that are 3 inches by 4 inches?

2. Jane and Mark are cycling to the shore but Jane rides at a rate of 15 mph, and Mark rides at a rate of 12 mph. What is the minimum distance they will ride if they each travel the same distance in a whole number of hours?

3. Rhonda earned $75 per week for 4 weeks. If Jane only earns $50 per week how many weeks will she have to work before she will have the same amount of money?

4. Paul can mow 12 lawns per week for 3 weeks. Robbie mows 6 lawns in 1 week. How many weeks will Robbie have to work before he’s mowed the same number of lawns as Paul?

5. What is the length of the side of the smallest possible square formed by placing rectangles side by side that are 5 cm by 6 cm?

6. Tara read 8 books/month for 3 months. How many books will John have to read for each of 4 months if they are to read the same number of books?

7. Harold earned $150/week for 8 weeks. Sarah earned $90/week for 10 weeks. What is the least common multiple of both their salaries?

8. Bob types 40 words per min. for 5 minutes. Julie types 50 words per min. How long before she will have typed the same number of words?


Find the LCM of 15 and 20

Method (A): 15, 30, 45, 6020, 40, 60

15

3

20

2

LCM = 2 x 2 x 3 x 5 = 60

LCM = 60

Method (B):

5 2 5

1520

= 8090

= 2128

=

936

= 1751

= 3240

=

4860

= 3857

= 1230

=

112

= 2 13

= 3 14

= 4 15

= 5 16

=

135

= 2 47

= 3 59

= 4 34

= 5 23

=

1025

= 20 58

= 30 57

= 40 12

= 50 35

=

1934

= 7 23

= 6 12

= 8 19

= 1113

=

Reduce each fraction to lowest terms.


I. Reduce:

II. Change mixed number to improper fraction:

III. Find missing number to form equivalent fraction:

Change each mixed number to an improper fraction.

12

=6

23

=10 3

=1520 9

=1618

57

=21

79

=28 3

=2432 5

=3050

910

=30

611

=18 19

=3848 4

=120160

Find the missing number to form equivalent fractions.

68 ÷

÷2

2 =

34

35

7=

21+ 5

7=

26

7

3

4=

32:3 × 8

4 × 8=

32

24


724

,5

18,

812

58

,7

20,

624

78

,1230

,1115

135

, 127

, 134

1

2,

2

3,

1

8:

3

24<

12

24<

16

24

Write > or < to make a true statement.

23

35

49

78

29

311

56

45

311

29

57

68

712

811

613

45

417

316

720

516

23

1823

38

211

2730

710

85100

1621

3250

1520

2122

1314

Write in order from least to greatest.

< <

< <

< <

< <

1834

2056

3 54 6

<. ..<


23

79

58

+56

+13

+ 45

125

57

184

56

+ 234

+ 35

12+11

29

35

5 73

10

+149

+ 623

+ 547

412

635

1238

3 23

5 1745

+ 514

+ 4 29

+ 2114

Add the following fractions and mixednumbers and reduce answer

28

+ 58

+ 18

=

3 211

+ 5 711

+ 6 =

3 521

+ 6 421

+ 1 321

=

Write each sum in simplest form.

33

4= 3

9

12

+5

6= +

10

12

319

12= 4

7

12


Write each difference in simplestform.

Subtraction of fractional and mixed numbers

32

3 = 3

8

12 = 2

20

12

– 13

4 = 1

9

12 = 1

9

12

111

12

1112

–9

12=

1720

–5

20=

1278

– 538

=

1921

1112

910

– 37

– 23

– 45

3 56

71415

12 1924

–145

– 2 14

– 5 23

18 23

16 59

27 38

–4 78

– 8 78

– 14 910

84 28 331

42

– 635

–19 – 16 511


Write each product in simplest form. Multiplication of fractions

25

× 103

× 64

=

59

× 23

× 910

=

712

× 45

× 214

=

2 × 314

= 512

× 89

=

312

× 4 = 16 × 134

=

212

× 312

= 513

× 418

=

21

3 × 3

3

4 =

7

3×

15

4=

35

4= × 8

3

4

Multiplication of mixed numbers

5

1

2

3×

4

5×

10

6=

1 × 4 × 2

3 × 1 × 3=

8

9

23

× 3 × 412

= 56

× 12 × 11

10=

315

× 10 × 25

= 46

× 24 × 14

12=

2

3

1

1

12

÷ 34

=

25

÷ 13

=

37

÷ 65

=

2 ÷ 34

= 56

÷ 2 =

212

÷ 3 = 512

÷ 14

=

335

÷ 217

= 423

÷ 123

=

6 ÷ 8 = 325

÷ 10 =

Division of fractions

Division of mixed numbers


Write each quotient in simplest form.

34

÷

38

+

12

÷

14

=

56

÷

13

+

18

÷

14

=

2

÷ 34

+ 3( ÷ 9) = 2

12

÷

24

+ 3

14

÷

23

=

Find the quotients and add to find their sum.

21

2 ÷ 5 =

5

2×

1

5 =

1

2

2

3 ÷

4

5 =

2

3×

5

4 =

10

12 =

5

6

Evaluate each expression given

a = 2, b = 3, c = 4, d = 12.

Complete each table.


d e f d ÷ f + 2 e

24 7 6

16 3 4

30 12 5

8 2 2

a b 3 a + b 4 b – a

1 2

5 2

2 4

9 10

c d c d – 2 2 c ÷ d

1 2

6 4

8 2

9 3

a b c 2 a + b c – a c

1 5 2

3 8 4

2 9 1

5 8 3

Evaluate the following expression givena = 2, b = 3, c = 4.

a b +

2 (3) +

– b + 5 a

– 3 + 5 (2)

6 + 2 – 3 + 10

c

a

4

2

15

a + c =

a b =

4a + 1 =

6a ÷ d =

b – a =

d ÷ b =

5b – 3 =

a b c =

x + 19 = 26 y – 24 = 30 a – 4 = 9 m + 17 = 26

d – 7 = 30 c – 4 = 12 b + 9 = 81 n + 72 = 78

t + 2 = 20 v – 13 = 6 w – 13 = 4 z + 5 = 20

e + 7 = 9 r – 12 = 6 p – 3 = 4 g + 6 = 6


Solve the following equations.When finished, add all answers. The sum should total 310!

Solve the equation for the variable

x + 85 = 91

– 85 – 85

x = 6

y – 14 = 60

+ 14 + 14

y = 74

2 × = 42y5

= 6a5

= 4 7b = 21

R24

= 6 5t = 185 2m = 100n82

= 6

c7

= 18 9d = 180w3

= 5 4v = 28

8f = 16 12g = 36j4

= 5k5

= 2


Solve the following equations. When finished, add all the answers. The sum should total 1000!

Solve the equation for the variable

3 ×3

=

213

y7

= 3

× = 7 7y7

= 7 3( )

y = 21

WORD PROBLEMS

1. Jake hit 3 more home runs than Rhajon. Jake hit a total of 11 homeruns. How many homers did Rhajon hit?

2. Sallie is 4 inches shorter than Marie. Sallie is 61 inches tall. How tall is Marie?

3. Josie ate 360 fewer calories than Mark. Josie ate a total of 1250 calories. How many did Mark eat?

4. Miguel drove 75 miles further than James. Miguel drove 350 miles. How far did James drive?

5. Rochelle types 23 words per minute faster than Wanda. If Rochelle types 88 words per minute, how fast does Wanda type?

6. Amy’s salary is $2450 less than Joan’s salary. If Amy’s salary is $15,500, how much is Joan’s salary?

7. Josè scored 13 points higher on the final exam than Frank. Frank earneda score of 77. What was Josè’s score?

8. Barbara ran the marathon in 3h. 27 min. which was 14 minutes slowerthan Julie. What was Julie’s time?

9. There are 36 cookies in a package of Mrs. Buttermaker Cookies. Thereare 14 more cookies in a package of Blue Ribbon Cookies. How many cookies are in the Blue Ribbon package?

10. Last fall Sal read 13 books which was 6 less than the number of bookshe read last summer. How many books did he read over the summer?



WORD PROBLEMS

1. Becky earns $14.25 per hour which is 3 times more than Joe’s hourlywage. How much does Joe make per hour?

2. Marty drove 1/3 of the distance between St. Louis and Kansas City. He drove 84 miles. How far is St. Louis from Kansas City?

3. Jennifer’s weight is 3/4 the weight of Sam. Jennifer weighs 120 lbs. How much does Sam weigh?

4. Fred scored twice the number of points in the basketball game as John. Fred scored 26 points. How many did John score?

5. Krista tripled her yearly salary. Her new salary is $24,600. What was her old salary?

6. The cupcakes were divided evenly among the 27 students. Each student got two cupcakes. How many cupcakes were there originally?

7. Loretta cycled twice as far as Julio. Julio cycled 23 miles. How far didLoretta cycle?

8. The cost of the party was divided evenly among 18 people. The total cost was $99.00. How much did each person chip in?

9. Michael drove 3 times as fast as Marla. Michael drove 57 mph. How fast did Marla drive?

10. Hughie’s yearly salary was divided evenly over 12 months. Each month he received $800. How much was his yearly salary?

Solve each equation and checkyour solution.


Solving two-step equations

1.“Undo” addition/subtraction

2.“Undo”multiplication/division

2 × + 3 = 7– 3 = – 3

2 × = 4

2 ×2

=

42

∴ × = 2

Check:×3

– 1 = 4 153

– 1 = 4

+ 1 = + 1

3 ×3

= 3 5( ) 5 – 1 = 4

× = 15 4 = 4

4 × + 5 = 21 ×4

+ 5 = 21 3 × – 2 = 7

×3

+ 2 = 7 9 × + 1 = 19 ×5

– 4 = 2

8 × – 2 = 22 ×7

+ 4 = 8 2 × – 42 = 44

×3

+ 3 = 3 5 × – 5 = 5 ×11

– 2 = 4

✔

Length (l) 8 9 6

Width (w) 5 7 5

Perimeter (p)


Substitute data into formula: e.g.

area of circle = π x (radius)2

a = π r2

If r = 3 cm

a = 3.14 (3)2 = 3.14(9)

= 28.26 cm2

FORMULAS

Complete each chart by substituting data into eachformula.

Radius (r) 2 4 1.5

Area (a)

Radius (r) 2 3.5 5

Circumference (c)

Length (l) 7 12 14.5

Width (w) 5 3 6

Area (a)

a = π r2

c = 2 π r

p = 2(l + w) a = l x w

Rate (R) 55 40 62

Time (t) 3 8 7

Distance (d)

Distance (d) 300 480 85

Gallons (g) 6 16 5

Mileage (m)

d = R x t m = dg

13 + –18 + –5 = –13 + 16 + –5 =

–24 + 20 + 6 =

26 + –12 + –4 =

–42 + 38 + –4 =

56 + 8 + –10 =

246 + –138 + –56 =

–6 + –8 + 2 + 4 =

5 + –4 + 6 + –6 =

–9 + 7 + 2 + 3 =

6 + –3 + –8 + 1 =

–5 + –5 + 6 + –7 =

–560 + 450 =

–246 + –424 =

–2000 + –455 =

2465 + –3460 =

–3000 + –467 =

40 + –32 + 6 =

–13 + 15 + –30 =

32 + –48 + 14 =

52 + –34 + 9 =

20 + 42 + 13 =

346 + –129 + 48 =

3 + –2 + 5 + 0 =

–3 + 4 + 3 + –4 =

–4 + 5 + –6 + 8 =

–7 + 8 + 2 + 5 =

3 + 4 + –3 + –5 =

–840 + 760 =

832 + –832 =

6000 + –4500 =

8888 + –6468 =

4642 + –5000 =

–40 + 80 + –30 =

–6 + 8 + 9 =

–25 + 50 + 75 =

–29 + –13 + –6 =

–124 + 68 + –56 =

2 + –3 + –4 + 5 =

–7 + 9 + –1 + –2 =

6 + –5 + –4 + –3 =

4 + –5 + –5 + 4 =

7 + 6 + –2 + –3 =

450 + –230 =

–345 + 500 =

–4000 + 842 =

–2830 + 1460 =

–4256 + 5642 =


Find the sum.

2 + –3 + 5 =

–5 + 6 + –7 =

10 + –7 + 6 =

–3 + 1 + –5 =

1 2 3 4 5 60–5 –4 –3 –2 –1

+3

–2

–7

Addition of integers

3 + –2 + 4 + –7

–6

+4


Subtraction of integers(Add the opposite)Find the difference.

8 – 5 =

–9 – 4 =

10 – –6 =

–7– –2 =

12 – –3 =

–20 – 20 = 101 – –303 =

32 – 40 =

–13 – –14 =

100 – –46 =

250 – –75 =

–200 – 48 =

–40 – –60 =

8 – –4 =

76 – –82 =

2 – 49 =

13 – –14 =

–202 – 404 =

14 – 464 =

126 – 300 =

76 – 84 =

99 – 88 =

32 – –5 =

0 – –4 =

37 – 100 =

–62 – –41 =

72 – –27 =

82 – –5 =

–20 – –20 =

–50 – 55 =

50 – –50 =

3 – –58 =

–242 – –50 =

–28 – –36 =

7 – 58 =

146 – 530 =

–43 – –43 =

24 – 16 = 24 + –16 = 8

24 – –16 = 24 + 16 = 40

–24 – 16 = –24 + –16 = –40

–24 – –16 = –24 + 16 = –8


Find the product. Multiplication of integers

–24 x –2 =

–4 x 3 =

–7 x –7 =

–41 x 2 =

–2 x –19 =

2 x –2 x 4 = –3 x –2 x –1 =–3 x 4 x –5 =

3 x 2 x 3 = –2 x 4 x –4 =4 x 2 x –1 =

–1 x –2 x –3 = 4 x 5 x 6 =5 x 6 x –2 =

–3 x 4 x –2 = 5 x 10 x –10 =6 x –2 x 4 =

–5 x –5 x 5 = 4 x –3 x –3 =2 x –30 x –1 =

4 x 5 x 2 = –6 x 5 x 2 =–2 x –3 x –11 =

–2 x –1 x –1 = 4 x –3 x 6 =–3 x –4 x 8 =

–2 x 3 x –4 x –1 = 5 x –2 x 1 x –1 =

–2 x 5 x –2 x –4 = –1 x –1 x –1 x –2 =

3 x 3 x –1 x –1 x 1 = –2 x 3 x 4 x –1 =

–2 x –2 x –2 x –2 x –2 = –1 x –1 x 2 x 3 x –1 =

–3 x 2 x 2 x 2 x –3 = –2 x –5 x 2 x 3 x 5 =

1 x 2 x 3 x 4 x 5 = 7 x –6 x 5 x –4 x 3 =

2 x –3 x –2 x –3 x 2 = –3 x 2 x 3 x –2 x 3 =

2 x 1 x 3 x –2 x –3 x –1 = 1 x –4 x –1 x 1 x –4 x –4 =

–3 x –2 x 4 = 24

“Even” number of signs produces apositive product.

–3 x –2 x –4 = –24

“Odd” number of signs produces anegative product.

Find the quotient.

8 ÷ 4 =

–4 ÷ 2 =

–1 ÷ –1 =

6 ÷ –3 =

–9 ÷ –3 =


Division of integers

24 ÷ –6 = –4

Division involving one negative numberwill produce a negative quotient.

–24 ÷ –6 = 4

Division involving two negative numberswill produce a positive quotient.

–10 ÷ –2 =

0 ÷ 4 =

14 ÷ –2 =

16 ÷ 8 =

–18 ÷ –2 =

–20 ÷ –4 =

–28 ÷ 7 =

–54 ÷ –9 =

–68 ÷ 17 =

62 ÷ –31 =

100 ÷ –20 =

150 ÷ –50 =

400 ÷ –20 =

–320 ÷ –160 =

1000 ÷ –50 =

–1500 ÷ –150 =

–12 ÷ –2 =

–6 ÷ –2 =

–11 ÷ 1 =

15 ÷ –5 =

17 ÷ –17 =

20 ÷ –5 =

22 ÷ –11 =

–35 ÷ 7 =

63 ÷ –7 =

72 ÷ –9 =

–64 ÷ –16 =

–100 ÷ 25 =

–300 ÷ –75 =

–600 ÷ –40 =

–450 ÷ 9 =

–2400 ÷ –60 =

–2000 ÷ –1000 =

–3 ÷ 1 =

–8 ÷ 2 =

–14 ÷ 7 =

–16 ÷ –2 =

18 ÷ –9 =

–21 ÷ –7 =

–20 ÷ –2 =

–42 ÷ –21 =

–65 ÷ –13 =

75 ÷ 25 =

81 ÷ –9 =

–100 ÷ –50 =

225 ÷ –15 =

121 ÷ 11 =

490 ÷ 70 =

–3000 ÷ 600 =

4500 ÷ –900 =

0 ÷ –2 =

7 ÷ –1 =

–13 ÷ –1 =

–15 ÷ 3 =

16 ÷ –4 =

–18 ÷ 3 =

24 ÷ –8 =

56 ÷ –7 =

66 ÷ –11 =

–58 ÷ 2 =

–85 ÷ –17 =

100 ÷ –10 =

–275 ÷ 25 =

–625 ÷ 5 =

–630 ÷ 90 =

2500 ÷ 50 =

8500 ÷ 1700 =

5 ÷ –5 =

12 + –3 x –6 = –18 x 2 + 3 = 16 ÷ –4 + 3 =

28 – 3 x –2 = –64 + –8 ÷ –4 = –30 x –2 – 4 =

63 ÷ –9 – 5 = 13 – 4 x –5 = 27 + –8 x 6 =

18 – 3 ÷ –3 = –65 ÷ 13 – 5 = 14 x –5 – 8 =

Evaluate.

–3 + 2 x –5 =


Order of operations

–2 + 3 x –5 –2 + –15 = –17

–20 ÷ 4 + –13–5 + –13 = –18

Evaluate.

4 + 2[–5 x 2 + 1] =


More order of operations

–2 + 3[–4 x 5 – 6]

–2 + 3[–20 – 6]

–2 + 3[–26]

–2 + –78 = –80

3 + 5[2 + 3 x –2] = –1 + 2[5 x 2 – 3] = 8 – 2[6 ÷ 3 – 2] =

–10 – 4[2 + 3 ÷ –3] = 20 + 2[3 ÷ 3 – 1] = 2[5 x 2 – –6] + 1 =

5[8 ÷ 4 – 1] – 2 = 6 – 3[2 + 3 x –4] = –17 + –2[4 x 5 – 2] =

12 – 3[4 + 8 ÷ –4] = 5[20 ÷ –5 – 1] – 1 = –2 + –3[6 + 8 x 2] =

10zy

+ 3 × – y =

2x + 3y – z = 2y – 4x + 72 =

3z + 4x – 5z = xy + yz + 2x =

zy

+ 2 × =

If x = –4, y = 2, z = –6evaluate each of the following expressions.


Given a = 2, b = –3, evaluate the expression

5b + a

5 (–3) + 2

–15 + 2

–13

×y + 2y× + z =

x + y = y – z = 4z + x = –2y + 5x =

2x + 3y = xy + 2 = 6y – 4z =


INTEGER WORD PROBLEMS

Write and solve a linear equation for each problem.

1. If x is increased by 14, the sum is 12. What is x?

2. If y is decreased by 17, the difference is 3. What is y?

3. If w is multiplied by 7, the product is –63. What is w?

4. If t is divided by –3, the quotient is 42. What is t?

5. –16 is 5 more than q. What is q?

6. 24 less than c is 13. What is c?

7. –3 times m is –105. What is m?

8. A number divided by 9 results in a quotient of –117. What is thenumber?

9. When a certain number is increased by 57, the result is 38. What is the number?

10. A certain number is 14 less than –9. What is the number?


WORD PROBLEMS USING RATIONAL NUMBERS

1. William gained 4 lbs., lost 3 lbs., gained 6 lbs. and finally lost 11 lbs. What was his net weight change?

2. Jackie’s average of 84 increased by 2 points, then fell by 4 points, then increased by 9 points, and finally fell by 1 point. What was her final average?

3. The average temperature on Monday was 5 degrees below 0. It rose7 degrees on Tuesay, fell 8 degrees on Wednesday and rose 4 degrees on Thursday. What was Thurday’s average temperature?

4. In the first quarter of Saturday’s football game, Wayne gained 7 yards, lost 3 yards, lost another 5 yards, then gained 15 yards. What was his net gain or loss in the first quarter?

5. The stock market rose 1-1/4 points on Monday, fell 3/4 of a point on Tuesday, rose 1/2 point on Wednesday, rose 7/8 of a point of Thursday, and fell 1-1/2 points on Friday. What was the net change for the week?

6. The submarine dove 75 feet, rose 25 feet, then dove 140 feet and finally ascended 85 feet. What was the net change in depth?

7. Cindy lost 1-3/4 lbs., gained 2-2/3 lbs., gained 1-1/2 lbs., then finally lost 3-1/2 lbs. What was her net change in weight?

8. Maureen climbed to an altitude of 1500 feet above sea level. She then descended 750 feet, climbed 850 feet, and then descended 620 feet where she finally decided to stop. At what altitude did she rest?

9. The temperature at the ski resort was 22° C when the ski lifts opened. During the course of the day it fell 3.8° C, rose 2.9°C, rose another 5.3° C, and finally fell 4.7°C. What was the temperature at the close of the day?

–158

+ – 2 34

= 2 712

+ – 3 13

= – 2.45 – 3.1 = 4.2 + – 3.14 =

2.5 – – 3.4 = 3 12

+ –114

= 78

+ – 35

= – 2.9 + – 5 =

23

–– 5

6= 3.4 + – 5.6 = –1 – .46 = –12

3+ 1

6=

–3.4 – 5 = 49

+–23

= 125

+ – 2 14

= 1.4 + – 5 =


Combining rational numbers

–78

+34

= –.3 – –.5 =

–78

+68

= –.3 + .5 =

–18

.2


2 + – 3 + – 4 = 5 + – 8 + 7 = – 6 + 8 + –10 =

21 + – 8 + – 2 = –13 + – 4 + 9 = 17 + – 2 + 6 =

24 ÷ – 6 + 3 = 2 × – 4 – 4 = 3 + 8 × – 3 =

– 6 + 8 + – 3 = 8 + 6 + –1 = 8 – 3 – – 4 =

– 3 =

16 =

– 21 =

– 2 + 0 = 3 + –1 = – 5 + – 3 = 8 + – 2 =

8 – – 3 = 3 × – 5 = 11 + – 7 = 8 – – 9 =

4 + – 8 = – 6 + – 2 = 8 ÷ – 2 = 24 ÷ 6 =

– 20 + 6 = –18 ÷ – 3 = 6 + – 8 = – 2 + –1 =

8 + – 2 0 + – 7 4 – 1 17 + – 2


Absolute valueDetermine absolute value.– 2 = 2

6 + – 10 = – 4 = 4

– 2 × – 3 = 6 = 6

1.

2.

3.

Comparing rational numbers

–46 < 2 –18 > –50

–3 12

–4

–2 1.2

–3 34

–2 12

–3.2 2 37

36

– 49

.4

–10 –212

–3.2 –.32 –3 12

–2.5 23

–.6

–2.3 –2.31 –3 12

–3 14

2.45 –3 2 14

–125


Write > or < in each .

Put numbers in order from least to greatest.

________ < _______ < _______ < ______

________ < _______ < _______ < ______

________ < _______ < _______ < ______

________ < _______ < _______ < ______

________ < _______ < _______ < ______

3 –3.2 –3 45

–.2

–1.4 1.04 –.14 114

2 35

–2.4 –2 12

2

13

–.45 25

–.3

–4 12

4.2 –4.3 4 13

23 –5 –1 2

– 5 < – 1 < 2 < 23

Ordering rational numbers

Solving one-step equations

× + – 8 = 2

+ 8 + 8

× + 0 = 10

× = 10

–2 × = 16

–2 × = 16

–2 – 2

× = – 8


Solve for x.

× + – 9 = 7 × – 2 = –18 ×–3

= 6 5 × = – 35

× + 12 = 7 × – – 3 = 4 –7 × = – 63 ×7

= – 4

× – 15 = – 3 × + – 6 = 14 12 × = – 48 ×–3

= – 4

–3 × = – 51 × – 13 = – 27 ×6

= –18 × + – 6 = – 50

Add 8 to each sideof equal sign:

Divide each side ofequal sign by –2:

Solve for x.


Solving two-step equations

2 × + – 3 = –15

→ + 3 = + 3

2 × + 0 = – 12

2 × = – 12

→ 2 = 2

× = – 6

×5

+ 2 = – 4

–3 × + 5 = 65 4 × – 6 = – 26 ×–2

– 4 = 6

×3

+ – 4 = – 7 –7 × – 3 = 18 6 × + 16 = – 2

–12 × + –4 = 8 ×–9

– 7 = – 6 –8 × + 6 = – 50

Add 3 toeach sideof equalsign.

Divideeach sideof equalsign by 2.

2 –4 = 5 – 2 = 3 – 1 = 7 – 4 =

10 – 2 = 4 – 5 = 6 – 2 = 8 – 9 =

9 – 8 = 6 – 6 = 2 – 5 = 4 – 2 =

Write each decimal as a power of 10.

.1 = ________

.00001 = ________

1000 = ________

.001 = ________

100 = ________

.000001 = ________


Negative exponents

Write each power with a positive exponent.

Write each power with a negative exponent.

19 2 = 1

73 = 14 2 = 1

31 =

154 = 1

26 = 16 4 = 1

83 =

110 2 = 1

79 = 13 4 = 1

2 5 =

A. .01 =1

100=

110 2 = 10−2

B. 15 4 = 5−4

C. 3−2 =132

Write in scientific notation.

.004 =

.0012 =

.0204 =


Using scientific notation

.0003 = 3 x 10–4

2000 = 2 x 103

Using a decimal

3.2 x 10–4 = .00032

4600 = .048 .15 =

.00005 = 3200 = .0003 =

270 = .018 = .123 =

Write the equivalent decimal.

2.84 x 10–2 = 3.2 x 10–3 = 4.8 x 102 =

1.2 x 103 = 5 x 10–4 = 1.04 x 10–1 =

5.6 x 10–3 = 2 x 102 = 4.1 x 10–2 =

6 x 10–3 = 5 x 103 = 1.8 x 10–1 =

4.56 x 10–2 = 7.1 x 10–1 = 2.9 x 102 =

23

34

56

78

215

18

49

37

910

89

38

45

56

23

12

35

67

49

511

67

29

311

34

715

23

813

617

34

513

611

23

56

98

76

118

107


Using cross-products

23

34

46

56

2024

1822

14

37

28

38

1540

1236

25

37

615

27

39

13

511

1824

1216

23

49

2030

38

2156

49

58

48

1016

34

1428

36

78

1416

59

Write > or < in each . Which is bigger: 34

or 58

?

2434

2058

>

3 54 8

>. ..

Circle which two ratios are equal in each group.


Determine the unit price of eachitem. Circle the “better buy.”

Find the “unit price”

Item: MilkPrice: $2.56 per gallonQuantity: 1 gallon or 128 oz.Unit Price per ounce =

Item Price Quantity Unit Price

Milk (A) $1.28 64 oz.

Milk (B) $ .48 16 oz.


Apples (A) $3.20 1 lb.

Apples (B) $1.76 1/2 lb.


Pizza (A) $1.20 3 slices.

Pizza (B) $1.50 5 slices.


Jelly (A) $ .45 6 oz.

Jelly (B) $ .56 8 oz.


Ice crm.(A) $.90 2 scps.

Ice crm.(B) $1.05 3 scps.


Soap (A) $1.92 64 oz.

Soap (B) $1.68 48 oz.


Bologna (A) $1.20 1/4 lb.

Bologna (B) $2.40 1/2 lb.


Pencils (A) $1.50 1 doz.

Pencils (B) $1.20 8


Gum (A) $.75 5 sticks

Gum (B) $1.04 8 sticks

$2.56128 oz.

= $.02 per ounce


Solving proportions

×4

= 2432

–32

= 15y

1112

= w18

710

= m50

t9

= 45

3n

= 49

815

= 3c

v4

= 56

7d

= 89

420

= e5

f24

= 68

312

= 8g

68

= 3p

w3

=8

14

14w = 24

w =157

Solve for the variable.


How far is it from New York to St. Louis?

Use the scale: 1" = 500 mi.

NY to St. Louis = 2"

Determine the actual distancebetween each pair of cities.Use the scale.

×2

=500

1

× = 1000 miles

1. New York to Miami 9. Seattle to Chicago2. Boston to Washington, D.C. 10. Denver to Washington, D.C.3. St. Louis to San Francisco 11. St. Louis to Denver4. Dallas to Seattle 12. San Francisco to Washington, D.C.5. Chicago to Denver 13. Boston to Chicago6. Boston to Dallas 14. Miami to Seattle7. New York to San Francisco 15. New York to Dallas8. Miami to St. Louis

St. Louis •

Boston •New York•

Washington,D.C.

•Chicago •

Dallas •

Denver•

Seattle•

SanFrancisco

•

Miami•

×100

×100

Reduced Decimal PercentFraction


Complete the chart, filling in all equivalent values.

Example:

34

75100

12

20100

15100

38

25100

710

.65

.05

30%

6%

60%

ReducedDecimal PercentFraction

.75 75%

Write an equation for each question and solve.

What is 35% of 80?

12 is what % of 60?

15 is 40% of what?

What is 47% of 60?

8 is what % of 32?

24 is 30% of what?

What is 95% of 240?

48 is what % of 64?

34 is 17% of what?

3 is what % of 2?


What is 20% of 30?

x = .20 (30)

x = 6

Write an equation for each question, substituting x for the word“what.” Solve for x.

8 is 25% of what?

8 = .25 (x)

8.25

=.25 .25

32 = ×

(x)

(x)


WORD PROBLEMS

1. A VCR costs $325. The sales tax is 8% of the price. What is the total priceof the VCR including tax?

2. A coat was originally priced at $280. The department store had a 25%off sale. What was the sale price of the coat?

3. The bicycle which originally sold for $400 was on sale for $320. Whatpercent was the bicycle marked down?

4. Last year, Ms Stewart earned $64,000. This year she got a raise and now makes $67,200. What percent increase did Ms Stewart receive?

5. Sam weighs 160 lbs. but wants to weigh 152 lbs. What percent of his weight does he want to lose?

6. Terry used to be 125 cm. tall. She is now 7% taller. How tall is she now?

7. Franklin has an average of 75 and wants to raise it to 90. What % increase would this be?

8. The sale price of a radio is $81. It was marked down 10%. What was theoriginal price?

9. Tommy bought a sweater at a moonlight madness sale for $20. It used to be $100. What % savings did he receive?

10. Jeri got a promotion and a 14% increase. Her old salary was $24,000.What is her new salary?

Old Price New Price Increase % Increase

$50 $70$100 $125

$64 $96$75 $90

$250 $300$400 $440

$2500 $3250$5000 $5050

$10,000 $20,000

Old Price New Price Decrease % Decrease

$50 $30

$100 $75

$64 $32

$12 $9

$450 $405

$500 $490

$2800 $2772

$4600 $3680

$20,000 $19,400


What % did the price of the sweater increase?

Old Price = $40

New Price = $50

Increase = $10

% Increase = IncreaseOld Price

=10 40

= 25%

Determine increase and %or decrease and %.


25% OFF SALE!

Original Price of Sweater = $40

$40 x .25 = $10 = Discount

$40 – $10 = $30 = Sale Price

Original Price % Discount Savings Sale Price

$50 20%$75 40%$64 25%$87 10%

$124 30%$156 8%$79 50%

$2000 5%$850 20%

$250 15%

$450 45%

$600 33%

$4600 18%

$27 20%

$30 25%

$950 12%

$10,000 40%

$25,000 15%

$64,000 8%

$100,000 19%

Determine savings and sale price.


Percents using ratios

What is 30% of 50? (write a proportion)

Solve using a proportion

What is 20% of 50?

15 is what % of 60?

17 is 50% of what?

What is 5% of 650?

37 is what % of 370?

48 is 40% of what?

What is 7% of 92?

600 is what % of 500?

24 is 30% of what?

What is 150% of 84?

×=

× =

× =

50.

30

100

100 30 50

100 1500

( )

35100

(Hint: Always write the % as a

fraction with denominator “100.”

e.g. 35% =


Given 3, 8, 7, 1, 0, 3, 6

Mean =

Median = 0, 1, 3, 3, 6, 7, 8 = 3

Mode = 3

Find the Mean, Median, Modefor each set of data.

Test Scores Hourly Wages Heights

78, 92, 90, 78, 96 $6.50, $20.00, $32.00 72", 60", 58", 62", 60", 72"

$29.00, $6.50, $10.00, 60", 76"

$15.00

Mean Mean Mean

Median Median Median

Mode Mode Mode

Weights Homeruns Driving Speeds

194, 206, 128, 102, 128, 7, 10, 7, 24, 3, 7, 6, 24, 55, 45, 55, 60, 60, 70, 55,

240, 100, 128, 128, 206 7, 11, 26 55, 62, 68, 75, 60

Mean Mean Mean


Mode Mode Mode

Ages Hours of Sleep Phone Calls

14, 15, 13, 13, 15, 12, 17, 2, 8, 10, 8, 7, 10, 6, 4, 7, 3, 10, 1, 0, 2, 5, 5, 3, 2, 7,

15, 15, 12, 15, 12, 14 7, 10, 7, 7, 9, 3 8, 3, 4, 3, 4

Mean Mean Mean


Mode Mode Mode

3 + 8 + 7 + 1 + 0 + 3 + 67

= 4


Using the 3 graphs answer the following exercises.

1. How many schools are in Summit?

2. Compare Jamestown and Fox. How many more schools are inJamestown?

3. Powell Schools represent what %of the total number of schools?

4. How many districts have less than20 schools?

5. How many students attend FoxDistrict?

6. How many more students does Summerville have than James-town?

7. How many districts have morethan 3000 students?

8. Summit has what % of the totalstudent population.

9. What was the population of Hope HS in 1965? in 1970? in 1980?

10. During what 5 year period was itsfastest rate of growth?

Number of Schools

50

40

30

20

10

0

SUMMIT

POWELL

SUMMERVILLE

JAMESTOWN

FOX

18

28

48

32

14

Fox

Jamestown

Summerville

Powell

Summit

Each represents 1000

Number of Students

2500

2000

1500

1000

500

1960

Population Growth of Hope H. S.

1965 1970 1975 1980 1985 1990


+ = +

+ = + =

= =

= =

= =

4 2 4 2

4 9 2 3 5

3 4 3 2 6

9 4 3 2 1

16

4

4

22

– –

( )

– –

NUMBERS WITH PERFECT SQUARE ROOTS

Simplify each radical.

49 100

81 25

36 64

Simplify each radical. Then add or subtract.

121 100 225 4 16 49

81 9 64 625 169 144

100 25 900 400 196 256

–

– –

–

+ +

+

+ +

Simplify each radical. Then multiply by the coefficient.

5 9 7 4 11 16 4 4

6 49 10 225 8 81 100 64

Simplify each radical. Then multiply or divide.

4 9 16 1 25 25 49 4

64

16

100

25

121

49

225

81

• • • •


REDUCING RADICALS

Reduce to simplest form.

98 = 49 • 2

= 49 • 2

= 7 2

3 48 = 3 16 • 3

= 3 16 • 3

= 3 (4) • 3

= 12 • 3

45 32 50 28

200 242 162 75

1000 72 44 80

12 8

18 6

20 27

2 24 6 125 3 98

9 18 5 40 15 27

7 450 2 90 8 54

4 1350 2 363 5 147

7 7 7 12 18 20

300 – 27 75 + 27 98 – 32 12 – 3

200 + 128 6 + 24 63 – 7 8 + 18

72 – 50 150 – 24 121 + 100 242 + 8

243 + 192 175 – 28 3 + 27 48 – 27


Combining square roots

Only radicals that are “exactly” alike can be added:

28 + 63

4 • 7 + 9 • 7

2 7 + 3 7

5 7

Simplify the sums and differences.

24 + 54


More combining square roots

All square root radicals can be multiplied or divided.

Simplify products and quotients.

3 • 27 = 3 • 27 = 81 = 92 • 8

24

6=

246

= 4 = 2

5 • 125 273

6 • 6 88

3 • 2 155

5 • 7 168

7 • 14 328

2 • 32 1004

11 • 3 555

13 • 4 7525

PYTHAGOREAN THEOREM

Find the missing side of eachtriangle using the PythagoreanTheorem.


bc

a

4c

3

a2 + b2 = c2

a2 + b2 = c2

32 + 42 = c2

9 + 16 = c2

25 = c2

5 = c

12

5 3

5c b 6 8

c

13

a

5

26

24b

c 3

3

35

c

15

8

c 8 10

a

15

12

a6

12

a

25

20 a

Example:4 155 ft. 3 inch 7 ft. 6 inch 7 qt. 1 pt.

– 2 ft. 7 inch + 4 ft. 9 inch +2 qt. 1 pt.2 ft. 8 inch

3 gal. 1 qt. 18 yds. 2 ft. 17 m 56 cm–1 gal. 3 qt. + 37 yds. 1 ft. –4 m 85 cm

5 qt. 11 oz. 15 mi. 370 ft. 85 cm 43 mm– 2 qt. 3 oz. – 8 mi. 2000 ft. + 17 cm 65 mm

18 lbs. 7 oz. 5 qt. 7 c 6 oz.+ 5 lbs. 9 oz. – 3 qt. 1 cup –5 c 7 oz.

UNITS OF MEASURE

Write the equivalent measure.

24 inch = ______ ft.

12 feet = ______ yd.

8 qts. = ______ gal.

32 oz. = ______ cups

6 c. = ______ pints


Equivalent measures

12 inch = 1 foot 8 oz. = 1 cup

3 feet = 1 yard 2 c. = 1 pint

36 inches = 1 yard 2 p.t = 1 quart

5280 feet = 1 mile 4 qt. = 1 gal.

1000 mm = 1 m 16 oz. = 1 lb.

100 cm = 1 m

10mm = 1 cm

Add or subtract. (Reduce measure)


Answer Keypage 1

200150330100800

2134 1630 14,763 11,978 20,00015,924 1516 128,507 121,435 8892

1111 792 3346 3663 1041337 3195 341 1559 1111

5556 3087 47,524 2222 11,862

page 8

page 510

13.417.5

209

4.035 48.72 11.95 11.95 16.88

11.8 11.73 6.01 5.78 1.76329.32 2.705 3.65 4.35 .99

9.8 22.3329.98 22.07

6.7

page 220,172 106,785

546,750 2,356,249 974,848 3,077,7452,814,000 4,577,903 1,142,301 4,068,240

33 31 25 2049 321 43

page 32

1219 8 19 49 25 1 26

45 7 27 3711 46 6 137 24 12 10

page 64.5

1.25.74.4

8.881.96 .27 1.107 .0912 7.29.493 1.222 .2772 00492 .602

42 4.2 420 422.5 25 .25 250

8 50 .9 .006300 40 .14 20020 .3 .02 2

page 7<<><>< > >< > >> > << > >

7 9 17 221 0 2 1

.2 .2 2.4 .5

2.46 .05 1.18 2.01

.046 .123 .234 .060

page 4494 53 28

53 18 54113 4242 126

3

4

5

3

3

4 3 5

2 4 6

7 7

1 2 11

12 7 7

6

3

5

1

2

2.4

10 9 7

3.2 8 6

4 25 49 1 81

27 64 8 512 125

256 16 1 81 625

100 10,000 10 1 1000

243 64 1 16 3125

2 8 7

5 4 6

3 9 10

2.5

( )

( )

( )

9


page 9240

371050.68371700.89230 84.05

62,040 230,0001,490,000 37555,000,000 810,000

74,200 900,000,000

page 16

page 17

page 14

page 15

page 104 25

27 624 1020

page 11126066

306

36004 min.

page 13> << >> < < <> > < >> > < >

page 12

34

84

34

14

13

45

45

23

25

32

73

134

215

316

85

187

329

194

173

525

1658

2157

812

2535

794

233

132

739

343

3 15 4 815 36 4 327 33 24 3

518

724

812

624

720

58

1230

1115

78

27

35

134

1 1 1

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1

14

6

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13 15 51

911

47

12

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320

2936

118

24 5

23

6170

512

3745

1740

2

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14 28

8 22

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12

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34

45

13

23

15

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23

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56

1725

45

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78

1

2

22

1 2

4 3

3 9


page 263

–1316–515

–40 404–8 371 4

146 –63325 –21

–248 9920 8712 0

158 –105–47 10027 61

–606 –192–450 8–174 –51

–8 –38411 0

page 18669114

1224

5, 7 0,117, 3 22, 3

10, 14 14, 837, 31 25, 6

10 1826 1011 3019 8

page 197 54 13 9

37 16 72 618 19 17 152 18 7 0

page 28–2–21

–235 3 –4 –70 –11 –2 13

–7 –3 8 –52 –1 –2 –49 –4 3 –65 –2 10 –3

–4 –5 2 –86 –9 5 –6

–4 –8 3 –29–2 4 –9 5–5 –4 2 –10–3 4 –15 –11

–20 15 11 –1252 –50 7 –7

–20 40 –5 5010 2 –5 56 –3 0 –1

page 254

–69

–7–10 –2 1410 2 –2811 10 –2

100 –8 27–48 54 75

–112 52 2650 –8 6

–1 1 0–6 3 3–2 –4 88 –11 –1

220 –110 –80155 –670 0

–3158 –2455 1,500–1370 –955 2,4201386 –3467 –358

page 29–1330 –33 –134 –62 56

–12 33 –2119 –10 –78

page 2748

–1249

–823860 –16 –6–8 18 32

–60 –6 120–48 24 –50060 125 36

–66 40 –6096 –2 –72

–24 10–80 2

9 24–32 –672 300

120 2.520–72 108–36 64

page 2412.56 50.24 7.065 12.56 21.98 31.4

26 32 22 35 36 87165 320 434 50 30 17

page 2021 30 20 3

144 37 50 492126 20 15 7

2 3 20 10

page 30–14–17 13 8–14 20 33

3 36 –536 –26 –68

page 31–2 8 –28 –24–2 –6 –11 364 92 –15

–4 –44 –28

page 234 64 3

15 2 303 28 430 2 66

page 218

65”161027565

$17,9503h. 13 min.

5019

page 22$4.75

252160 lbs.

13$8,200

5446 min.

$5.5019 mph

$9,600


page 32–220–9

–126–213735

–1,053–19–23

page 33Lost 4

90–2˚

14 yds.+3/8

–105 ft.–1 1/12 lb.

+980 ft.21.7˚

page 34page 39

page 45

page 43

page 353

16212 2 8 6

11 15 4 174 8 4 4

14 6 2 36 7 3 155 4 8

11 8 211 12 211 13 9

page 3716 –16 –18 –7–5 1 9 –2812 20 –4 1217 –14 –108 –44

page 38–30–20 –5 –20–9 –3 –3–1 –9 7

page 40

.0284 .0032 4801200 .0005 .104.0056 200 .041

.006 5.000 .18.0456 .71 290

page 42$.02 per oz.$.03 per oz.$.20 per oz. $.03 per oz.$.22 per oz. $.035 per oz.

$.40/slice $4.80 lb.$.30/slice $4.80 lb.$.075/oz. $.125 each

$.07/oz. $.15 each$.45/scoop $.15/stick$.35/scoop $.13/stick

page 441 – 1250 9 – 1937.52 – 375 10 – 1687.53 – 1875 11 – 8754 – 2000 12 – 2687.55 – 1000 13 – 10006 – 1875 14 – 30007 – 2875 15 – 1687.58 – 1187.5

page 36><< < < <> < < >> < > >

page 41<<> > > <> < > << > < << < < <


page 462820

37.528.2

2580

22875

200150

page 5010

25%34

32.510%1206.44

120%80

126

page 471 $3512 $2103 20%4 5%5 5%6 133.75 cm7 20%8 $909 80%

10 $27,360.

page 4820 4025 2532 5015 2050 2040 10

750 3050 1

10,000 100

20 4025 2532 503 25

45 1010 228 1

920 20600 3

page 49$10.00 $40.00$30.00 $45.00$16.00 $48.00$ 8.70 $78.30$37.20 $86.80$12.48 $143.52$39.50 $39.50

$100.00 $1900.00$170.00 $680.00

$37.50 $212.50$202.50 $247.50$198.00 $402.00$828.00 $3772.00

$5.40 $21.60$7.50 $22.50

$114.00 $836.00$4000.00 $6000.00$3750.00 $21,250.00$5120.00 $58,880.00

$19,000.00 $81,000.00

page 53

page 54

page 5186.8 $17.00 65”

90 $15.00 61”78 $6.50 60”

156 12.63 60128 7 60128 7 55

14 7 414 7 315 7 3

page 521 182 183 20%4 25 approximately 15006 approximately 17507 38 approximately 11.76%9 approximately 750, 875, 1800

10 1973 – 1978


page 55 page 56 page 57

page 5824243

(ex) 12’ 3” 10 qt.1 gal. 2 qts. 56 yds. 12m 71cm3 qts. 1 cup 6 mi. 3650 ft. 112 cm 8mm24 lbs. 1 qt. 3 cups 1 cup 7 oz.

Milliken Publishing Companya Lorenz company

P.O. Box 802Dayton, OH 45401-0802

www.LorenzEducationalPress.com

Grades 7-9

Motivate your students to improve their math skillswith these fun, easy-to-use workbooks!

MP4041 Beginning Algebra grades 6-8MP4050 Algebra grades 7-9MP4054 Math Workbook grade 7MP4055 Math Workbook grade 8MP4056 Geometry grades 6-8MP4057 Advanced Geometry grades 7-10MP4065 Math Workbook grade 5MP4066 Math Workbook grade 6MP4075 Fractions grades 5-6MP4076 Decimals grades 5-7MP4078 Word Problems grades 4-6

17 =2•6

2448 =

a

Milliken Publishing CompanyISBN 978-1-4291-1033-4

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