Math Computation Skills & Strategies Level 7 (Math Computation Skills & Strategies)

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Saddleback Math Covers

10/22/06

6:24 PM

Page 5

MATH COMPUTATION SKILLS & STRATEGIES Every book in the Math Computation Skills and Strategies series contains over 100 reproducible pages.These highinterest activities combine computation practice with strategy instruction. Featuring a Scope and Sequence chart, the books allow educators to supplement their math lessons with the extra math practice all students need. In addition, periodic reviews allow for reinforcement and assessment of skills.

H I G H - I N T E R E S T M AT H C O M P U TAT I O N S K I L L S & S T R AT E G I E S

HIGH-INTEREST

• LEVEL 7

The books are grade specific, but they were created with students of all ages in mind. Each book features ready-to-use pages with instructional tips at the beginning of each lesson. Math Computation Skills and Strategies reproducible books are the perfect choice for educators.

HIGH-INTEREST

MATH COMPUTATION SKILLS & STRATEGIES Operations Fractions and Decimals Whole Numbers Perimeter and Area Regrouping

Three Watson • Irvine, CA 92618-2767 • 888-SDL-BACK • www.sdlback.com

S A D D L E B A C K E D U C AT I O N A L P U B L I S H I N G

Saddleback E-Book

Solving Word Problems Money Measurement

LEVEL

7

100 plus+ REPRODUCIBLE ACTIVITIES

MATH COMPUTATION SKILLS & STRATEGIES

LEVEL

7

ISBN 1-56254-970-7 Copyright © 2006 by Saddleback Educational Publishing. All rights reserved. No part of this book may be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system without written permission of the publisher, with the following exception. Pages labeled Saddleback Educational Publishing ©2006 are intended for reproduction. Saddleback Educational Publishing grants to individual purchasers of this book the right to make sufficient copies of reproducible pages for use by all students of a single teacher.This permission is limited to an individual teacher and does not apply to entire schools or school systems. Printed in the United States of America

Table of Contents Page Lesson 5 . . . . . . . . . Introduction Unit 1 . . . 6 ......... 7 ......... 8 ......... 9 ......... 10 . . . . . . . . 11 . . . . . . . . 12 . . . . . . . . 13 . . . . . . . . 14 . . . . . . . . 15 . . . . . . . . 16 . . . . . . . . 17 . . . . . . . . 18 . . . . . . . . 19 . . . . . . . . 20 . . . . . . . . 21 . . . . . . . . 22 . . . . . . . . 23 . . . . . . . . 24 . . . . . . . . 25 . . . . . . . . 26 . . . . . . . . 27 . . . . . . . . 28 . . . . . . . . 29 . . . . . . . . 30 . . . . . . . . 31 . . . . . . . .

Numbers and Number Sense Understand Integers Add and Subtract Integers Find Absolute Values Read Coordinate Graphs Find Squares and Square Roots Express Powers of Ten Use Exponents Identify Equivalent Fractions Convert Decimals and Fractions Work with Non-terminating Decimals Compare Integers Order Integers Rounding Rounding and Estimating Find Percentages Find Percentages Convert Percents and Decimals Convert Fractions and Percents Understand Ratios Find Ratios Understand Irrational Numbers Solve Word Problems Solve Word Problems Solve Word Problems Review Numbers and Number Sense Review Numbers and Number Sense

Unit 2 . . . . 32 . . . . . . . . 33 . . . . . . . . 34 . . . . . . . . 35 . . . . . . . . 36 . . . . . . . . 37 . . . . . . . . 38 . . . . . . . . 39 . . . . . . . . 40 . . . . . . . . 41 . . . . . . . . 42 . . . . . . . . 43 . . . . . . . . 44 . . . . . . . . 45 . . . . . . . . 46 . . . . . . . . 47 . . . . . . . . 48 . . . . . . . . 49 . . . . . . . . 50 . . . . . . . .

Addition and Subtraction Use Addition Properties Add Two Digits Add Up to Four Digits Add Up to Seven Digits Add Decimals Practice Addition Practice Addition Subtract Two Digits Subtract Up to Four Digits Subtract Up to Seven Digits Subtract Decimals Practice Subtraction Practice Subtraction Add and Subtract Greater Integers Check Addition and Subtraction Solve Word Problems Solve Word Problems Review Addition and Subtraction Review Addition and Subtraction

Unit 3 . . . . 51 . . . . . . . . 52 . . . . . . . . 53 . . . . . . . . 54 . . . . . . . . 55 . . . . . . . . 56 . . . . . . . . 57 . . . . . . . . 58 . . . . . . . . 59 . . . . . . . . 60 . . . . . . . . 61 . . . . . . . . 62 . . . . . . . . 63 . . . . . . . . 64 . . . . . . . . 65 . . . . . . . . 66 . . . . . . . . 67 . . . . . . . . 68 . . . . . . . . 69 . . . . . . . . 70 . . . . . . . . 71 . . . . . . . . 72 . . . . . . . . 73 . . . . . . . . 74 . . . . . . . . 75 . . . . . . . .

Multiplication and Division Find Multiples List Factors Identify Prime and Composite Numbers Identify Prime and Composite Numbers Check Multiplication and Division Multiply 2 Digits by 1 Digit Multiply 4 Digits by 1 Digit Multiply 7 Digits by 1 Digit Multiply Decimals Multiply 2 Digits by 2 Digits Multiply 4 Digits by 2 Digits Multiply 7 Digits by 2 Digits Multiply Decimals Divide 2 Digits by 1 Digit Divide 4 Digits by 1 Digit Divide 7 Digits by 1 Digit Divide With Remainders Decimal Quotients Divide 2 Digits by 2 Digits Divide 4 Digits by 2 Digits Divide Decimals Solve Word Problems Solve Word Problems Review Multiplication and Division Review Multiplication and Division

Unit 4 . . . . 76 . . . . . . . . 77 . . . . . . . . 78 . . . . . . . . 79 . . . . . . . . 80 . . . . . . . . .......... 81 . . . . . . . . 82 . . . . . . . . 83 . . . . . . . . 84 . . . . . . . . 85 . . . . . . . . .......... 86 . . . . . . . . 87 . . . . . . . . 88 . . . . . . . . 89 . . . . . . . .

Fractions Add Fractions with Like Denominators Add Fractions with Unlike Denominators Subtract Fractions with Like Denominators Subtract Fractions with Unlike Denominators Add and Subtract Positive and Negative Fractions Understand Multiplying Fractions Multiply Mixed Numbers Divide Fractions Divide Mixed Numbers Multiply and Divide Positive and Negative Fractions Solve Word Problems Solve Word Problems Review Fractions Review Fractions

Table of Contents Unit 5 . . . . 90 . . . . . . . . 91 . . . . . . . . 92 . . . . . . . . 93 . . . . . . . . 94 . . . . . . . . 95 . . . . . . . . 96 . . . . . . . . 97 . . . . . . . . 98 . . . . . . . . 99 . . . . . . . . 100 . . . . . . . 101 . . . . . . . 102 . . . . . . .

Equations and Graphs Use Order of Operations Write Equations Solve Equations Solve Equations Understand Functions Graph Functions Graph Functions Graph Functions Graph Rates Graph Rates Review Equations and Inequalities Review Equations and Inequalities Review Graphing Functions

Unit 6 . . . . 103 . . . . . . . 104 . . . . . . . 105 . . . . . . . 106 . . . . . . . 107 . . . . . . . 108 . . . . . . . 109 . . . . . . . 110 . . . . . . . 111 . . . . . . . 112 . . . . . . . 113 . . . . . . . 114 . . . . . . . 115 . . . . . . .

Measurement Use Time Measurements Convert Temperatures Use Weight Measurements Identify Angles Find Angles Find and Convert Customary Lengths Find and Convert Metric Lengths Convert Customary to Metric Convert Metric to Customary Solve Word Problems Solve Word Problems Review Measurement Review Measurement

Unit 7 . . . . 116 . . . . . . . 117 . . . . . . . 118 . . . . . . . 119 . . . . . . . 120 . . . . . . . 121 . . . . . . . 122 . . . . . . . 123 . . . . . . . 124 . . . . . . . 125 . . . . . . . 126 . . . . . . . 127 . . . . . . . 128 . . . . . . .

Geometry Find Perimeters Use the Pythagorean Theorem Find Circumferences Find Area of Parallelograms Find Area of Triangles Find Area of Circles Find Area of Irregular Figures Find Surface Area Find Volume Solve Word Problems Solve Word Problems Review Geometry Review Geometry

Unit 8 . . . . 129 . . . . . . . 130 . . . . . . . 131 . . . . . . . 132 . . . . . . . 133 . . . . . . . 134 . . . . . . . 135 . . . . . . . 136 . . . . . . .

Probability Find Averages Figure Probability Understand Odds Identify Mean, Median & Mode Solve Word Problems Solve Word Problems Review Probability Review Probability

137 138 139 140 141 142 143 144

Scope and Sequence Answer Key Answer Key Answer Key Answer Key Answer Key Answer Key Answer Key

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

About This Series This series was created by Saddleback Educational Publishing to provide extensive math practice as a supplement to in-class instruction. Math Computation Skills and Strategies can easily be integrated into math curricula to reinforce basic skills.The lessons focus on practice, with up to 70 items a page. In addition, the lessons are designed to challenge students as their skills grow stronger. As the students progress through the individual lessons, the degree of difficulty increases. Closely adhering to state standards, this series provides grade-level appropriate lessons that are approachable for students at a range of abilities. Review lessons are interspersed throughout the book to allow students to reinforce their skills. Furthermore, the Scope and Sequence chart at the back of the book will help you choose lessons that are applicable to your curriculum.This series covers a range of topics, allowing students to build skills in multiple areas. Additionally, the lessons provide a variety of approaches, including word problems that emulate real-life situations. Each book is designed to challenge students who are learning skills at the corresponding grade level. However, the lessons were created not just for younger children, but for students of all ages. Saddleback Educational Publishing believes in allowing students to strengthen their skills with fun and exciting practice lessons.We hope you enjoy using this series to supplement class instruction and help students gain skills for proficiency in math computation.

Understand Integers Integers can be positive, negative, or zero.

Directions: Circle the integers and cross out the non-integers. a

b

c

d

e

1 3

-709

f

1.

-35

0.5

1200

2.

3 4

18

9 10

-25,976

5.72

3.

97

-62

0.359

960,448

1

4.

573,068

3 10

-571

-6.003

28

0

-3960

40

2.54

-298

610

5.

2

4

17 19

-10.6

121

Directions: Complete the number line and then define the word integer.

-8

-6

-4

-2

0

Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006

2

4

6

8

Date 6

3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com

Add and Subtract Integers When you add or subtract integers, pay close attention to whether they are positive or negative. This will affect the sum or difference. Subtracting a negative integer is like adding its opposite. 3- -4 = 7 Adding a positive number and a negative number is like subtracting two positive numbers.The sum will be positive or negative, depending on which addend is greater. -5 + 9 = 4 -7 + 3 = -4 Directions: Solve. a

b

c

1. - 4 + - 8 =

-12 -13 =

-10 +15 =

2. 5 + - 9 =

5-9=

-7 - 8 =

3. 13 - - 8 =

-7 + 13 =

- 20 - - 40 =

4. - 6 - - 4 =

10 - 15 =

500 + - 600 =

a

b

c

d

e

5.

80 + 240

2200 + 1900

340 + 50

306 + 204

27 + 62

6.

130 + 450

600 + 700

950 + 951

532 + 472

130 + 900

7.

25 75

68

653

871

75

+ 32

+ 500

+ 13

+ 33


Date 7


Find Absolute Values The absolute value of a number tells how far it is from zero. |-5| = 5 |5| = 5

Directions: Solve. a

b

1.

|9|

|-57|

|-2.3|

2.

|-17|

-|57|

|5705|

3.

|-378|

|4.5|

|-3 1/3|

4.

|-1/5|

-|-4927|

-|- 489|

5.

|-94|

- |-3 + 2|

|0-14|

6.

|7 - 9|

-|32|

|13 - 7|

7.

-|13-5|

|-32|

-|35 ÷ 5|

8.

|-3 + 2|

(-|-3|)2

|9 - 15|

c

Directions: Write , or = to complete the math sentence. a

9.

|-7|

10.

|3-4|

b

7 -|3-4|

c

-|5-2|

|-3|

-|-5|

|-5|

-|-25|

-52

|7-9|

(-|7-4|) +4


Date 8


Read Coordinate Graphs Plotting points on a coordinate graph is easy. Just remember that the distance along the horizontal x-axis, is listed first.

Directions: Name each point.The first one is done for you. 1. A (2,7) B C

•A

D

•F •B

E F

•E •G

•C •D

G H

•

H

Directions: Plot the point at the correct place. 2. M (0, 3) N (7, 7) O (8, 5) P (9, 1) R (3, 8) S (5,7) T (1, 9) V (4, 6)


Date 9


Find Squares and Square Roots If you know your squares, it’s easy to find square roots. 9 = 3 32 = 9

Directions: Find the square or the square root. a

b

16

121

1.

52

2.

152

122

3.

225

152

4.

36

62

5.

c

72 64

252

4

92

6.

100

7.

400

8.

112

9.

302

10.

252

162 196

142 49

102 2500

22 25

12


d

132

625 202 81

502 900

42 256

202

289

402

324

Date 10


Express Powers of Ten Using exponents can save time and space. For example 106 is the same as 1,000,000, or one million.

Directions: Write the number and its name.The first two are done for you.

a

b

1.

100 = 1, one

105 =

2.

101 = 10, ten

106 =

3.

102 =

107 =

4.

103 =

108 =

5.

104 =

109 =

Directions: Write the number using powers of ten. a

b

6.

100 =

1,000,000 =

7.

11 =

100,000,000 =

8.

11,000 =

10,000,000 =

9.

110 =

1,000,000,000 =

110,000 =

100,000 =

10.


Date 11


Use Exponents Exponents are handy when a number is multiplied by itself repeatedly.

5 x 5 x 5 = 53 =125 base exponent

5 to the power of 3

Directions: Write the equation and solve. a

b

c

1.

82 =

54 =

63 =

2.

26 =

23 =

110 =

3.

33 =

74 =

84 =

4.

61 =

45 =

38 =

5.

92 =

07 =

93 =

Directions: Write the exponent, then solve. a

b

6.

2x2x2=

6x6x6x6=

7.

4x4x4x4x4=

9x9

8.

7x7x7x7x7x7x7 =

3x3x3x3x3x3x3x3x3x3=

9.

8x8=

10 x 10 x 10 =

5x5x5=

1x1x1x1x1x1=

10.


Date 12


Identify Equivalent Fractions Remember: Equivalent means equal.

Directions: Complete each number sentence with = or . a

b

c

7 3 ___ 8 4 2 1 ___ 6 3

12 6 ___ 16 8 2 1 ___ 12 4

4 2 ___ 5 3 4 2 ___ 16 8

3.

1 4 ___ 2 8

1 3 ___ 3 9

1 2 ___ 7 14

4.

2 10 ___ 3 12

3 1 ___ 12 3

5 9 ___ 6 12

1. 2.

Directions: Write equivalent fractions. a

5. 6. 7. 8. 9. 10. 11.

b

c

7 = 8 5 = 10 1 = 3

1 = 6 1 = 4 8 = 16

11 = 12 3 = 5 3 = 9

3 = 4 3 = 10 1 = 2 2 = 3

2 7 7 9 5 8 5 6

4 = 8 4 = 5 2 = 4 10 = 12

= = = =


Date 13


Convert Decimals and Fractions Fractions and decimals are different ways of writing the same amount.

4 = 0.8 = .8 5 Directions: Write the equivalent fraction or decimal. a

b

1 = 2 3 = 10

3 = 4 19 = 20

3.

0.75 =

0.1 =

0.60 =

4.

.4 =

1 = 2

2 = 5

5.

1 = 5

.25 =

.9 =

6.

0.125 =

3 = 5

1 = 100

7.

0.09 =

0.80 =

0.90 =

8.

59 = 100

.66 =

0.003 =

1. 2.

c

1 = 4 0.5 =

Directions: Complete the number sentence by writing , or =.

9. 10. 11.

a

b

c

1 1 ___ 3 4 1 ___ 0.2 4

5 ___ 0.5 8 9 0.9 ___ 10 1 ___ 0.4 3

3 7 ___ 4 9 1 ___ 0.5 2 1 0.3 ___ 3

0.75 ___

75 100


Date 14


Work with Non-Terminating Decimals Some decimal numbers just never end! Here are some ways to deal with non-terminating decimals. Round to the nearest tenth.

7 = 2.6457513 = 2.6

Put a bar over the digits that repeat. 1 = 0.166666666 = 0.16 6 Use an established number. 3.1416

= 3.14159265358979323846264338 =

Directions: Find the decimal equivalent. If it is non-terminating, use a solution from above. a

b

2=

1.

6=

2.

1 = 8

13 =

3.

1 = 7

1 = 18

5.

1 = 9

3 = 7 11 = 12

5=

6. 7.

11 =

8=

4.

5 = 6

8.

7= 2 = 11

3=


Date 15


Compare Integers To compare integers, first look at the signs, then look at digits in the same place value. 38 < 41

- 256 > -276

Directions: Circle the number that is greater than the number in dark print. 1.

51

-52

55

49

-100

50

2.

478

469

379

380

480

-479

3.

-62

-60

-63

-65

-70

-100

4.

-300

-301

-298

-310

-350

-360

Directions: Complete the number sentence by writing < or >. a

b

178

c

8.13

8.14

-1

0

5.

175

6.

23

7.

643

633

7061

7062

1081

8.

-97

-96

4231

4321

354

9.

2576

10.

-5.3

-5.2

11.

809

12.

609

23.4

2476

-8

-0.3

-9

-0.31 1180 345

-50

2675

3675

0.51

0.5

4873

-4872

798

6498

6488

31,568

690

757

-52

758


-697

31,468 698

Date 16


Order Integers The sign can make all the difference.

Directions: Write the numbers in order from least to greatest. 1.

52, -51, 357

2.

75, 68, -76

3.

0.8, 8, -8

4.

3157, 3298, 3536, 3300

5.

0.623, 0.236, 0.326

6.

51, 5.1, -51, -5.1, 5, -5

7.

40,579; 40,569; 41,559

8.

1, 0.001, 0.1, 0.01

Directions: Write the numbers in order from greatest to least. 9.

0.7, -7, 0.07

10.

5230, 5320, 5302

11.

-58, -59, 60

12.

2.5, 2.4, 2.45


Date 17


Rounding Sometimes you don't need to use exact numbers.You can round a number to the nearest ten or hundred, for example. To round a number, look at the digit in the place to the right of the place you are rounding to. Round up if it is 5 or greater. Round down if it is 4 or less. Directions: Look at the number in dark print. Circle the number next to it that is the same number rounded to the nearest ten. a

1.

14

2.

37

3.

50

10

b

14

15

20

88

80

85

90

100

30

35

40

50

96

80

90

95

100

40

50

55

60

121

100

110

120

130

Directions: Round the decimal to the nearest whole number. a

b

c

4.

0.3

3.09

72.25

5.

2.8

1.46

58.82

6.

4.04

9.5

416.707

Directions: Round the number to the nearest ten, hundred, and thousand. nearest ten 7.

737.5

8.

1,154

9.

2,608.06

10.

4,380.3

nearest hundred


nearest thousand

Date 18


Rounding and Estimating Rounding and estimating can help you check your answers.

76 + 31 80 + 30 = 110 The symbol means “is approximately” or “is about equal to.” The exact answer is 107, which is close to 110. Directions: Round each addend and estimate the answer.Then find the exact answer. a

b

1.

89 + 19 =

56 + 2 =

2.

54 + 77 =

423 + 160 =

3.

452 + 36 =

807 + 998 =

4.

607 + 528 =

5,352 + 736 =

5.

3,121 + 4,094 =

62 + 80 =

6.

94 + 45 =

109 + 583 =


Date 19


Find Percentages Percent means “out of each hundred.” Directions: Solve. a

b

1.

60% of 80 =

88% of 100 =

2.

50% of 90 =

75% of 150 =

3.

90% of 30 =

200% of 6 =

4.

70% of 200 =

35% of 50 =

5.

25% of 4000 =

10% of 30 =

6.

65% of 20 =

150% of 8 =

Directions: Find the percentage for each set of numbers. a

b

7.

20 out of 80 =

9 out of 9 =

8.

9 out of 15 =

3 out of 300 =

9.

6 out of 54 =

12 out of 8 =

10.

5 out of 75 =

6 out of 12 =

11.

11 out of 110 =

12 out of 6 =

12.

50 out of 200 =

5 out of 500 =


Date 20


Find Percentages Working with percentages is like working with decimals.You may need to round percentages to the nearest whole number. 4 out of 12 = 33.333333...% round to 33%

Directions: Find the percentage for each set of numbers, rounding if needed. Show your work. a

b

1.

2 out of 7 =

10 out of 60 =

2.

400 out of 900 =

25 out of 20 =

3.

5 out of 6 =

1 out of 3 =

4.

1 out of 30 =

22 out of 24 =

5.

50 out of 30 =

17 out of 20 =

6.

0.5 out of 1 =

17 out of 19 =

7.

18 out of 24 =

400 out of 600 =

8.

60 out of 45 =

3 out of 4 =

9.

700 out of 800 =

28 out of 30 =

10.

30 out of 200 =

1 out of 12 =

11.

Tanner spent 50 minutes doing homework. Of that time, 40 minutes was on math. What percentage of his time did Tanner spend doing math homework?

12.

The next night,Tanner spent 80 minutes doing homework. Of that time, he spent about 45 minutes on math.What percentage of his time did Tanner spend doing math homework?


Date 21


Convert Percents and Decimals Percents and decimals are very similar to each other. Directions: Convert each decimal to a percent and each percent to a decimal. a

b

c

1.

85% =

200% =

1.5 =

2.

0.47 =

.34 =

10% =

3.

.72 =

98% =

40% =

4.

29% =

1.0 =

0.001 =

5.

50% =

15% =

0.8 =

6.

0.9 =

0.56 =

82% =

7.

0.06 =

99% =

132% =

8.

3% =

0.835 =

2.5 =

Directions: Write =, to compare the numbers. a

b

c

9.

0.4

0.39

10.

37%

0.4

0.7

75%

0.5

11.

0.9

90%

2.1

21%

200%

12.

0.05

50%

1.3

130%

0.61

62%


0.19

4%

20% 50% 0.2 0.4

Date 22


Convert Fractions and Percents Converting percents and fractions is tricky, but you can do it!

To convert a fraction to a percent: Divide the numerator by the denominator, multiply by 100, and add the percent sign. 3 = 3 ÷ 4 = 0.75 100 = 75% 4 To convert a percent to a fraction: Make the percent the numerator with a denominator of 100. Simplify. 80 4 80% = = 100 5 Directions: Convert each fraction to a percent and each percent to a fraction. a

1.

1 = 2

2. 40% = 3. 4.

b

c

7 = 8

1% =

30% =

1 = 20

9 = 10

2 = 3 5 = 9

99% =

1 = 4

110% =

Directions: Write =, to compare the numbers. a

5.

1 1 ___ 4 3

1 3 7. 85% ___ 17 20 8. 15% ___ 1 8 6.

35% ___

b

c

50% ___

3 5

3 ___ 31% 10 9 ___ 9% 100 5 110% ___ 4


7 ___ 7% 1000 99 99% ___ 100 21 42% ___ 50 3 ___ 80% 4 Date

23


Understand Ratios A ratio compares two amounts. A ratio can be expressed using a fraction, and can be simplified, or reduced to lowest terms. In the 2000 census, the U.S. Government counted 96 men for every 100 women in the country. The ratio of men to women was 96 out of 100, or 24 to 25.The ratio can also be expressed in these ways: 24 or 24:25. 25 Directions: Write a ratio for each. Garfield Middle School has an intramural sports program. The basketball team has 7 boys and 4 girls. The softball team has 5 boys and 7 girls. The volleyball team has 8 boys and 8 girls. 1.

girls in basketball to the basketball team

2.

boys in basketball to girls in basketball

3.

boys in basketball to boys in softball

4.

the basketball team to the boys in basketball

5.

boys in basketball to boys in the whole program

6.

girls to boys in volleyball

7.

girls in basketball to girls in volleyball

8.

girls in volleyball to students in the whole program

9.

boys in softball to boys in basketball and volleyball

10.

girls in volleyball to students in the program

11.

boys in the program to students in the program

12.

girls in the program to boys in the program


Date 24


Find Ratios Setting up a ratio can help you find a number.

The ratio of men to women is

24 . 25

If 2,000 women lived in a town, how many men (m) would there be?

24 m = 25 2000 25m= 24 2, 000 = 48, 000 m=1,920

Directions: Complete the ratio. a

b

c

1:4 = ?:44

2 6 = 9 ?

2. 5 to 9 = 10 to ?

15 to 18 = 5 to ?

4:5 = 16:?

3. 1:3 = 9:?

3 6 = 2 ?

18 to 27 = ? to 3

1.

3 ? = 4 16

4.

3 6 = 10 ?

7:10 = ?:40

15 ? = 3 1

5.

5 = ? to 35 7

24 to 26 = 12 to ?

80:1000 = 8:?

? 19 = 20 100

5 ? = 6 18

6. 1:6 = ? :18


Date 25


Understand Irrational Numbers An irrational number is a decimal that doesn't repeat or end and isn't a fraction. Other numbers are rational. is the ratio of the circumference of a circle to its diameter.This ratio is the same for all circles. = 3.1415926535897932384626433832795028841971... The points after the 1 at the right (... ) mean that the number continues on without repeating or terminating.

Directions: Write I if the number is irrational.Write R if it is rational. a

1.

2.

4.

3 = 0.75 4

2 = 1.4142135K 2 9

3.

b

= 0.222222K

9.3 = 3.04959K

11 = 0.9166K 12

2 = 0.6666K 3

3 = 1.732050K

6.5 = 2.5495K

5 = 0.625 8

5. e = 2.718281...

6.

3 = 0.42857K 7

7 = 2.64575K

7. 0.573

321.321321321...

8. 0.33333333...

2.673473


Date 26


Solve Word Problems Use what you know about numbers and number sense to solve these word problems. Directions: Solve. 1. Gabe ran seven laps around the track each day for seven days in a row. How many laps did he run in all? Express the total in standard form and using an exponent.

2. After his daily run, Gabe is only 50% done with his workout. Some days he lifts weights next. He met his friend Sabrina in the gym one day. She said that 2 she was done with her workout.Who was further along? 3 Show your conversion.

3. Sabrina has been weight training for years. Sabrina told Gabe that she can bench press 102 pounds. How many pounds is that?

4. Gabe lifted 125 pounds to build bulk, then subtracted 45 pounds and lifted that amount to build strength.What amount did he lift to build strength? Write the equation and the amount.


Date 27


Solve Word Problems Use what you know about numbers and number sense to solve these word problems. Directions: Solve. 1. Julia scrapbooked her pictures. She bought special paper in squares to glue her photos onto.The area of the square was 49 square inches.What size was the paper?

2. The area of another square Julia bought was 64 square inches.What size was the paper?

3. Julia realized that two pictures were too big for her scrapbook. She wanted to scale them down by half. She wrote ratios to compare width and length. Complete the ratios. 8 4 6 ? = = 10 ? 10 5

4. The length of a square picture is 8 inches. Julia reduced it to 4 inches.What percentage of the area of the larger picture is the area of the smaller picture?


Date 28


Solve Word Problems You already have the skills — now practice applying them. Directions: Solve. 1. Scientists have measured extremely cold liquids.Which of the following readings is the coldest? -7°, -26°, 32°, 0°

2. Scientists have weighed seeds.Write these weights in order from lightest to heaviest, or least to greatest mass. 0.1273 g, 0.1327 g, 0.1237 g, 0.1372 g

3. When the scientists tried to grow their seeds, only 24 out of 32 grew. 24 Write three fractions equivalent to . 32

24 4. What is the decimal number equivalent to ? Is it a rational or irrational 32 number? How can you tell?


Date 29


Review Numbers and Number Sense Now you have the chance to show what you know!

Directions: Look at the number.Write IN for integer, IR for irrational number, or R for ratio. a

1.

-27

2.

1,400

b

1 8

3.

c

0.5

3

2

-439

d

-2.7 60,571

11 12

0

Directions: Solve. Show all your work. a

4.

b

1.09

121 =

5.

6x6x6x6=

3:4 = 15:

6.

-40 + 70 =

108 =

7.

83 =

36 to 9 = 8 to

8.

-|-7| =

13 - -8 =

9.

95

10.

81 =

Callie did an experiment with plants.At the end of the experiment she measured the height of the plants to see which grew the tallest.Write the heights in order of least to greatest to help her. 3.6 in, 3.24 in, 3.42 in, 2.9 in, 3.5 in, 2.09 in


Date 30


Review Numbers and Number Sense Here’s another chance to show what you know.

Directions: Write , or = to show how the numbers compare. a

1. 2.

b

8 4 ___ 10 5 1 0.1 ___ 9

3. 50% ___ 0.05 4.

1 ___ 0.125 8

5.

13% ___

1 7

6.

3 ___ 1.75

7.

17 ___ 85% 20

8. -15 ___ -16

c

5 ___ 0.85 6

200% ___ 2.0

-0.34 ___ -0.23

0.4 ___ 4%

2 ___ 45% 5

61 100 1 30%___ 3 0.6 ___

15% ___ 1.5

14 7 ___ 36 18 1 ___ 21% 5

2 ___ 1.5

9 ___ 9% 100 1 0.33 ___ 4

0.8 ___ .80

3 ___ 75% 4

10% ___0.2

Directions: Name where points A-E are located, then plot points F-J at the correct places. 9. A B C D E

F (8, 3) G (10, 7) H (6, 10) I (4, 3) J (3, 6)

•B •A

•D

•C • Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006

E

Date 31


Use Addition Properties Learn the properties of addition below to help you add more quickly and easily. The Identity Property says that the sum of any number and zero is that number. The Commutative Property says that you can add two numbers in either order and get the same sum. The Associative Property says that you can group three or more numbers in any way and get the same sum.

Directions: Write C if the equations demonstrate the Commutative Property, A for Associative, and I for Identity. a

b

1.

6 + 7 = 13

7 + 6 = 13

2.

15 + 0 = 15

0+3=3

3.

(1 + 2) + 3 = 6

1 + (2 + 3) = 6

4.

95 + 5 = 100

5 + 95 = 100

5.

20 + (6 + 4) = 30

(20 + 6) + 4 = 30

6.

0 + 3700 = 3700

62 + 0 = 62

7.

48 + 4 = 52

4 + 48 = 52

Directions: Write two examples to demonstrate each property. 8.

Identity

9.

Commutative

10.

Associative


Date 32


Add Two Digits Always start by adding the ones column. Remember to regroup into the next greater place value, if needed. Directions: Add. a

b

c

35

68

76

89

75

+ 24

+ 71

+ 76

+9

+ 65

2.

16 + 43

49 + 38

38 + 25

52 + 37

49 + 47

3.

58 + 60

92 + 40

47 + 58

64 + 18

38 + 63

4.

84 + 54

53 + 47

22 + 67

40 + 46

72 + 28

5.

8 + 85

16 + 94

96 + 81

58 + 23

37 + 28

1.


d

e

Date 33


Add Up to Four Digits Try adding numbers in the thousands.

Directions: Add. a

1.

573 + 425

2.

962

b

284 + 76

c

d

e

697 + 328

837 + 629

508 + 757

537

5228

3041

653

+ 468

+ 829

+ 554

+ 748

+ 2346

3.

2512 + 4396

6683 + 741

7052 + 8353

7236 + 4543

2834 + 2834

4.

5485 + 3333

3691 + 6317

4493 + 1857

3958 + 4062

8751 + 6352

Directions: Rewrite in vertical form, then add. Remember to line up the digits in the ones place. a

b

5. 475 + 366 =

598 + 3702 =

6. 7086 + 3259 =

6113 + 987 =


Date 34


Add Up to Seven Digits Adding numbers in the millions is the same as adding other numbers.You Tip may need to regroup more than once. Directions: Add. a

b

c

d

1.

7390 + 4386

52,174 + 2,583

84,528 + 3, 471

58, 496 + 785

2.

33,673 + 26,325

38, 209 + 43,352

62,630 + 584

95,332 + 22, 257

3.

461, 037 + 32,843

249, 426 + 75,185

326,124 + 173,859

608,892 + 372, 209

4.

876,958 + 98,167

735, 245 + 466,729

2, 093, 461 + 1,357, 477

6,738,745 + 3, 017, 283

Directions: Rewrite in vertical form, then add. Remember to line up the digits in the ones place. a

b

5. 93,158 + 46,873

698,543 + 56,781

6. 843,420 + 750,985

4,256,329 + 327,466

Name Math Computation Skills and Strategies, Level 7 Saddleback Publishing, EducationalInc. Publishing ©2006 ©2006

Date 35


Add Decimals When adding decimals, line up the numbers on the decimal points. Regroup Tip as you would other numbers. Directions: Add. a

b

c

d

e

5.3

4.8

5.5

12.8

3.2

+ 6.4

+ 3.7

+ 7.9

+ 3.6

+6

2.

6.21 + 2.36

3.25 + 6.33

8.47 + 3.26

2.4 + 6.03

21.34 + 0.25

3.

0.336 + 0.283

1.803 + 0.089

0.521 + 0.359

2.1 + 0.683

0.685 + 2.37

4.

41.3 + 3.76

7.75 + 0.98

23 + 0.23

4.5 + 0.45

7.02 + 2.98

1.

Directions: Rewrite in vertical form, then add. Remember to line up the decimal points. a

b

5. 3.5 + 2.6

6.3 + 9

6. 10.22 + 3.79

3.04 + 0.974


Date 36


Practice Addition See how quickly — and accurately — you can complete these addition equations. Directions: Add. a

b

c

597

3489

9.35

684

96

+ 23

+ 504

+ 7.19

+ 97

+ 345

2.

672 + 934

96.7 + 82.7

854 + 3986

81.76 + 57.79

7.39 + 68.71

3.

8143 + 5589

6235 + 4745

338 + 572

59 + 33

853 + 276

1.

a

b

d

e

c

d

4.

7,671 + 26, 286

21,680 + 74,532

852,873 + 464,566

407,325 + 3,598,633

5.

93,507 + 46,868

368,192 + 485

283,938 + 62,338

567, 433 + 3,557,942


Date 37


Practice Addition Always remember to line up the numbers on the ones or on the decimal points. Directions: Rewrite the equations vertically, then add. a

b

1. 47 + 58

3,672 + 362,759

2. 2398 + 4871

8.037 + 2.58

3. 2.5 + 3.7

76,521 + 8,797

4. 3673 + 5436

968 + 786

5. 52,370 + 36,389

25,300 + 30,435

6. 45.35 + 75.25

6,543,219 + 876,123


Date 38


Subtract Two Digits Start subtracting at the ones place. Regroup as needed.

Directions: Subtract. a

b

c

d

e

1. 86 - 35

13 - 8

39 - 18

44 - 21

71 - 59

2. 97 - 34

29 - 18

82 - 73

90 - 56

47 - 18

3. 56 - 38

64 - 34

78 - 39

32 - 4

64 - 37

4. 60 - 47

85 - 37

93 - 46

87 - 38

38 - 6

5. 83 - 43

51 - 40

33 - 27

62 - 35

94 - 35

6. 75 - 16

21 - 8

46 - 38

73 - 44

50 - 23


Date 39


Subtract Up to Four Digits You might have to borrow more than once. Remember to keep track each time. Directions: Subtract. a

b

c

d

e

1.

657 452

934 733

688 471

590 322

2.

684

805

427

4726

6738

277

74

359

624

514

3.

3986 1122

5139 3621

9455 7440

6107 328

8265 931

4.

2835 2826

6928 4717

7863 3598

9072 7203

4120 1517

365 49

Directions: Rewrite in vertical form, then subtract. Remember to line up on the ones place. b

a

5. 475 - 389 =

682 - 590 =

6. 6851 - 3632 =

9332 - 782 =


Date 40


Subtract Up to Seven Digits Subtracting in the millions is just like subtracting other numbers.

Directions: Subtract. a

b

5,876

67,745

38,696

72, 457

4,766

53, 224

15, 473

69,342

2.

93, 067 72,749

85, 436 8,732

77,512 46,331

544,680 321,547

3.

476,375 259, 260

700,000 351, 289

517, 289 366,198

270,834 9,851

4.

2, 483,599 1,352,479

4,325,928 627,635

6,817,500 3,921,622

8,351,701 7,892,663

1.

c

d

Directions: Rewrite in vertical form, then subtract. Remember to line up on the ones place. a

b

5. 65,723 - 27,641

875,400 - 6,785

6. 380,452 - 276,368

5,423,167 - 3,246,897


Date 41


Subtract Decimals You can always add zeroes after a decimal point to hold a place.

Directions: Subtract.Write the answer in its shortest form. a

b

c

8.9

6.9

5.24

7.577

9.346

4.5

2.8

3.33

4.034

4.394

2.

3.57 2.2

12.5 3.4

4.6 0.75

8 0.5

10.63 3.07

3.

1 0.001

5.75 2.28

6.203 3.4

7.36 5.36

15 0.15

4.

14.43 8.702

3 1.75

7.1 2.68

8.9 0.89

2.48 1.09

1.

d

e

Directions: Rewrite in vertical form, then subtract. Remember to line up on the decimal point. a

b

5. 7.2 - 5.6

6 - 3.17

6. 5 - 2.25

2.1 - 0.308


Date 42


Practice Subtraction The biggest mistake people make is regrouping when it's not needed or forgetting to borrow when it is. Directions: Subtract.

1.

2.

3.

a

b

c

85

157

62

39

d

e

623

582

73

476

93

18

367

2361

285

487

4759 2892

5000 2541

a

5932

7184

85

89

377

62

6079 2184

9645 2763

4540 3636

b

c

d

4.

46,300 18,596

583, 256 34,164

920,157 6, 221

632,700 270, 070

5.

721,361 719,275

867, 073 668, 069

7,834,603 6,934,747

3,525, 400 1, 287,364


Date 43


Practice Subtraction Always remember to line up the numbers on the ones or on the decimal points. Directions: Rewrite the equations in vertical form, then subtract. a

b

1. 87 - 35

9216 - 4775

2. 7436 - 279

4.523 - 0.36

3. 5 - 3.75

76,921 - 6,877

4. 31,455 - 28,364

600 - 147

5. 570 - 248

5,432,198 - 1,234,567

6. 671,388 - 87,500

59,723 - 6,894


Date 44


Add and Subtract Greater Integers Apply the same rules for adding and subtracting greater integers.You may wish to change the order of some problems for easier computation.

17 + 35 18

35 + 17 18

Directions: Rewrite the equations in vertical form, then solve. a

b

1. - 4385 + -5927

-23.6 + - 33.27

2. 508 - -926

-5281 + 6572

3. 67,293 + -36,198

-485 - 672

4. 7.6 + -1.9

-83,436 - 24,754

5. -2364 - -6374

75 - 6308

6. 1615 - 2739

1268 + - 3522


Date 45


Check Addition and Subtraction Because addition and subtraction are inverse operations, you can use one to check the other. Directions: Write and solve a subtraction problem to check each sum, and an addition problem to check each difference. Circle correct answers. a

b

c

1. 435 + 627 = 1162

9114 - 2477 = 7637

74,331 + 25,388 = 100,291

2. 3379 - 2859 = 620

8675 + 7863 = 16,538

971 - 795 = 166

3. 58,210 + 3,586 = 61,796

61,300 - 39,282 = 21,018

697,343 + 486,304 = 1,083,647

4. 4663 - 2738 = 1935

5768 + 5789 = 11,557

8405 - 2377 = 5028

5. Adrian once counted 77 steps from the street to his locker.Today he's already walked 29 steps, so he figures he has 58 more to go. Is he correct? Write the equation he used and the equation to check it.


Date 46


Solve Word Problems Look for key words to help you decide which operation to use.

Addition word problems often involve putting sets of numbers together or gaining a certain amount. Clue words that may indicate addition include altogether, total, or in all. Subtraction word problems often involve comparing sets of numbers or losing a certain amount. Clue words that may indicate subtraction include difference, more, or borrow. Directions: Write the letter of the expression that matches each word problem.Then solve. A 475 + 104

B 475 - 104

C -475 + -104

D -475 + 104

1. Most of the year, the town of Sagebrush has a population of 475. During the hot summer, 104 people leave for cooler areas. How many people live there in the summer? 2. Stony Mountain path goes to where the mountain is 475 feet tall.The last 104 feet of the mountain is a sheer rock wall that no one can climb. How tall is the mountain altogether? 3. Little Canyon is 475 below sea level. If one climbs from the bottom to the first overlook, you will have climbed 104 feet. How far below sea level will you be now? 4. You can take a whitewater rafting trip starting in Little Canyon.The canyon is at 475 feet below sea level, but the river takes you 104 feet even lower. How much lower will you be at the end of the rafting trip? Directions: Write the equation and solve. 5. One night, the temperature on Stony Mountain got down to -20.The temperature rose by 47 degrees the next day. How warm did it get that day?


Date 47


Solve Word Problems If you're not sure of an answer, you can always use the inverse operation to check yourself. Directions: Write an equation, then solve. Show your work. Remember to line up the numbers in the equation correctly and to label your answers. 1. Luke was learning a new card game. His score the first hand was -243 and the second hand was 368.What was his total score after two hands?

2. Meg skiied down Bull Hill in 58.78 seconds.The next time she tried, she did it in 58.69 seconds. How much faster was she the second time?

3. Meg had only 207 pages left to read of her graphic novel.The next day, she only had 132 pages more to read. How many pages had she read?

4. Luke read 93 pages of a book one day and 118 the next. How many pages had he read in all?

5. At the football game, 34,264 people sat on one side of the stadium and 33,987 sat on the other. How many people were sitting in the stadium in all?

6. How many more people sat on one side than the other in the football stadium?

7. Luke lives in a city of 35,207 people.The city next to his has 27,655 people. Luke says that there are 8,652 more people where he lives. Is he correct? Write the subtraction equation he used and an addition equation to check his subtraction.


Date 48


Review Addition and Subtraction Be careful to watch the signs!

Directions: Add or subtract. a

b

c

1.

682 + 739

836 556

4597 + 8384

2.

9056 + 8477

7039 4254

52.3 26.35

3.

42,963 35,956

d

5701 2342

846,213 + 352,749

92, 461

4.367 + 7.88

3567 2438

+ 356,878

Directions: Solve.Write the inverse equation to check yourself. a

b

c

4. 4183 + 2877

8500 - 3423

55,576 - 29,048

5. 9216 - 6636

76,309 + 8,931

6718 + 7894


Date 49


Review Addition and Subtraction You have all the information you need to solve them all!

Directions: Rewrite the equation in vertical form, then solve. a

b

1. 10 - 0.503 =

4.8 + 5.94 =

2. 68 + 735 =

941 - 736 =

3. 6829 - 3144 =

54,328 + 97,143 =

4. 72,038 + 57,358 =

9633 - 5727 =

5. 852,316 - 39,427 =

845,365 + 2,635,354 =

Directions: Write the equation and solve it. 6. Dylan bought a new shirt for $29 and new pants for $37. How much did his new clothes cost in all?

7. Erin looked at one cell phone that cost $127 and another that cost $65. What was the difference in cost?

8. Erin had a gift certificate for $50, but her phone cost $127. She said she spent $72 of her own money. Is that correct? Show her equation and the equation you can use to check it.


Date 50


Find Multiples When you multiply any integer by 1, 2, 3, and so on, the product is a multiple of the first number: 6 x 1 = 6; 6 x 2 = 12; 6 x 3 = 18 4 x 5 = 20; 4 x 6 = 24; 4 x 7 = 28 6, 12, and 18 are multiples of 6. 20, 24, and 28 are multiples of 4. Directions: Fill in the blank with the correct number. a

b

.

4, 10, 14, and 18 are multiples of

.

1.

6, 9, and 12 are multiples of

2.


.

28, 35, 42, and 56 are multiples of

3.


.

12, 18, and 24 are multiples of both

4.


.


,

. and , and

. .

Directions: Circle the number that is a multiple of the first number. a

b

5.

5

22

16

20

11

21

22

23

6.

9

54

19

39

4

34

43

64

7.

3

23

31

21

7

70

27

17

8.

6

58

42

16

14

34

42

45

9.

8

18

42

24

19

119

91

114


Date 51


List Factors Numbers that you multiply together to get a product are called the factors of that number. 1 x 12 = 12 12 x 1 = 12 3 x 4 = 12 4 x 3 = 12

2 x 6 = 12

6 x 2 = 12

1, 2, 3, 4, 6, and 12 are the factors of 12. Directions: Circle the one or more numbers that are factors of the first number. a

b

1.

16

32

2

8

6

14

1

2

4

7

2.

20

5

2

10

9

18

4

8

12

18

3.

9

3

4

5

6

48

2

6

8

24

4.

30

5

6

3

10

90

6

11

15

45

5.

5

25

15

5

1

55

25

20

11

6

Directions: List all the factors of each number. a

b

6.

8

56

7.

15

22

8.

16

35

9.

19

4

10.

24

28


Date 52


Identify Prime and Composite Numbers All positive integers greater than 1 are either prime numbers or composite numbers. A prime number is a positive integer that has as factors only 1 and itself: A composite number has other factors as well as 1 and itself. 4 is composite because its factors are 1, 2, and 4. 6 is composite because its factors are 1, 6, 2, and 3. 7 is prime because its only factors are 1 and 7. Directions: Circle the number in each group that is a prime number. a

b

1.

6

11

9

21

12

31

2.

5

8

14

34

43

44

3.

16

18

19

16

13

25

4.

29

39

49

73

15

35

5.

17

170

54

51

72

37

Directions: Write the factors of each number. If the number is prime, write a P in the blank next to the number. 6.

47 Factors:

7.

38 Factors:

8.

42 Factors:

9.

19 Factors:

10.

51 Factors:

11.

65 Factors:

12.

77 Factors: Date


53


Identify Prime and Composite Numbers Composite numbers are the products of factors other than 1 and the number itself. 6 is a composite number because 1 x 6 = 6 and 2 x 3 = 6. 15 is a composite number because 1 x 15 = 15 and 3 x 5 = 15. Directions: Write the factors of each number.Then, if the number is prime, write a P in the blank next to the number. If the number is composite, write a C in the blank next to the number. 1.

18 Factors:

2.

27 Factors:

3.

63 Factors:

4.

41 Factors:

5.

49 Factors:

6.

70 Factors:

7.

97 Factors:

8.

29 Factors:

9.

58 Factors:

10.

81 Factors:

11.

105 Factors:

12.

125 Factors:

Directions: Write the first ten prime numbers. 13.


Date 54


Check Multiplication and Division Just as addition and subtraction are inverse operations, so are multiplication and division. Use one to check the other. 7 x 12 = 86? Check by dividing. 86 ÷ 7 = 12 remainder 2. No, 7 x 12 does not equal 86. Try again. 7 x 12 = 84? Check by dividing. 84 ÷ 7 = 12. Yes, you are correct. Directions: Write an inverse problem to check each equation, then solve it. a

b

1.

8 x 14 = 112

6 x 19 = 106

2.

67 x 3 = 204

76 ÷ 4 = 19

3.

34 ÷ 11 = 3

9 x 18 = 166

4.

234 ÷ 9 = 26

45 ÷ 3 = 15

5.

94 ÷ 6 = 16

6 x 71 = 426

6.

4 x 24 = 71

144 ÷ 18 = 6

7.

Kaylee scored 5 goals for her lacrosse team in one game. She hoped to do this in each of her team’s 16 games. If she did, she said that she would reach 84 goals and set the team record. Is her multiplication correct? Write Kaylee's equation.Then write a division equation to check it.


Date 55


Multiply 2 Digits by 1 Digit You’ll solve problems like this in real life all the time. Remember to regroup as needed. 24 5 20

65 9 45

87 6 42

10 120

54 585

48 522

Directions: Multiply. a

b

c

d

e

1.

59 6

83 3

48 9

92 3

36 5

2.

42 3

14 8

97 5

84 6

58 2

3.

60 2

91 9

62 5

29 9

70 7

4.

37 7

52 8

51 9

17 4

39 9

5.

75 2

73 4

73 4

40 8

56 4


Date 56


Multiply 4 Digits by 1 Digit Multiply numbers in the thousands just as you would other numbers. Remember to regroup as needed. Directions: Multiply. a

b

c

d

e

1.

9, 021 7

6, 490 6

3,964 6

6, 423 3

4,849 9

2.

5,386 2

4,371 4

5,803 2

5,510 8

9,321 2

3.

2,974 9

5,575 9

9,182 9

9,893 4

8, 456 8

4.

3, 002 5

9, 007 8

7,105 4

7,370 7

7,789 3

5.

8,853 6

7, 201 3

4, 484 7

2, 445 6

5, 413 7

6.

7,979

2,376

7, 290

5,509

6, 094

8

5


8

5

5

Date 57


Multiply 7 Digits by 1 Digit Multiply numbers with seven digits (millions) just as you would other numbers. Remember to regroup as needed. Directions: Multiply. a

b

7,348,901

1.

4

c

1,722,300

8

d

9,947,983

2

2,556,998

5

2.

2,955,571 7

4, 412,939 6

5,736, 029 4

4,567,212 8

3.

5,711,904

8,809,942

8,637,782

7, 224,228

4.

3,600,518

3

2

6,948, 226 5

5

7

3

6,822, 245 9

6

7

4

2, 434,871

3,399,574

7

9

5, 014, 484 6

6,366,105 3

3,409,970 3

7,820,625


3,556,669

9,957,382

5.

6.

9

1,145,669

Date 58


Multiply Decimals If both factors have a decimal, count the places in both and move the decimal in the product from the right that amount. 6.92 0.8 5.536


b

1.

2.6 5

59 0.9

4.57 0.3

71.19 8

2.

8.7

8.6

45.7

3.37

31

6

0.3

0.3

5

0.05

3.

57 0.3

0.38 0.8

4.57 3

0.392 0.6

9.63 0.6

4.

32 0.8

0.44 0.6

45.7 3

45.29 0.4

90.9 0.9

5.

7.3

4.76

457

4.6

c

7


d

3

e

715 0.6

66.5

23.7

8

0.004

Date 59


Multiply 2 Digits by 2 Digits To multiply a number by a two-digit number, first multiply by the digit in the ones place.Then multiply by the digit in the tens place. 57 23 171 114 1311


b

c

d

1.

62 93

76 32

35 75

27 54

2.

88 12

51 27

98 17

52 98

3.

37 33

93 62

44 68

31 41

4.

48 74

71 91

82 45

72 38

5.

29

42

64

58

56

69

70 23


Date 60


Multiply 4 Digits by 2 Digits Multiplying four-digit numbers is the same as multiplying two-digit numbers.


4,959

1.

2.

25

b

7, 202

9,938

49

c

8, 498

16

5,832

d

49

5, 029

1,832

54

35

27

3,845

53

3.

1, 245 93

3, 445 78

4,771 61

9,541 88

4.

8, 285

2,948

2, 257

5,748

5.

37

6, 031 65

39

9,788 22

6, 003 70


14

17

7, 226 94

Date 61


Multiply 7 Digits by 2 Digits Multiplying with seven digits may look complicated—but it’s not.

Multiplying numbers in the millions is the same as multiplying other numbers. Start by multiplying the ones place. Directions: Multiply. a

b

5,938,964 72

3, 471,109 53

1, 201,905 49

4,586,873 52

2.

7,849,338 43

6, 048,722 35

7,527,394 23

2,770,638 64

3.

2, 255,830

9,339, 020

3, 449,723

8,311,194

1.

4,733,837

4.

5.

68

26

1,983,674 18

c

88

8, 203, 478

92

7,374,599 63


d

39

9,885,752

6, 299,715

74

5,639,826 13

39

83

3, 266,686

43

Date 62


Multiply Decimals Keep an eye on the decimal—and put it in its proper place!

Multiplying numbers with decimals is no different than with other numbers. Remember to put the decimal point in the correct place. Directions: Multiply. a

b

c

d

1.

37 0.6

57 0.32

0.638 28

5.675 0.81

2.

7.3 9

5.21 8.7

56.6 5.6

3.497 4.9

3.

4.2

17.4

37

6.6

8.3

7.7

37.92

5.6

7.7

0.44

95.7 8.9

3.82 4.3

3.892 7.6

4.

5.

63.03


9

34.97

4.9

349.7

4.9

3, 497

4.9

Date 63


Divide 2 Digits by 1 Digit Don't let the numbers overwhelm you—take division one step at a time.

Directions: Divide. a

b

c

d

6 96

)

3 60

)

4 68

)

9 54

)

4 78

)

3 87

)

4 84

)

2 56

)

4 92

)

3 69

3 63

)

4 96

)

2 42

)

6 78

)

6 66

)

5 35

)

8 96

)

5 70

)

7 63

)

6 84

1.

)

2.

4 76

)

3.

9 45

)

4.

)

5. 7 84

)

6.

8 88


)

Date 64


Divide 4 Digits by 1 Digit Practice dividing with some larger numbers.


b

c

d

1.

)

6 3,168

)

9 6,156

)

8 7,616

)

7 2,506

)

4 2,564

4 1, 908

)

5 9,735

)

7 4,564

)

2 4,822

)

6 2, 580

)

5 8,860

)

8 3,192

)

)

6 3, 282

)

8 6,104

)

3 6, 768

)

4 2,332

2.

5 4, 230

)

3.

8 2,936

)

4.

2 4, 428

)

5.

3 5,874


)

Date 65


Divide 7 Digits by 1 Digit Is division getting easier for you? If you’ve been doing well, this page will be a breeze! Directions: Divide. 1.

6,504,279 ÷ 3 =

2.

2,310,232 ÷ 4 =

3.

6,663,000 ÷ 5 =

4.

6,502,210 ÷ 2 =

5.

4,251,312 ÷ 9 =

6.

6,508,012 ÷ 4 =

7.

5,621,937 ÷ 3 =

8.

4,598,100 ÷ 5 =

9.

3,150,270 ÷ 9 =

10.

7,770,120 ÷ 5 =

11.

6,536,470 ÷ 2 =

12.

8,231,073 ÷ 3 =

13.

6,508,308 ÷ 4 =

14.

2,707,860 ÷ 5 =

15.

4,241,970 ÷ 2 =


Date 66


Divide With Remainders Sometimes a number does not divide another evenly.The letter R stands for remainder.

3R1 4 13

Directions: Divide. Remember to write the remainder if there is one. a

b

c

d

1.

8 42

5 326

6 2, 476

8 265

2.

7 87

4 1,380

3 1,557

6 1, 284

3.

9 245

7 7, 077

2 115

7 349

4.

5 8,304

2 3, 471

5 3, 297

4 1,618

5.

6 7,738

5 1,050

9 349

3 2,164


Date 67


Decimal Quotients When a number does not divide another evenly, you can continue dividing. The quotient will be expressed as a decimal. 3.25 4 13.00

)


b

c

d

1.

4 15

7 44

6 146

8 4,967

2.

5 26

3 20

3 101

6 5, 052

3.

7 24

8 32

2 355

3 2,333

4.

9 54

2 19

5 600

4 4,570

5.

6 41

5 63

9 532

7 6, 248


Date 68


Divide 2 Digits by 2 Digits To divide by two-digit numbers, use the same steps as dividing by one-digit numbers. Directions: Divide. a

b

c

d

1.

21 63

17 85

24 86

15 90

2.

12 88

35 95

45 90

23 86

3.

38 76

22 66

14 84

37 71

4.

40 90

11 74

19 95

26 98

5.

13 91

39 99

30 85

18 24


Date 69


Divide 4 Digits by 2 Digits Divide larger numbers using the usual strategy–do one step at a time.


b

c

1.

71 4, 402

57 4,617

63 3,848

2.

72 2,808

45 2, 020

72 4,680

3.

14 1, 442

36 5,112

90 1, 269

4.

66 6, 470

87 4,528

17 4,307

5.

43 3,526

29 1,824

74 6,808


Date 70


Divide Decimals To multiply or divide numbers with decimals, remember these rules.

To divide a decimal, first place a decimal point in the quotient above the decimal point in the dividend. Add a zero if needed to hold a place.

10.1 5 50.5

. 5 50.5

If there is no decimal point in the dividend, but there is one in the divisor, add a zero to the dividend for each place value after the decimal point in the divisor. 100 5.12 51200

)

5.12 512

Directions: Divide. Remember to write the remainder if there is one. a

b

c

d

6 14.5

8 32.8

1.

6 4.2

8 22.4

2.

3 8.7

9 0.58

0.04 92

0.5 510

3.

0.2 68

0.03 64

0.7 273

0.2 0.0037

4.

0.05 45

0.6 270

5 3.58

9 6.61

)


Date 71


Solve Word Problems Use your multiplication and division skills to solve these real-life problems.

Directions: Solve. Show your work. 1. Maria worked at a summer camp. Each week she earned $95. If she worked for 9 weeks, how much money did she make that summer?

2. If Maria worked 40 hours each week, how much did she make per hour?

1 3. The lifeguard at the camp earned 1 times as much for the summer as 2 Maria did. How much did she earn for the summer?

4. The lifeguard worked 25 hours per week. How much more per hour did she earn than Maria?

5. At each session of the camp, there are 96 campers.These campers live in 8 cabins. How many campers live in each cabin?

6. At one popular camp session, 120 campers signed up.The extra campers had to sleep in 4-person tents. How many tents did the camp need to set up?


Date 72


Solve Word Problems You have all the skills you need to solve these word problems.

Directions: Solve. Show your work. 1. Maria’s friend Andy works in the camp kitchen. He is serving fruit cocktail to 96 campers and 16 staff members. If each can of fruit cocktail contains 24 servings, how many cans will he need?

2. Andy is baking sheet cakes for dessert. Each sheet cake can be cut into 18 pieces. If he bakes 6 cakes, will there be enough pieces of cake for everyone?

3. The cook at the camp buys 76 pounds of flour for $30.40. How much is the flour per pound?

4. The high diving board at the camp lake is 10 feet high. If 1 foot is .33 of a yard, how many yards high is the diving board?

5. The lifeguard is organizing a swimming meet. 48 campers sign up to take part. How many teams of 8 swimmers can the lifeguard create?

6. At the last minute, 16 more campers sign up for the swimming meet. How many teams with the same numbers of campers can the lifeguard make now?

7. At the swimming meet, first place earns 6 points, second place 3 points, and third place 1 point. One team, the Dolphins, won 2 races.They finished second in 3 races and third in six races. How many total points did the Dolphins earn?


Date 73


Review Multiplication and Division Use what you know about multiplication and division.

Directions: Solve. Show your work. a

1.

b

126 2

45 71

6, 203

2.

c

5

5,331

d

0.4 147.4

0.64 23

5 41

0.65 128

63

3.

4 84

7,942,735 24

3 90

1.47 3

4.

6 1, 068

78 13

72 936

5.2 4.65

5.

6 6,785, 442

8 7, 048

7 7, 070

0.15 737.9

6.

8,500, 213 9

13 78

4 3, 434

54.81 2.3


Date 74


Review Multiplication and Division Look at how much you've learned!


b

c

d

1.

6,930,952 x 47 =

2,959 ÷ 62 =

3 x 6,093,951 =

4.8 ÷ 0.7 =

2.

8,944,478 ÷ 7 =

67 x 5,919 =

49 ÷ 6 =

7.72 x 4.2 =

3.

82 x 76 =

7,553 ÷ 6 =

34 x 8 =

73.68 ÷ 1.45 =

4.

97 ÷ 13 =

8 x 4,092 =

56 ÷ 8 =

91.66 x 0.55 =

Directions: Write the first 6 multiples of these numbers. a

5.

b

4

c

7

13

Directions: List all the factors of these numbers. a

6.

32

b

c

56

96

Directions: Circle the prime numbers in this list. 7.

11

46

50

29

21

19

2

33


18

5

9

41 Date

75


Add Fractions with Like Denominators To add fractions with like denominators, simply add the numerators.To add mixed numbers, add fractions first, regroup if needed, then add the whole numbers. Directions: Add. Remember to reduce fractions to simplest terms. a

b

1.

1 1 + = 3 3

3 1 + = 8 8

2.

3 1 + = 4 4

7 7 + = 10 10

3.

3 4 + = 5 5 3 5 + = 9 9

1 4 +6= 5 9 7 +2 = 16 16

5.

1 2 1 + = 3 3

2 2 5 +1 = 3 3

6.

5 5 4 +1 = 6 6

1 1 9 + = 4 4

7.

1 3 3 +2 = 5 5

3 5 + = 7 7

8.

2 2 6 +3 = 3 3

2 5 + = 9 9

9.

3 7 6 +3 = 8 8

7 1 + = 11 11

10.

1 5 5 +3 = 9 9 1 7 + = 12 12

2 4 + = 9 9 1 2+2 = 4

1 2 3 +7 = 3 3

1 1 4 +4 = 3 3

4.

11. 12.


Date 76


Add Fractions with Unlike Denominators To add fractions with unlike denominators, convert them to like fractions using the least common multiple of the denominators. Directions: Add. Remember to reduce fractions to simplest terms, if needed. a

b

1.

2 1 + = 3 2

3 1 3 + = 10 2

2.

1 1 + = 4 6

2 1 +2 = 3 4

3.

5 5 + = 8 16 2 3 + = 3 7

1 7+6 = 4 4 1 1 +2 = 9 5

5.

5 4 + = 6 9

3 3 3 + = 4 5

6.

6 1 + = 7 6

1 2 2 +4 = 3 7

7.

1 2 + = 4 3

1 1 3 +4 = 2 3

8.

2 4 + = 5 7

1 3 +2 = 2 5

9.

1 5 + = 4 8

1 2 + = 5 4

1 5 + = 2 7 3 3 2 +2 = 4 5

5 1 1 + = 8 4 7 2 + = 9 3

4 1 1 +3 = 9 2

1 3 3 +1 = 5 4

4.

10. 11. 12.


Date 77


Subtract Fractions with Like Denominators To subtract fractions with like denominators, simply subtract the numerators. To subtract mixed numbers, subtract fractions first, borrowing from the whole number if needed.Then subtract the whole numbers. Directions: Subtract. Remember to reduce fractions to simplest terms. a

b

c

1.

3 1 = 4 4

11 7 = 15 15

5 1 = 11 11

2.

4 1 = 5 5

3 1 = 7 7

7 5 = 8 8

3.

7 3 = 8 8

7 5 = 9 9

1 1 = 3 3

4.

3 5 1 2 5 6

6

5

1 2

3

1 2

5.

2 7 6 1 7

1 3 1 1 3

1 3 2 1 3

6.

6

5 8 3 2 8

1 5 4 3 5

4

1 3

2

6

5

8


Date 78


Subtract Fractions with Unlike Denominators To subtract fractions with unlike denominators, convert to like fractions using Tip the least common multiple of the denominators. Directions: Subtract. a

b

c

1.

5 3 = 7 5

7 2 = 8 3

7 1 = 10 7

2.

1 1 = 2 4

8 1 = 9 4

5 1 = 6 9

3.

4 2 = 5 3

2 1 = 3 2

15 2 = 16 3

1 2 1 1 4

1 3 1 2 2

5.

4 5 3 2 4

2 9 5 1 7

1 2 3 3 8

6.

7 9 2 2 3

1 4 2 3

2 3 3 1 5

4.

3

3

6

6

4

2

5

1

3


5 8

Date 79


Add and Subtract Positive and Negative Fractions Tip are the rules for adding and subtracting positive and negative fractions. Here

The sum of two negative fractions is always negative.

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

Adding a negative fraction to a positive is like subtracting. 5 1 1 + = It will be positive or negative, depending on which addend 3 2 6 is greater. Subtracting a negative fraction is like adding. 1 1 = 7 2 5 10 Directions: Write P if the answer is positive or N if the answer is negative. a

b

1.

5 1 = 8 2

4 1 = 5 4

2.

3 1 + = 8 2

3 1 + = 5 4

3.

2 1 + = 3 5

4 1 = 5 7

Directions: Add or subtract. a

b

c

4.

5 1 = 8 2

2 1 = 3 5

3 5 = 8 8

5.

5 1 + = 8 2

3 3 + = 5 8

1 5 + = 2 7

6.

3 1 + = 4 3

3 1 = 5 8


3 4 + = 10 5 Date

80


Understand Multiplying Fractions When you multiply fractions, multiply the numerators and then the denominators. A shortcut when multiplying fractions is to cancel out compatible numbers when they occur. 1

3 51 1 = 5 5 15 1 65

Directions: Multiply. Remember to reduce or express products in simplest form. a

b

c

1.

3 2 = 4 3

2 1 = 3 2

5 2 = 8 3

2.

3 4 = 5 9

3 3 = 10 5

4

3.

4 1 = 7 2 1 1 = 3 4

1 = 3 2 9 = 3 10

1 7 = 10 9 3 9 = 4

4.

10

5 = 16

5.

5 1 = 8 4

3 1 = 5 3

1 5 = 3 7

6.

3 5 = 5 8

7 1 = 8 4

2 4 = 5 5

7.

1 4 = 3

18

5 = 6

1 12 = 4

8.

3 3= 5

1 10 = 5 11

2 3 = 3 4

9.

5 7= 7

1 2 = 2 7

3 14 = 7

2 = 3

3 7 = 5 10

1 1 = 2 2

10.

3


Date 81


Multiply Mixed Numbers When multiplying mixed numbers, convert them to improper fractions first. Remember to cancel out compatible numbers when you can. Directions: Multiply. a

b

c

9 2 = 10 3

1 3 2 = 10 5

1.

2 1 2 = 3 2

4

2.

3 1 1 = 4 4

4 7 2= 5

3 2 2 = 7 7

3.

1 5 8= 8

7 2 3 = 9 5

1 3 2 = 3

2 = 3

1 1 2 = 2 7

4 4 2 = 5 9

2 5 3 = 3 8

1 33 = 3

4.

5.

12

12 2

3 = 4

6.

1 7 2 = 3 8

1 3 3 3 = 3 5

3 1 6= 4

7.

1 1 3 = 4 4

1 2 2 = 2 3

1 1 3 3 = 6 3

8.

1 1 3 3 = 3 4

3 53 = 4

4 6 7 2 = 5 7

9.

1 6 3= 5

24

10.

2 3 3 = 3 4

2 1 1 = 3 5

1 = 2


7 2 5= 10 1 64 = 3

Date 82


Divide Fractions Dividing by a fraction is the same as multiplying by the divisor's reciprocal.

1 1 1 4 4 2 ÷ = = = =2 2 4 2 1 2 1

Directions: Rewrite each division problem as a multiplication problem using the divisor's reciprocal.Then solve. a

b

1 = 3

1 3 ÷ = 5 10

1.

12 ÷

2.

1 1 ÷ = 3 3

3.

7÷

4.

9÷2=

5.

8÷

1 = 4

1 1 ÷ = 4 4

6.

1 ÷8= 4

1 2 ÷ = 2 3

7.

3 1 ÷ = 7 2

3 4 ÷ = 4 5

8.

10 ÷

1 = 9

5 2 ÷ = 9 3

9.

3 1 ÷ = 4 4

5 1 ÷ = 6 3

10.

3 3 ÷ = 4 8

4 6 ÷ = 5 7

7 1 ÷ = 9 3

1 = 2

7 1 ÷ = 10 2 3 1 ÷ = 4 3


Date 83


Divide Mixed Numbers When dividing mixed numbers, convert them to improper fractions first.


b

1.

1 3 ÷3= 2

1 3 ÷6= 6

2.

1 4÷2 = 3

1 1 8 ÷ = 5 5

3.

3 7 7 ÷ = 5 10

1 9÷4 = 3

4.

2 1 3 ÷1 = 3 10

7 2 3 ÷ = 8 7

5.

4 1 ÷1 = 7 7

3 3 ÷3= 4

6.

7.

18 ÷ 4 4

2 = 3

7 1 ÷3 = 6 16

1 1 ÷ = 4 2

4÷4

1 = 12

8.

5 2 ÷ = 7 3

3 2 3 ÷2 = 5 5

9.

1 1 1 ÷ = 5 2

1 1 2 ÷6 = 2 5

10.

1 6÷4 = 3

1 3 6 ÷2 = 3 4


Date 84


Multiply and Divide Positive and Negative Fractions Here are the rules for multiplying and dividing positive and negative fractions.

When you multiply or divide two positive fractions, the answer is always positive. When you multiply or divide two negative fractions, the answer is always positive. When you multiply or divide a negative by a positive or a positive by a negative, the answer is always negative.

Directions: Write P if the answer is positive or N if the answer is negative. a

b

c

1.

3 1 = 5 4

1 1 = 3 4

1 1 = 6 4

2.

3 ÷ 6 = 10

1 9 ÷ = 3

1 2 ÷ = 3 5

3.

1 2 = 4 3

2 1 = 3 5

1 1 = 6 2

Directions: Multiply or divide. a

b

4.

7 ÷ 4 = 10

6 ÷

5.

5 2 ÷ = 6 3

6.

8÷

2 = 7

2 = 3

3 2 ÷ = 4 3

5 3 = 7 8


c

1 2 ÷ = 9 3 8

4 = 5

1 1 ÷ = 3 3 Date

85


Solve Word Problems Multiplication word problems often involve putting together sets of equal numbers. Division word problems often involve splitting up a group into equal parts. Directions: Solve. 1 1. Jessie was studying for a big math test. One day she studied for 2 2 hours. 2 For of that time, Jessie studied fractions. How many hours did she work 3 on fractions?

2 1 hours studying. of that time was 5 3 spent on math. How many hours did Jessie spend on subjects other

2. Jessie told a friend that she spent 8 than math?

1 3. Jessie decided she needed to study history for 6 hours. If she 3 1 divided her history studying over 4 days, how long would she 2 spend studying history each day? 1 4. Jessie’s friend Rex spent 5 hours working on his project for history class. 5 3 Jessie spent 3 hours on hers. How many hours did they spend together on 4 their projects?

5. How much more time did Rex spend on his history project than Jessie did on hers?

3 6. Rex thinks Jessie spends too much time studying. He suggests she spend 1 hours per night, 5 nights a week, to leave more time for skateboarding. 4 If Jessie follows Rex’s advice, how many hours will she study per week?


Date 86


Solve Word Problems Now for some real-world fraction problems.

Directions: Write the letter of the equation that matches each word problem.Then solve. Remember to label your answers. A. 1 1 4 4 5 B.

3 4 1 ÷ 4 5

C. 13 1 ÷ 3 2 4 4 D. 96 11

E. 13 1 3 2 4

1 1. Li and Genna are painting Li’s bedroom.The longest wall is 13 feet long.The 2 3 roller they are using is foot wide. How many passes with the roller will 4 they need to paint the entire wall? 4 of the wall. If the area of 11 the wall they need to paint is 96 square feet, how much of the wall is taken

2. There’s a window on one of the walls. It takes up

up by the window?

4 1 gallons of wall paint. But the girls used only of what 5 4 Li mixed. How much paint was used?

3. Li mixed up 1

3 1 hours to paint the entire room. If they finished of 4 2 the job on a Saturday, how many hours did they work?

4. It took the girls 13

4 of a foot wide. How many brush strokes would it 5 3 take to make a brush mark 1 feet wide? 4

5. A big brush they used is


Date 87


Review Fractions Make sure to watch the signs so that you perform the correct operation!


b

c

1.

1 1 + = 3 3

1 4 1 = 5 5

1 1 = 2 5

2.

4 3 + = 5 5

4 1 = 7 2

3 3 2 = 4 5

3.

5 7 +1 = 8 8

2 4 + = 7 5

5 2 ÷ = 8 3

4.

3 1 + = 5 3

3 1 = 4 3

3 1 ÷ = 4 2

5.

8 5 = 9 9

2 1 = 5 4

2 1 2 ÷ = 3 6

6.

3 4 = 4 7

1 2 ÷5= 4

2 5 = 3 8

7.

1 5 3 +4 5

1 4 1 +5 3

2 3 4 +1 5

8.

4

4 7 6 2 7

2 5 3 6 8

4

1

1 4

1

3

6

8


Date 88


Review Fractions Now you can solve fraction problems in half the time.


b

c

1.

3 1 + = 4 4

1 5 ÷ = 4 7

5 ÷5= 8

2.

2 1 + = 3 3

3 3 = 4 4

2 6 1 = 3

3.

1 1 = 6 4

4 1 + = 7 3

1 3 + = 3 5

4.

3 1 + = 7 3

4 1 = 9 5

7 7 = 8 8

5.

4 5 2 1 = 5 8

3 23 = 10

7 3 ÷1 = 10 10

Directions:Write the letter of the matching equation, then solve. Remember to label your answers and show all your work. C. 11 ÷ 3 = 2 2 3 6. Li used of a small can of paint. It took of what she used to paint a 3 4 stool for her room. How much of the paint did it take to paint the stool?

A. 1 ÷ 1 = 3 2

B. 3 2 = 4 3

7. Genna wants to mix up some wallpaper paste to use for Li’s room. She 1 1 only has enough paste mix to make of a bucket, the amount she 3 2 wants to make. How much wallpaper paste does she want to make?

1 quarts of varnish. If she wants to finish 3 end tables for her 2 room, how much varnish can she use on each table?

8. Li has 1 Name

Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006

Date 89


Use Order of Operations To solve any equation, always perform the operations in the order given below. 3 (4 + 6) + 2 – 3 = ? operations in parenthesis multiplication, then division from left to right addition or subtraction from left to right

3 (10) + 2 – 3 = ? 30 + 2 – 3 = ? 32 – 3 = 29

Directions: Follow the order of operations to solve each equation. Show your work. a

b

c

1. 2 x 4 + (6 + 1) – 4 =

64 ÷ (8 + 6 + 1 + 8) =

(4 x 15 + 3) x 15 =

2. (7 + 9) + 3 x 4 =

64 ÷ 8 + (6 + 1 + 8) =

4x8–4x3=

3. 8 – 4 ÷ 3 – 2 =

(5 x 30) + 40 =

4 x (8 – 4) x 3 =

4. 5 + 2 x 5 + 2 =

5 x (30 + 40) =

4 x (8 – 4 x 3) =

5. (5 + 4) x (3 + 1) =

5 x 30 + 40 =

(5 + 1) x 3 + 7 =

6. (2 + 3) x 5 + 2 =

4 x 15 + 3 x 15 =

5 + (1 x 3) + 7 =

7. 72 ÷ 9 + 6 + 2 + 5 =

4 x (15 + 3) x 15 =

5 + 1 x (3 + 7) =


Date 90


Write Equations An equation is a math sentence with equal amounts on both sides of an equals sign. A variable often stands for an unknown amount.

1 Francis has a radio-controlled (R/C) monster truck that is 24 the size of a real truck. If the headlights on the actual car are 3 inches tall, how tall are they on the R/C car? 1 h stands for the height of the headlight 3 24 = h 3 =h 24 The headlights on the R/C car are 1 =h 1 inch tall. 8 8

Directions: Solve. Use a variable that makes sense to you. 1. Francis has a R/C speedboat with a rudder on the back that is 2 inches long. If the full-size speedboat is 26 times larger than the R/C speedboat, how large is its rudder? 2. To run his R/C cars and boats, Francis charges his batteries for 30 minutes to get 20 minutes of running time. About how much charging time does it take to make a minute of running time? 3. Francis added up the value of the R/C cars and boats he owned. He owned 4 R/C cars that cost around $30. He owned 3 R/C trucks that cost around $40. He owned 1 R/C speedboat that cost $120. How much were all his R/C vehicles worth together? 4. For his birthday Francis's parents gave him $25. His grandmother gave him 4 $20. Francis used of his birthday money to buy parts for his R/C vehicles. 9 How much did he spend on parts?


Date 91


Solve Equations To solve equations, first perform all calculations. Then isolate the variable using inverse operations. Whatever you do to one side of the equation, you must do to the other side. 5x – 1 = 29 5x –1 + 1 = 29 + 1 5x = 30 5x ÷ 5 = 30 ÷ 5 x=6 Directions: Use inverse operations to solve the equations. Show your work. a

b

c

1. 4n = 24

j + j + 3 = 15

h – 9 = 14

2. x – 3 = 4

5 + n = 18

70 ÷ p = 5

y =5 3

6f – 2 = 5f

f

4. 4 + z = 0

11 = 2t + 3

3q – q = 12

5. 3k = 24

y÷8=9

c2 – 3 = 46

6. m + 4 = 17

4=9–k

5t – 2t = 21

3.

7. 2x + 2 = 16

8.

n +2=5 5

1 z= 9 z 2 72 ÷ r = 24


1 =7 2

13 – m = m + 7

2x = x + 3 Date

92


Solve Equations Tip more practice in solving equations. Here’s

Directions: Use inverse operations to solve the equations. Show your work. a

b

c

1. x + x – 5 = 27

4n = 8

h – 9 = 22

2. y – 2 = 9

5 + n = 11

75 ÷ p = 15

3. 3f + 2 = 4f

y = 30 3

z

4. 4 + z = 1

19 = 2t + 3

5q – q = 12

5. 3k = 15

y÷4=9

c2 – 3 = 33

6. 56 ÷ r = 8

14 = 9 + k

7x – 2x = 30

7. 2x – 2 = 16

1 z = z 30 2

16 – n = n + 10

m + 4 = 10

3x = x + 16

8.

n +2=5 6


1 =8 2

Date 93


Understand Functions Tipfunction is a special kind of equation with two variables. A

In a function, there is only one value of x for each value of y, and vice versa. x=y+3 x=y–5 x = 3y y x= 4

When x is 4, y can only be 1. When x is 7, y can only be 2. When x is 6, y can only be 2. When x is 2, y can only be 8.

Directions: Answer each question. 1.

In the function x = y + 2, if x is 3, then y is

.

2.

In the function x = y – 4, if x is 6, then y is

.

3.

In the function x = 4y, if x is 8, then y is

4.


.

5.


.

6.

In the function x = y/4, if x is 8, then y is

.

7.

In the function x = y/4, if x is 12, then y is

8.

In the function x = 4y – 2, if x is 10, then y is

.

9.

In the function x = 2y + 6, if x is 12, then y is

.

10.

In the function x = 3y + 2 , if x is 14, then y is

.

11.

In the function x = y/4 – 2, if y is 12, then x is

.

12.

In the function x = y/4 – 2, if y is 16, then x is

.

13.


.

14.


.

15.

In the function x = 3y + 1, if y is 4, then y is

.


.

.

Date 94


Graph Functions It’s easy to graph a function.

To graph a function, plot two pairs of points on the x (horizontal) and y (vertical) axis.Then draw a straight line through both points. Put an arrowhead at the end of the line to show that it continues off the graph. To graph the function x = y + 1, find and plot any two pairs of values of x and y. x=y+1 x y 2 1 3 2 4 3 5 4 6 5

Directions: Complete the tables and graph each function. a

1.

b

x=y+2 y x 2 3 4 5 6

x = y -1 y x 0 1 2 3 4


Date 95


Graph Functions Here’s more practice in graphing functions.

Directions: Complete the tables and graph each function. a

1. x = 2y x y 2 4 6

y x= 3 x y 1 2 3

x = 2y + 1 x y 3 5 7

x = 2y – 1 x y 3 5 7

b

2.


Date 96


Graph Functions Here’s more practice in graphing functions.

Directions: Complete the tables and graph each function. 1.

y x= 2 x y 2 4 6

2.

x 1= x

a

x =y 3 x y 1 2 3

y 3 y 3 6 8

x = 2y – 1 x y 1 2 3


b

Date 97


Graph Rates A rate is a special kind of function or ratio.

A rate compares different units. For example, a car gets 25 miles to a gallon of gas.The rate is 25 miles to 1 gallon, or 25 miles:1 gallon, or 25 miles /1 gallon. You can graph rates the same way you graph a function.With a rate, however, the axes are labeled differently.

Directions: Read the description. Label the axes and mark the scale. Then graph each rate. 1. A 5-pound bag of flour costs 3 dollars.


Date 98


Graph Rates Now try these.

Directions: Read the description. Label the axes and mark the scale.Then graph each rate. 1. For each half-hour Martin exercises, he burns 300 calories.

2. Jerome has two plants. For each inch his jade plant grows, the snake plant grows 2 inches.


Date 99


Graph Equations and Inequalities Graphs can be used to display inequalities.

All points in the shaded area are solutions to the inequality. x y–2 y x 0 2 1 3 2 4 3 5

Directions: Match the inequality with its graph. 1.

3.

A. x < y + 3 B. y > 2x C. x < 3y - 2 D. y < 2x + 2

2.

4.


Date 100


Review Equations and Inequalities Use what you know about equations to solve these.


b

c

1. x + x – 1 = 15

4n = 12

4x = x + 27

2. 2 – -y = 4

6 + n = 17

h–8=0

3. 3a + 3 = 4a

y =15 3

60 ÷ p = 15

4. 3 + z = 11

15 = 2t + 3

z

5. 4k = 20

y÷3=9

5q – q = 16

6. 45 ÷ r = 5

27 = 9 + k

b2 – 22 = 42

7. 5x – 3 = 12

1 z = z 10 2

7x – 2x = 35

m + 4 = 16

12 – n = n + n

8.

n +2=6 4


1 =9 2

Date 101


Review Graphing Functions Here’s a chance to use what you learned about functions, rates, inequalities, and graphs. Directions: Graph each function. 1.

2.

x y1= 2 y x

x y+1 y x

3. Thomas is raising cavies (guinea pigs) for the county fair. He finds that for each 100 grams of food he feeds his cavies, they gain 50 grams in weight.


Date 102


Use Time Measurements You can multiply, divide, and convert using units of time.

Directions: Fill in the blank. Show your work. a

b

1.

A quarter of a day is

2.

A quarter hour is

3.

A half day is

4.

A half hour is

5.

4 hours =

6.

3 days =

7.

4

8.

6 days =

hours. minutes.

hours.

days = 52 hours

2 hour = 3 1 5 days = 2

minutes

190 min =

hours

days minutes hours hours

1 min = 5 hours 2

minutes hours

7 days =

hours = 325 minutes

9.

minutes

166 hours =

minutes.

1 hours = 2

1 3 hours = 4

hours

minutes = 164 hours

Directions: Write the equation, then add or subtract. 10.

A group’s hike lasted five hours, forty minutes from start to finish.They rested for fifteen minutes once and ten minutes another time. How long were they actually walking?


Date 103


Convert Temperatures The Metric System measures temperatures using the Celsius scale. On this scale, water freezes at 0° and boils at 100°.

5 (F 32) = C 9 9 To convert Celsius to Fahrenheit, use this formula: C + 32 = F 5 9 Hint:To multiply a number by , you can multiply using the fraction, you 5 can multiply by the decimal (1.8), or you can multiply by 9 then divide by 5. To convert Fahrenheit to Celsius, use this formula:

Directions: Convert the temperature to the nearest degree. a

b

c

1.

92°F =

°C

60°F =

°C

19°F =

°C

2.

21°C =

°F

–2°C =

°F

4°C =

°F

3.

80°F =

°C

8°F =

°C

–15°F =

4.

–15°C =

0°C =

°F

40°F =

5.

4°C =

°F °F

°F

92°C =

°C °C °F

–78°C =

Directions: Write , or = to show how the temperatures compare. a

b

c

6.

100°F

100°C

22°C

57°F

85°C

185°F

7.

32°C

32°F

–15°F

–15°C

212°F

100°C

8.

12°F

12°C

25°C

77°F

–95°C

-–175°F

9.

6°C

48°F

–100°C

10.

32°F

0°C

125°F

45°C


–30°F

–16°C

0°F

60°F

15°C Date

104


Use Weight Measurements In the Customary System, weight is measured in ounces, pounds, and tons.To find part of a unit of weight, divide.To find multiples of a unit of weight, multiply. oz = ounce lb = pound T = ton 16 oz = 1 lb 2000 lbs = 1 T


b

1.

1 lb = 2

oz

2.

32 oz =

lb T = 1000 lb

3. 4.

5 lb =

5.

52 oz =

oz lb

3T =

c

lb =

1 T 4

lb

2 oz =

1 lb = 2

lb oz = 3 lb

oz

4.5 lb =

1

1 2 T= 2

lb

oz

1 5 T= 4

lb

12 oz =

lb

1 oz = 2

lb

Directions: Write , or = to show how the weights compare. a

1 lb 2

6.

2

7.

6000 lb

8.

6 oz

b

36 oz

2 3 lb 4

1 T 2

6T

12,000 lb

1

3 lb 4

8 oz

2 lb 3

9000 oz

1 T 2

800 lb

64 oz


c

25 oz

1 T 4 3 lb

Date 105


Identify Angles Angles are the measure of turning where two lines meet.

Directions: Answer the questions. A.

B.

C.

D.

1. Which two shapes have right angles?

2.

Which two shapes have acute angles?

3. Which shape has obtuse angles?

4. Draw a shape to show each type of angle. Label each angle with its angle name.


Date 106


Find Angles Two angles whose sum is 90° are called complementary.Two angles whose sum is 180° are called supplementary. Directions: Answer the questions.

1.

Name 2 sets of complementary angles.

2.

Name 2 sets of supplementary angles.

3.

What type of angle is angle D?

4.

What is the measure of angle D?

5.

What type of angle is angle K?

6.

What is the measure of angle K?

7.

What type of angle is angle L?

8.

What is the measure of angle L?

9.

What is the measure of angle M?

10.

What is the measure of angle B?

11.

Draw a set of supplementary angles and a set of complementary angles below and label each.


Date 107


Find and Convert Customary Lengths The U.S. Customary System measures length using inches, feet, yards, and miles. inch = in foot = ft yard =yd mile = mi

12 in = 1 ft 3 ft = 1 yd 5280 ft = 1 mi


b

1.

1 mi =

yd

2.

36 in =

ft

1 mi = 3

3.

36 in =

yd

9240 ft =

4.

8

5.

1 mi = 4

1 ft = 2

in

c

2 ft 3

in =

ft mi yd

11 ft =

ft

3 mi 5

ft =

20 ft =

yd

32 in =

ft yd

5280 ft = yd

2 mi =

1 mi = 2

yd

Directions: Write , or = to show how the lengths compare. a

b

3

1 ft 2

20 yd

6.

36 in

7.

9 ft

8.

3 mi

9.

1 1 yd 3

5 ft

16 in

10.

75 in

2 yd

27 in

3 yd 15,000 ft

c

2

1 mi 2

21 in

1

13,000 ft

10 yd

3 ft 4 1 yd 3 1 2 ft 3

_1


1 mi 2

20 ft

2200 yd

7000 ft 30 ft

1

1 mi 2

6 mi

30,000 ft

9 in

3 ft 4 Date

108


Find and Convert Metric Lengths In many places, people measure length with the Metric System instead of the Customary System. A centimeter is shorter than an inch and a kilometer is shorter than a mile. A meter is a little longer than a yard. centimeter = cm meter = m kilometer = km

100 cm = 1 m 1000 m = 1 km

Directions: Fill in the blank with the units you would use to measure the length. a

b

1.

a pencil

a paper clip

2.

a woman

a flagpole

3.

a mouse

the distance to the moon

4.

a car trip

a basketball player


b

c

10 cm =

m

6.

10 m =

cm

3000 m =

7.

10 m =

km

500 m =

km

m

80 cm =

m

8. 9.

1 km = 2 1 m= 2

cm = 2 m

cm

1 m= 2 3 km = 4 1 1 km = 3

m

50 cm =

km

4 km = 5

cm

7

5.

km

km = 15,000 m

cm

m


10.

1m

b

100 cm

10 cm

1m


c

1 m 2

500 cm

Date 109


Convert Customary to Metric Converting from Customary to Metric isn’t hard. Just use this table.

1 1 1 1

in = 2.54 cm ft = 0.3048 m yd = 0.9144 m mi = 1609 m

Directions: Solve.You may wish to round your answers. a

b

1. 4 in =

cm

200 yd =

2. 6 ft =

m

48 in =

cm

3. 10 in = 4. 2

1 mi = 2

m

c

km m m

7 ft =

km

18 mi =

18 in =

cm

20 in =

m

1 ft = 2 1 mi = 3

m km


b

5. 40 in

40 cm

1m

6. 30 in

3m

1 804 m 3

7. 3 mi

3000 m

6 cm

8. 2 yd

2m

3m=

9. 1 mi

2 km

70 cm

40 in

1 mi 2 2 in


c

8m

8 ft

4 yd

4m

10 km

5 mi

90 in

15 in

15 cm

7 in

10 m

11 yd

Date 110


Convert Metric to Customary Here’s a table you can use to convert Metric to Customary.

1 cm = 0.3937 in 1 m = 39.37 in 1 km = 0.621 mi

Directions: Solve.You may wish to round your answers. a

b

1. 4 cm =

in

1200 m =

2. 2 km =

mi

12 cm =

3. 50 cm =

ft

2m=

mi

100 km =

4.

1 km = 2

c

ft in in

3 m= 4 200 m =

mi

mi

4000 m =

1 km =

in yd yd


5. 22 km 6. 2 m

b

18 mi 6 ft

1 km

621 ft

39 m

3937 in

7. 1 km

3270 ft

6m

8. 621 m

1 mi

1 cm

9. 2 m

72 in

3 yd

1 m 10 1 km 2

9 3 in 10 5280 ft

161 km

100 mi

2.54 in

50 cm

1 y yd 2

1 mi

50 cm

17 in

1609 m


c

Date 111


Solve Word Problems Look back in the book to find conversion tables, if you need help.

Directions: Write the equation, then solve. Remember to label your answers and show all your work. 1. The movie Shauna is watching is 130 minutes long. How many hours and minutes is that?

2. It took Shauna one and three-fourths hours to do her homework. It took her younger sister, Darcie, thirty minutes to do hers. How much longer did it take Shauna to complete her homework?

3. The temperature outside dropped to freezing.Then it went down another eight degrees Fahrenheit.What was the temperature?

4. Shauna helped Darcie heat a pot of water until it boiled. On the Fahrenheit scale, how hot was the water?

5. How hot is boiling water using the Celsius scale? Freezing water?

6. Darcie compared her braid with her friend's. Darcie's braid is one-and-onefourth foot long. Her friend's is fourteen inches long.Whose is longer?

1 7. Shauna bought 1 pounds of apples at the store. How many ounces is that? 3 3 8. One bag of grapes was 1 pounds, another was 20 ounces.Which bag 4 was heavier?


Date 112


Solve Word Problems Sarah wrote her pen pal Mia in Sweden.When Mia replied, Sarah had to convert the measurements to understand how they compared. Directions: Read the letters.Then answer the questions by converting the measurements in the letters. Hi Mia,

1

We're fine here in Ohio.Today it was 89°F at 9:00 in the morning.Yow! I had to walk 1 mile 3 to the pool.You wouldn’t believe how hot I was by the time I got there! Last month I went to the county fair. I saw a gourd that grew to be 150 pounds! Do you have gourds in Sweden? I think about what you are doing when I am writing.You’re six hours ahead of us. So, when I’m eating dinner, you’re already asleep. Talk 2 yu later, Sarah

Hello, Sarah, I am glad you are well. It is 23°C here.That’s about as hot as it usually gets here. How hot and cold does it get where you live? The lake where we swim is two km away. Sometimes I walk there, and sometimes my mother drops me off on her way to work. Yes, we have gourds. But the biggest one I’ve ever seen weighed about 60 kg.We also have vegetables like carrots, tomatoes, onions, and peppers—and, of course, potatoes. Hej då (it means "bye") Mia

1. Which place is warmer in the summer, Sweden or Ohio? How hot was it in Sweden in F? How hot was it in Ohio in C? 2. Who lives closer to a place to swim, Mia or Sarah? 3. How heavy was the gourd Sarah saw (in kilograms)? Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006

Date 113


Review Measurement Let’s review what you’ve learned in this unit.

Directions: Use what you have learned to answer the questions. a

1. 2

2 hours = 5

2.

b

minutes

days = 78 hours days

3. 144 hours =

7 hour = 12 1 5. 3 hours = 3

°C

28°C =

°F

82°F =

°C

–36°C =

°F

minutes

115°F =

°C

days = 156 hours

37°C =

°F

days

380°F =

°C

–2°C =

°F

7. 120 hours = 8.

65°F =

minutes

4.

6.

c

2 hour = 3

days

6T =

lb lb =

3 T 4

2.2 lb =

oz lb

4 oz =

3 lb = 4 1 3 T= 10

oz lb

oz = 4 lb

15

1 T= 4

lb

9. Draw three shape to show a right, an acute, and an obtuse angle. Label each angle with its angle name.


Date 114


Review Measurement Did you know you’ve learned so much?

Directions: Use what you have learned to answer the questions. a

1.

in =

2.

1 mi = 8

3.

13,200 ft =

4.

14 ft =

3 ft 4 ft

5000 m =

mi

40 ft =

yd

7.

28 in =

ft

8.

10560 ft =

9.

2 in =

1 1 yd = 12

800 m =

km

km = 750 m

m

75 cm =

2 mi 5

6.

10.

c

cm = 3 m

yd

ft =

5.

b

mi = 100 km

cm

ft

2 km = 3

m

500 cm =

in

cm =

m = 21 in

1 1/2 m =


m=

2 mi = 3

km

1 km 5

cm

21 in =

5 m = 8 km yd 1

km

22 mi =

km = 11,000 m

7 1/2 m=

ft

in

1 ft 4 km

in = 16 cm

36 m =

ft

Date 115


Find Perimeters Perimeter is the distance around a shape. Find perimeter by adding the length of each side.

4 + 6 + 6 + 2 = 18 ft

Directions: Find the perimeter for each figure. Label your answer. a

b

4 x 4 in

5 + 5 + 3 ft

1.

2.

6+6+6+6+6m

8 + 8 + 3 + 3 mi

3.

top 4, bottom is 2 + 1 + 2, right is 6, left is 7 in.

all cutouts are 1 yard, top and bottom are 4, sides are 3


Date 116


Use the Pythagorean Theorem The Pythagorean Theorem helps you find the lengths of the sides of a right triangle. a2 + b2 = c2 32 + 42 = 52 9 + 16 = 25

Directions: Find the length of the unlabeled side. a

b

1. 15 in 9 in

15 in x

2. 10 in x 8 in

3.


Date 117


Find Circumferences Circumference is the distance around a circle.

Pi ( ) is often used when measuring circles. Use the number 3.14 for . To find circumference use the formula: C = d

Directions: Find the circumference. a

b

1.

2.

3.

4.


Date 118


Find Area of Parallelograms Tip is the space inside a figure. Area

If the four-sided figure has all right angles, simply multiply the length times width to find area. If the figure’s angles aren’t 90°, multiply the length times the height. You might have to use the formula for right triangles to find the height.

Directions: Find the perimeter and the area for each figure. a

b

1.

Perimeter:

Area:

Perimeter:

Area:

Perimeter:

Area:

Perimeter:

Area:

2.


Date 119


Find Area of Triangles To find the area of any triangle, multiply length by height and then divide in Tip half.

Directions: Find the area for each triangle. a

b

1.

2.

3.

4.


Date 120


Find Area of Circles r2

To find the area of a circle, use the formula: A =

The radius (r) is a line from any point on a circle to its center. The radius is half the length of its diameter.

Directions: Find the radius and the area for each circle. Use 3.14 for a

.

b

1.

2.

3.

4.


Date 121


Find Area of Irregular Figures Wondering how to find the area of irregular figures?

To find the area of an irregular figure, divide it up into regular figures, such as squares, triangles, rectangles, parallelograms, and circles.Then find the areas of the regular figures and add them together. For this figure, find the area of part A, a square with sides 2 in.Then find the area of part B, a rectangle 1 in by 2 in. Part A = 2 in x 2 in = 4 in

Part B = 1 in x 2 in = 2 in

4 in + 2 in = 6 in

Directions: Find the area. a

b

1.

2.

3.


Date 122


Find Surface Area Surface area is all the outside area of a three-dimensional figure.To find surface area, find the area of each face, then add to get the total. Remember that some faces may be hidden from view! Directions: Find the surface area for each figure. Show all your work. 1.

front: top: bottom: back: left side: right side: Total surface area:

2.

front: top: bottom: back: left: right: Total surface area:

3.

front: left side: right side: back: bottom : Total surface area:


Date 123


Find Volumes Volume is how much space is inside a three-dimensional figure. Find volume by multiplying the area of the base times height. Directions: Find the volume for each figure.

a

b

1.

Volume:

Volume:

Volume:

Volume:

Volume:

Volume:

2.

3.


Date 124


Solve Word Problems Real people use real geometry.

Directions: Solve the word problems. 1. Robert is wrapping a gift. Find the circumference to find the length of ribbon he should use to wrap around the gift, find the surface area to find how much wrapping paper he needs, and find the volume to find the amount of Styrofoam peanuts he needs for inside the gift. (Hint: to find the area of the long part of the cylinder, use the circumference of the circle as two sides and the height the other two.)

7 in height Ribbon length:

Amount of wrapping paper:

Amount of styrofoam: 2. Cassie is helping her mom form a concrete patio. Find the missing dimensions from the perimeter given. Find the surface area to know how much paint they'll need and find the volume to know how much concrete they'll need. (Hint: they won't paint the bottom of the patio.Also, you'll need to convert the feet to inches, then back again when working with volume and surface area.)

Height: 2 in Perimeter: 44 ft

Missing side length:

Area to be painted:

Amount of concrete:


Date 125


Solve Word Problems Here are some more real-world word problems to solve using geometry.

Directions: Solve the word problems. 1. Drake and his friends are building a skateboard ramp. It will look like the drawing below and be made of plywood. Plywood comes in sheets that are four feet by eight feet. How many sheets of plywood will they need to buy to make sure they have enough to build the ramp? (Hint:The ramp has no bottom.) 4 ft

5 ft 3 ft 5 ft

2. An oil storage tank is a cylinder fifty-five feet tall.The radius of the top and bottom is twenty-eight feet. An engineer wants to find out how much oil can be pumped into the tank to fill it to 90 percent of its capacity. Help her find the answer by drawing a picture of the tank, labeling its dimensions, and solving for the answer to her question.


Date 126


Review Geometry You may have to work backwards to find an answer.

Directions: Find the missing dimension on each figure.

1.

Missing side: Perimeter: 30 ft Area: 56 sq ft

2.

Missing side: Area: 72 sq cm

3.

Diameter: Circumference: 153.9 in

4.

Width: Volume: 140 cu yd

5.

Total Surface Area:


Date 127


Review Geometry Here are some more review problems.

Directions: Find the perimeter and area for each figure. 1.

2.

Directions: Find the circumference and area for each circle. 3.

4.

Directions: Find the volume and surface area for each figure. 5.

6.


Date 128


Find Averages When most people think of an average, they think of a mean.To find the mean, add to find the total, then divide by the number of addends. Directions: Find the average for each set of numbers. Show all your work. 1. 12, 18, 22 2. 54, 47, 80, 59, 38 3. 5, 10, 10, 5, 10, 5, 10, 5, 5, 5, 10 4. 200, 250, 100, 100, 400 5. 1.3, 0.4, 2.1, 0.9, 1.2, 1.8, 1.8 6. 4, 20, 5, 16, 7, 12, 13 7. A group of nine friends took a survey of how many people lived in their homes (including themselves). Find the average number of people in a home. 4, 5, 7, 3, 4, 2, 5, 2, 3

8. Eight students formed a study group. After a test, they compared their scores. What was their average score on the test? 88, 90, 92, 87, 82, 98, 91, 88

9. Ten movie reviewers saw the latest thriller.They all rated the movie on a scale of 1 to 10, 10 being the best. Find the average score of the reviewers. 7, 7, 9, 5, 3, 6, 7, 9, 10, 6

10. Marlie kept track of her math quiz scores for four weeks. Help her find her average for that time. 86%, 90 %, 79%, 82%, 88%, 86%, 91%, 91%, 96%, 89%


Date 129


Figure Probability Probability is the chance of an event occurring.There is a 1 in 6 or 1/6 chance of spinning 1 on the spinner.

1 outcome of a 1 6 possible outcomes

Directions: Figure the probability for each situation. Simplify fractions, if needed. 1. What is the probability of spinning an odd number? 2. What is the probability of spinning a 6? 3. What is the probability for spinning an even number sometime in two spins? 4. What is the probability for spinning four times and getting a 5 more than once? 5. What is the probability for spinning an even or an odd number? 6. What is the probability for spinning a 3 or a 4, then spinning again and getting a 3 or a 4?

You have a bag of 10 buttons: 1 is red, 3 are blue, and 6 are green. 7. What is the probability of pulling out a red button? 8. What is the probability of pulling out a blue button? 9. What is the probability for pulling out a blue button, keeping it out and pulling out another one? 10. What is the probability for pulling out a green button, keeping it out and pulling out a blue one? 11. What is the probability for pulling out a blue button, putting it back and pulling out a red button again? 12. What is the probability for pulling out three blue buttons in a row, keeping each of them out?


Date 130


Understand Odds Odds compare the possibility of an event happening to the event not happening. Just as in fractions, you can simplify odds.The odds against spinning an even number on this spinner are 2 to 2 or 1 to 1. Odds of spinning a 3 number of ways to spin a 3 1 1

number of ways to spin anything else to :

3 3

Directions: Write the odds for each situation. Simplify, if needed. 1. What are the odds for spinning an odd number? 2. What are the odds for spinning a five? 3. What are the odds for spinning an even or an odd number? 4. What are the odds for spinning a 1 or a 4, then spinning again and getting a 1 or a 4? 5. What are the odds against spinning a 2,3, or 4? 6. What are the odds for spinning a number greater than 3? 7. What the odds against spinning a number greater than 3? You have a bag of 10 buttons: 5 are red, 3 are blue, and 2 are green. 8. What are the odds for pulling out a red button? 9. What are the odds for pulling out a blue button? 10. What are the odds against pulling out a green button? 11. What are the odds for pulling out a red button, keeping it, then pulling another red button? 12. What are the odds against pulling out a red button, putting it back, and pulling a red button?


Date 131


Identify Mean, Median, and Mode You found the mean earlier. Here’s how to find two other types of averages.

The median is the “middle value” of a set of numbers. Half the numbers are greater, half are smaller. The mode is the number that appears most often in a set. If the numbers in a data set aren’t in order from least to greatest, put the numbers in order before you start working with the data set. Directions: Find the mean, median, and mode for each set of numbers. Show your work. 1. A group of friends wrote down the number of telephones each of their families had at home. 3, 4, 2, 3, 5, 4, 2, 1, 3, 4, 3

Mean:

Median:

Mode:

2. Here are Alicia’s math scores for the last month: 85, 89, 94, 91, 87, 88, 87, 93, 90

Mean:

Median:

Mode:

3. Ms. Fernandez decided to remodel her kitchen. She got these estimates of the cost from several builders: $22,500 $20,100 $19,999

$20,100 $17,800 $21,850

$18,000 $22,100 $24, 575

Mean:

Median:

Mode:


Date 132


Solve Word Problems You know how to solve these now.

Directions: Solve. Use the space below the problems to work out the answers. 1. Jason made a spinner for his little sister’s board game. It is a circle divided into eight equal parts. Four of them are red, four are yellow.What is the probability his little sister will spin a yellow on her first try?

2. If you had four blue t-shirts, three red t-shirts, and five white t-shirts in a drawer, what are the odds that you would pull out a blue shirt without looking?

3. Imagine you pulled a blue shirt out of your drawer. Now what is the probability that you will pull out a red one? A white one?

4. The probability that you will pull a clear marble out of a marble bag is 1 to 8. The probability that you will pull a green marble out of the same bag is 1 to 6. Are there more clear marbles or green marbles in the bag?

5. There are four kids named Sarah in your math class. If your odds of being paired with a Sarah for a partner project are 1 to 6. How many kids are in your math class?

6. There are 850 tickets for the door prize at a 4-H party.You and your brother each have two tickets.What are the odds of you or your brother winning the door prize?


Date 133


Solve Word Problems Now try these.

Directions: Solve. Use the space below the problems to work out the answers. 1. Five friends decided to pool all the money they had in their pockets to buy some pizza. Here’s what they pooled: $2.35, $1.70, $.90, $1.25, and $1.55. Find the mean amount the five friends had.Then find the median.

2. Here are the number of CDs a group of friends has: 23, 26, 18, 19, 31, 17, 22, 19, and 29. Is the mode 22, 19, or 23? Is the median 23, 26, or 19? What is the mean?

3. Rachel has a paper route. Here are the number of papers she delivered one week: 52, 56, 56, 59, 57, 52, and 64. She gets a bonus if she has a mean average of more than 56 papers a week. Did she earn a bonus this week? By how much did she earn or miss her bonus?

4. Donnell hopes to get a 90, or B+, quiz average for this grading period in math. Here are his scores on quizzes so far, with one quiz to go: 88, 90, 91, 87, 89, 84, 95. what grade does he need to get on the last quiz to end up with a 90 mean average?

5. Brandy plays basketball. In her last five games, she scored 15, 8, 12, 14, and 21 points. Her best friend Carly scored 16, 11, 38, 10, and 7.Which friend has the higher mean scoring average?


Date 134


Review Probability This review will help you remember how to find and write odds.

Directions: Look at the spinner and write the odds for each situation. Simplify, if needed.

1. What are the odds for spinning an even number? 2. What are the odds against spinning an even number? 3. What are the odds for spinning a six? 4. What are the odds against spinning a 3 or 4? 5. What are the odds for spinning a number greater than 3? 6. What are the odds against spinning a number greater than 3? 7. Are the odds greater for spinning an even number or a number above 6? 8. What are the odds for spinning a number greater than 3 or an odd number?


Date 135


Review Probability You’ll be surprised how much you’ve learned about probability!

Directions: Look at the spinner.Then answer the questions.

1. What is the probability of spinning an even number? 2. What is the probability of spinning an odd number? 3. What is the probability of spinning a six? 4. What is the probability of spinning an eight? 5. What is the probability of spinning a number greater than 4? 6. What is the probability of spinning a number less than 4? 7. Is the probability greater of spinning an even number or a number above 5? 8. Is the probability greater of spinning a number higher than 4 or an even number?


Date 136


Scope and Sequence

Students


137


Answer Key PAGE

6

PAGE

1. I NI I NI I NI 2. NI I NI I NI NI 3. I I NI I NI I 4. I NI I NI I I 5. NI I I NI I I An integer can be a positive whole number, its opposite, or zero. PAGE

7

1. -12 -25 2. -4 -4 3. 21 6 4. -2 -5 5. -320 300 6. 320 -1300 7. -50 36 PAGE

5 -15 20 -100 290 -1 -153

-510 35 60 -770 -884 -42

1. 9 57 2.3 2. 17 -57 5,705 3. 378 4.5 3 1/3 4. 1/5 -4,927 -489 5. 94 -1 14 6. 2 -9 6 7. -8 9 -7 8. 1 9 6 9. = < < 10. > > > PAGE

9

1. B (3,6) C (2,4) D (4,3) E (6,6)

•T •R •N

•V •O

PAGE

•M •P

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

10

2.5 225 15 6 81 10 20 121 900 625

11 144 9 36 2 196 7 4 5 1

4 49 8 625 256 14 100 50 400 1,600

PAGE

626 8 2,401 1,024 0 1,296 81 59,049 1,000 1

216 1 4,096 6,561 729

13

1. = 2. = = 3. = = = 4. Answers for items 5-11 may vary. Sample answers are listed. 5. 14/16 2/12 22/24 6. 1/2 2/8 6/10 7. 2/6 1/2 1/3 8. 9/12 4/14 1/2 9. 6/20 14/18 8/10 10. 4/8 10/16 1/2 11. 4/6 25/30 5/6

2.

PAGE

12

64 64 27 6 81 9 1,024 77 64 125

PAGE

F (8,7) G (8,4) H (9,0)

•S

PAGE

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

8

11

1. 1 or one 100,000 or one hundred thousand 2. 10 or ten 1,000,000 or one million 3. 100 or one hundred 10,000,000 or ten million 4. 1,000 or one thousand 100,000,000 or one hundred million 5. 10,000 or ten thousand 1,000,000,000 or one billion 6. 102 106 7. 101 + 100 108 8. 104 + 103 107 9. 102 + 101 109 10. 105 + 104 105

169 25 225 9 2,500 30 16 16 17 18


1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

14

0.5 0.33 3/4 2/5 0.20 1/8 9/100 0.59 < > > > = = = < =

0.75 0.95 1/10 0.5 1/4 0.6 4/5 2/3

138

0.25 1/2 3/5 0.4 9/10 0.01 9/10 3/1,000

15

1. 1.4 2. 0.125 3. 0.142857 0.05 4. 2.8 5. 0.11 6. 2.2 7. 0.833 8. 1.7 PAGE

1. 2. 3. 4. 5. 6.

17

18

10 40 50 0 3 4 740 1,150 2,610 4,380

PAGE

1. 2. 3. 4. 5. 6.

16

-51 -76 -8 3,157 0.236 -51 40,569 0.001 0.7 5,320 60 2.5

PAGE

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

3.3 0.4 0.916 2.6 0.18

55 480 -60 -298 < < < < > >

PAGE

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

2.4 3.6

19

7. 8. 9. 10. 11. 12.

> < > < >
>
< > >
> = >

< < =
> < < = < < A(1,5) B(2,9) C(2,2)

5. 6. 7. 8. D(6,6) E(7,10)

< < = >

= < =
=

1. 2. 3. 4. 5. 1. 2. 3. 4. 5. 6.

•G •J

•D

•A 7. 8. 9. 10. 11. 12. 27 20 2

4/8 8 to 34 5:15 8/39 20 to 39 20:19

4. 20 5. 25 6. 3

28 13 95

5 100 15

5. 6. 7. 8.

I R R R R I I R

3. 100 4. 80

28

7x7 8x8 8/10 = 4/5, 6/10 = 3/5 25%


•I • PAGE

1. 2. 3. 4.

E

32

C C 5. A A I I 6. I I A A 7. C C C C Answers for items 8-10 may vary. Sample answers are listed. 8. 100 + 0 = 0 + 100 5 + 0 = 0 + 5 9. 1 + 2 = 3 2 + 1 = 3 10. 5 + (7 + 3) = 15 7 + (5 + 3) = 15 PAGE

1. 2. 3. 4. 5.

33

59 59 118 138 93

PAGE

139 87 132 100 110

152 63 105 89 177

34

98 89 82 86 81

139

51 63 18 13 40 59

PAGE

1. 2. 3. 4. 5. 6. 1. 2. 3. 4.

1,265 2,999

13.4 11.75 0.880 23.23

16.4 8.43 2.783 4.95

9.2 21.59 3.055 10.00

37

38

105 7,269 6.2 9,109 88,759 120.6

39

366,431 10.617 85,318 1,754 283,435 7,419,342

5 11 30 48 11 13

40

205 407 2,864 9 86 3,219

PAGE

140 96 101 100 65

1. 998 350 1,025 1,466 2. 1,430 1,366 5,782 3,789

1. 2. 3. 4. 5. 6.

8.5 4.58 1.892 8.73 15.3 4.014

520 3,993 16.54 781 441 1,606 179.4 3,840 139.55 76.00 13,632 10,980 910 92 1,129 33,957 106,212 1,317,439 4,005,958 140,365 368,677 346,266 4,115,375

PAGE

•F

•C

36

11.7 8.57 0.619 44.06 6.1 14.01

PAGE

•B

35

11,796 54,757 87,999 59,281 59,998 81,561 63,214 117,789 493,870 324,611 499,973 981,101 975,125 1,201,974 3,450,938 9,756,028 5. 140,031 755,324 6. 1,594,405 458,795 PAGE

•H

< = =
> 12. < <
= < > < =

PAGE

1. 2. 3. 4.

PAGE

88 7. 25% 112.5 8. 60% 12 9. 11% 17.5 10. 6.66% 3 11. 10% 12 12. 25%

29% 44% 83% 3% 166% 50%

PAGE

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

20

48 45 27 140 1,000 13

21 9 39 47 6 8

201 731 1,518 2,211 92 8,550

23 34 28 49 27 29

217 68 2,015 4,265

12 29 27 32 59 27 268 4,102 5,779 1,869

316 6,224 7,334 2,603

41

1,110 14,521 23,223 3,115 20,318 76,704 31,181 223,133 217,115 348,711 151,091 260,983 1,113,120 3,698,293 2,895,8878 459,038 5. 38,082 868,615 6. 104.084 2,176,270


Answer Key PAGE

1. 2. 3. 4. 5. 6.

PAGE

1. 2. 3. 4. 5.

42

4.4 1.37 0.999 5.728 1.6 2.75

PAGE

4.1 1.91 9.1 3.85 3.47 2.803 1.25 442 2.83 1.792

43

44

1. 52 4,441 2. 7,157 4.163 3. 1.25 70,044 PAGE

4. 3,091 453 5. 322 4,197,631 6. 583,888 52,829

45

1. -10312 -56.87 2. 1,434 1,291 3. 31,095 -1157 PAGE

47

PAGE

5. 27˚

48

49

1,421 17,533 7,007 7,060 2,580

PAGE

1. 2. 3. 4. 5. 6.

3. D 371 4. C 579

125 0.09 seconds 75 pages 211 pages 68,251 people 277 people No, there are 7,552 more people where he lives.

PAGE

50

9.494 803 3,685 129,396 812,889 $66

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

3 7 5 9 20 54 21 42 24

PAGE

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

280 2,765 12.247 5,077 85,240

12,981 3,359 25.95 1,198,962 449,339 1,129 26,528 14,612

10.74 205 151,471 3,906 3,480,719 7. $62

1. 2. 3. 4. 5. 6.

8. $77


1,2,7 18 2,6,8,24 6,15,45 11 1,2,4,7,8,14,28,56 1,2,11,22 1,5,7,35 1,2,4 1,2,4,7,14,28

54

55

56

354 126 120 259 140

114 correct 162 correct correct 8

249 112 819 416 292

432 485 310 459 511

140

276 504 261 68 320

180 116 490 351 224

57

63,147 10,772 18,766 15,010 53,118 63,832

PAGE

53

correct 201 33 correct 96 9.6 80

PAGE

1. 2. 3. 4. 5.

52

1. 2. 3. 4. 5. 6.

C 1,2,3,6,9,18 C 1,3,9,27 C 1,3,7,9,21,63 P 1,41 C 1,7,49 C 1,2,5,6,10,14,35,70 P 1,97 P 1,29 C 1,2,29,58 C 1,3,9,81 C 1,3,5,7,15,21,35,105 C 1,5,25,125 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

PAGE

1. 2. 3. 4. 5. 6. 7.

PAGE

2 7 3 and 6 2,4, and 8 22 64 70 42 114

11 31 7. 1,2,19,38 5 43 8. 1,2,3,6,7,14,21,42 19 13 9. (prime) 1,19 29 73 10. 1,3,17 17 37 11. 1,5,13,65 (prime) 1,47 12. 1,7,11,77

PAGE

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

51

2, 8 5,2,10 3 5,6,3,10 5,1 1,2,4,8 1,3,5,15 1,2,4,8,16 1,19 1,2,3,4,6,8,12,24

PAGE

46

1. B 371 2. A 579 feet

1. 2. 3. 4. 5.

4. 5.7 108,190 5. 4,010 -6,233 6. -1,124 -2,254

1,062 6,637 99,719 520 correct 176 correct 22,018 1,183,647 1,925 correct 6,028 No, he has 48 to go.

PAGE

1. 2. 3. 4. 5. 6. 7.

4.952 7.56 14.85 1.39

23 118 247 489 55 82 1,874 5,843 6,807 23 1,867 2,459 3,895 6,882 904 27,704 549,092 913,936 362,630 2,086 199,004 899,856 2,238,036

PAGE

1. 2. 3. 4. 5.

3.543 7.5 2 8.01

38,940 17,484 50,175 72,056 21,603 10,880

58

1. 29,395,604 19,895,966 2. 20,688,997 22,944,116 3. 51,407,136 51,826,692 4. 10,801,554 23,797,018 5. 19,914,764 10,311,021 6. 34,741,130 19,098,315 PAGE

1. 2. 3. 4. 5.

PAGE

1. 2. 3. 4. 5.

60

5,766 1,056 1,221 3,552 1,682

PAGE

1. 2. 3. 4. 5.

59

13 52.2 17.1 25.6 33.58

61

1.371 13.71 13.71 137.1 1.371

2,432 1,377 5,766 6,461 2,352

2,625 1,666 2,292 3,690 4,416

115,232 314,928 268,710 114,972 215,336

62

1. 427,605,408 58,893,345 2. 337,521,534 173,130,062 3. 153,396,440 134,539,197 4. 123,079,762 466,178,910 5. 35,706,132 73,317,738 PAGE

1. 2. 3. 4. 5.

19,269 44,080 39,572 51,590 12,670 27,545

43,661 18,642 67,648 23,367 37,891 30,450

13,378,400 12,784,990 26,477,634 36,537,696 44,049,710 28,896,912 24,896,683 17,044,097 23,461,875 30,086,904 21,400,205 10,229,910

53.1 2.58 .304 .264 33.32

123,975 486,962 115,785 306,545 392,015

PAGE

23,784 11,626 82,638 28,420 31,388 58,320

569.52 16.85 .2352 18.116 532

429 1.55 5.778 81.81 .0948

1,458 5,096 1,271 2,736 1,610

416,102 64,120 291,031 31,598 420,210

135,783 203,785 839,608 97,716 679,244

183,968,777 238,517,396 211,705,270 177,320,832 821,833,760 324,136,566 754,719,976 820,517,416 464,599,737 140,467,498

63

22.2 65.7 155.4 46.48 851.73

18.24 45.327 114.84 59.29 16.426

17.864 316.96 567.27 16.6848 29.5792

4.59675 17.1353 171.353 1713.53 17,135.3


PAGE

1. 2. 3. 4. 5. 6.

PAGE

1. 2. 3. 4. 5.

1. 2. 3. 4. 5. 1. 2. 3. 4.

9. 10. 11. 12. 13. 14. 15.

350,030 154,024 3,268,235 2,743,691 1,627,077 541,572 2,120,985

65 R1 345 1,011 1,735 R1 210

412 R4 519 57 R1 659 R2 38 R7

33 R1 7,704 49 R6 404 R2 721 R1

68 6.29 6.667 4 9.5 12.6

24.33 33.667 177.5 120 59.11

620.875 842 777.667 1,142.5 892.57

5 2.714 3 6.72 2.54

3.58 2 6 5 2.838

6 3.74 1.92 3.77 1.33

70 81 44.88 142 52.05 62.90

61.08 65 14.1 253.35 92

71 2.8 0.064 2,133.33 450

2.42 2,300 390 0.716

4.1 1,020 0.0185 0.734

72

1. $855 2. $2.38 3. $1,282.50

PAGE

4. $3.32 5. 12 campers per cabin 6. 6 tents


74

252 31,015 21 178 1,130,907 76,501,917

4. 5. 6. 7.

3,195 335,853 190,625,640 1,014 881 6

3.39 yards 6 teams 8 teams 27 points 368.5 8.2 30 13 1,010 858.5

14.72 196.9 4.41 0.89 4,919.33 126.063

75

1. 325,754,744 47.73 18,281,853 6.86 2. 1,277,782.57 396,573 8.1667 32.424 3. 6,232 45,318 272 50.81 4. 7.46 32,736 7 50.413 5. 4,8,12,16,20,24 7,14,21,28,35,42 13,26,39,52,65,78 6. 1,2,4,8,16,32 1,2,4,7,8,14,28,56 1,2,3,4,6,8,12,16,24,32,48,96 7. 11,29,19,2,5,41 PAGE

1. 2. 3. 4. 5. 6. 1. 2. 3. 4. 5. 6.

78

1/2 3/5 1/2 4 2/5 2 3/7 5 2/3

PAGE

1. 2. 3. 4. 5. 6.

77

1 1/6 5/12 15/16 1 2/21 1 5/18 1 1/42

PAGE

1. 2. 3. 4. 5. 6.

76

2/3 1 1 2/5 8/9 2 5 5/6

PAGE

69

0.7 2.9 340 900

PAGE

652 547 763 2,256 583

1. 2. 3. 4. 5. 6.

PAGE

62 39 103 98.03 82

PAGE

1,947 2,411 430 1,772 399

67

3 7.33 2 2.25 7

PAGE

PAGE

66

3.75 5.2 3.43 6 6.83

PAGE

1. 2. 3. 4. 5.

528 684 952 358 641

73

1. 5 2. No, there will be 4 too few. 3. 2.5 yards

6 21 23 13 12 14

65

5 R2 12 R3 27 R2 1,660 R4 1,289 R4

PAGE

1. 2. 3. 4. 5.

17 29 23 21 7 9

2,168,093 577,558 1,332,600 3,251,105 472,368 1,627,003 1,873,979 919,620

PAGE

1. 2. 3. 4. 5.

PAGE

20 19.5 28 24 11 14

477 846 367 1,107 1,958

PAGE

1. 2. 3. 4. 5. 6. 7. 8.

64

16 19 5 21 12 11

1/2 1 2/5 10 1/5 3 7 1/3 9 1/2

7. 8. 9. 10. 11. 12.

5 4/5 10 1/3 10 1/4 8 2/3 2/3 11

3 4/5 7. 11/12 2 11/12 8. 34/35 13 1/4 9. 7/8 3 29/45 10. 1 3/14 4 1/2 11. 5 7/20 6 13/21 12. 4 17/18

7 5/6 3 1/10 7/10 1 7/8 1 4/9 4 19/20

PAGE

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

4/11 1/4 0 4 1/2 4 2/3 4 2/5

5/24 23/36 1/6 1 5/11 32/63 7/12

39/70 13/18 13/48 5 3/8 2 1/4 2 1/15

141

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

83

36 1 14 4 1/2 32 1/32 6/7 90 3 2

84

1 1/6 1 5/7 10 6/9 3 1/3 1/2 3 6/7 8 1/2 1 1/14 2 2/5 1 5/13

PAGE

1/4 3/14 -1 1/10

1/3 9/50 3 1/3 3/5 1/5 7/32 15 2/11 1/7 21/50

5/12 1 1/4 7/90 6 3/4 5/21 8/25 3 1/2 6 1/4

3 4/15 15 3/5 1 23/45 5/14 2 7/24 12 1 2/3 18 3/4 9 1/3

1 13/50 34/49 7 1 11/45 10 10 1/2 10 5/9 22 2/7 13 1/2 26

82

1 1/3 15/16 41 8 33 2 1/24 13/16 10 5/6 18 3/5 4 1/8

PAGE

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

81

1/2 4/15 2/7 1/12 5/32 3/8 1 1/3 1 4/5 5 2

PAGE

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

80

P P N N N P 1/8 13/15 -1 1/8 -39/40 -5/12 19/40

PAGE

4/15 2/7 2/9 3 1/2 1 3 2/8

79

4/35 1/4 2/15 2 1/4 1 3/5 4 1/9

1 1/7 7/9 8/11 2/3 4 1/4 8 2/3

1. 2. 3. 4. 5. 6.

85

1. N P P 2. N N P 3. N P P

2/3 2 1/3 1 2/5 2 1/4 1 3/4 15/16 5/6 2 1/2 14/15 19/36 41 2 1/13 13 9/16 1 1/4 8/165 48/49 1 1/2 25/62 2 10/33 4. -7/40 5. 1 1/4 6. -28

-9 -1 1/8 -15/56

1/6 10 -1


Answer Key PAGE

86

PAGE

1. 1 2/3 hours 2. 5 hours 3. 1 11/27 PAGE

1. 2. 3. 4. 5.

C D A E B

PAGE

1. 2. 3. 4. 5. 6. 7. 8. 1. 2. 3. 4. 5. 6. 7. 8.

18 34 10/11 1 gallon 10 1/8 2 3/16

88

89

-1/2 -1/3 5/12 -16/21 3 7/40 B 1/2 A 2/3 C 1/2

PAGE

1. 2. 3. 4. 5. 6. 7.

87

2/3 1 2/5 2 1/2 14/15 1/3 3/7 8 4/5 2 3/4

PAGE

90

11 28 4.667 17 36 27 21

PAGE

1. 2. 3. 4.

6 7 15 4

PAGE

1. 2. 3. 4.

11 11 2 -3

92

6 13 2 4

93

2 6 90 8

94

2. 6. 7. 8. 9. 10.

32 48 3 3 4

11. 12. 13. 14. 15.

•

1 2 2 1 13

9

1/10 1 13/20 15/16 1 1/2 16 5/12 5 7/15 2 1/40

PAGE

2.78 23 190 350 190 105 1,080

PAGE

•

6 5

•

4 3

95

•

2 1

0 1 2 3 4 5 6 7 8 9 jade plant growth in inches

96

PAGE

1. a. Plot these points: (2,1) (4,2) (6,3) 1. b. Plot these points: (1,3) (2,6) (3,9) 2. a. Plot these points: (3,1) (5,2) (7,3) 2. b. Plot these points: (3,2) (5,3) (7,4)

-1/8 -10 4/15 49/64 -91/100

•

8 7

1. a. Plot these points: (2,0) (3,1) (4,2) (5,3) (6,4) 1. b. Plot these points: (0,1) (1,2) (2,3) (3,4) (4,5)

7/20 -9/16 -5/21 -29/45 -1 3/10

91

1 10 2 3 2

PAGE

2/5 1/14 1 3/35 5/12 1/10 9/20 6 7/12 3 5/7

1. 52 inches 2. 1.5 minutes PAGE

1. 2. 3. 4. 5.

4. 8:57 5. 1 9/20 6. 8 3/4

100

1. D PAGE

1. 2. 3. 4.

8 2 3 8

PAGE

2. B

101 3 11 45 6

PAGE

1.

9 8 4 18

5. 6. 7. 8.

4. C

5 9 3 16

36 18 20 12

4 8 7 4

102

1. x: 2,4,6,8,10 y: 2,3,4,5,6

97

1. a. Plot these points: (1,2) (2,4) (3,6) 1. b. Plot these points: (3,1) (6,2) (9,3) 2. a. Plot these points: (2,3) (3,6) (4,8) 2. b. Plot these points: (0,1) (3,2) (5,3)

945 20 48 -16 25 15 50

3. A

• • • • •

98 2. x: 1,2,3,4,5 y: 0,1,2,3,4 •

27

•

24 21

• •

18 15

• •

12 9

3. $360 4. $20

6 3

23 14 14 6

5. 6. 7. 8.

8 13 7 15

72 5 6 3

7 7 3 3

31 5 16 2

5. 6. 7. 8.

5 7 7 18

36 5 60 14

6 6 3 8

•

•

•

•

•

•

• •

5 10 15 20 25 30 35 40 45 pounds

PAGE

1.

99

3. •

900

400

800 700

300

•

600 500 400 300

•

•

200

• •

•

100

•

200 100 0

1

2

3

4

100

200

300

400

food in grams

hours of exercise


142


PAGE

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

PAGE

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

104

6,000 500 72 1/8 24

1. 2. 3. 4. 5. 11.

106

1. 2. 3. 4. 9.

5,000 48 10,500 3/4 1/32

3. C 4. Answers will vary.

108

109

8 1,760 1.75 3.67 3,168

cm cm m m 0.1 200 1,000 3 0.01 0.5

6.67 6. 2.67 7. 1,760 8. 3,520 9. 880 10.

< = > < >

> > = >
= < > =

0.00005 8,000

0.18288 1.22 2.1336 28.96

PAGE

45.72 0.508 0.1524 0.536

249 29.53 218.72 1,093

5. 6. 7. 8.

< > >

1. 2. 3. 4.

1. Ohio is warmer. 73.4˚F 89˚F 2. Mia 3. 68 kilograms

114

> < >
= >

PAGE

1. 2. 3. 4. 5. 6. 7. 8.

110

10.16 1.8288 25.4 4,023.36 > > > < < < > > > < > > < >
= > > < > < > >

PAGE

8. 500 0.8 9. 50 15 10. = <
= > < = < = > < < < = >

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