math computation skills & strategies level 7 (math computation skills & strategies)

LEVEL

Operations

Fractions andDecimals

Whole Numbers

Perimeter and Area

Regrouping

Solving WordProblems

Money

Measurement

MATHCOMPUTATIONMATHCOMPUTATIONSKILLS & STRATEGIES

HIGH-INTEREST

7 100plus+ REPRODUCIBLE ACTIVITIES

HIG

H-IN

TE

RE

ST M

AT

H C

OM

PU

TAT

ION

SKIL

LS &

STR

AT

EG

IES •

LE

VE

L 7

Every book in the Math Computation Skills and Strategies series contains over 100 reproducible pages.These high-interest activities combine computation practice with strategyinstruction. Featuring a Scope and Sequence chart, the booksallow educators to supplement their math lessons with theextra math practice all students need. In addition, periodicreviews allow for reinforcement and assessment of skills.

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

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

MATH COMPUTATION SKILLS & STRATEGIESMATH COMPUTATION SKILLS & STRATEGIES

HIGH-INTEREST

SAD

DL

EB

AC

K E

DU

CA

TIO

NA

L P

UB

LISH

ING

Saddleback E-Book

Saddleback Math Covers 10/22/06 6:24 PM Page 5

MATHCOMPUTATIONSKILLS & 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 anyinformation storage and retrieval system without written permission of thepublisher, with the following exception.

Pages labeled Saddleback Educational Publishing ©2006 are intended forreproduction. Saddleback Educational Publishing grants to individualpurchasers of this book the right to make sufficient copies of reproduciblepages for use by all students of a single teacher.This permission is limited toan individual teacher and does not apply to entire schools or school systems.

Printed in the United States of America

Table of Contents

Page Lesson5 . . . . . . . . . Introduction

Unit 1 . . . Numbers and Number Sense6 . . . . . . . . . Understand Integers7 . . . . . . . . . Add and Subtract Integers8 . . . . . . . . . Find Absolute Values9 . . . . . . . . . Read Coordinate Graphs10 . . . . . . . . Find Squares and Square Roots11 . . . . . . . . Express Powers of Ten12 . . . . . . . . Use Exponents13 . . . . . . . . Identify Equivalent Fractions14 . . . . . . . . Convert Decimals and Fractions15 . . . . . . . . Work with Non-terminating Decimals16 . . . . . . . . Compare Integers17 . . . . . . . . Order Integers18 . . . . . . . . Rounding19 . . . . . . . . Rounding and Estimating20 . . . . . . . . Find Percentages21 . . . . . . . . Find Percentages22 . . . . . . . . Convert Percents and Decimals23 . . . . . . . . Convert Fractions and Percents24 . . . . . . . . Understand Ratios25 . . . . . . . . Find Ratios26 . . . . . . . . Understand Irrational Numbers27 . . . . . . . . Solve Word Problems28 . . . . . . . . Solve Word Problems29 . . . . . . . . Solve Word Problems30 . . . . . . . . Review Numbers and Number Sense31 . . . . . . . . Review Numbers and Number Sense

Unit 2 . . . . Addition and Subtraction32 . . . . . . . . Use Addition Properties33 . . . . . . . . Add Two Digits34 . . . . . . . . Add Up to Four Digits35 . . . . . . . . Add Up to Seven Digits36 . . . . . . . . Add Decimals37 . . . . . . . . Practice Addition38 . . . . . . . . Practice Addition39 . . . . . . . . Subtract Two Digits40 . . . . . . . . Subtract Up to Four Digits41 . . . . . . . . Subtract Up to Seven Digits42 . . . . . . . . Subtract Decimals43 . . . . . . . . Practice Subtraction44 . . . . . . . . Practice Subtraction45 . . . . . . . . Add and Subtract Greater Integers46 . . . . . . . . Check Addition and Subtraction47 . . . . . . . . Solve Word Problems48 . . . . . . . . Solve Word Problems49 . . . . . . . . Review Addition and Subtraction50 . . . . . . . . Review Addition and Subtraction

Unit 3 . . . . Multiplication and Division51 . . . . . . . . Find Multiples52 . . . . . . . . List Factors53 . . . . . . . . Identify Prime and Composite Numbers54 . . . . . . . . Identify Prime and Composite Numbers55 . . . . . . . . Check Multiplication and Division56 . . . . . . . . Multiply 2 Digits by 1 Digit57 . . . . . . . . Multiply 4 Digits by 1 Digit58 . . . . . . . . Multiply 7 Digits by 1 Digit59 . . . . . . . . Multiply Decimals60 . . . . . . . . Multiply 2 Digits by 2 Digits61 . . . . . . . . Multiply 4 Digits by 2 Digits62 . . . . . . . . Multiply 7 Digits by 2 Digits63 . . . . . . . . Multiply Decimals64 . . . . . . . . Divide 2 Digits by 1 Digit65 . . . . . . . . Divide 4 Digits by 1 Digit66 . . . . . . . . Divide 7 Digits by 1 Digit67 . . . . . . . . Divide With Remainders68 . . . . . . . . Decimal Quotients69 . . . . . . . . Divide 2 Digits by 2 Digits70 . . . . . . . . Divide 4 Digits by 2 Digits71 . . . . . . . . Divide Decimals72 . . . . . . . . Solve Word Problems73 . . . . . . . . Solve Word Problems74 . . . . . . . . Review Multiplication and Division75 . . . . . . . . Review Multiplication and Division

Unit 4 . . . . Fractions76 . . . . . . . . Add Fractions with Like Denominators77 . . . . . . . . Add Fractions with Unlike Denominators78 . . . . . . . . Subtract Fractions with Like Denominators79 . . . . . . . . Subtract Fractions with Unlike Denominators80 . . . . . . . . Add and Subtract Positive and . . . . . . . . . . Negative Fractions

81 . . . . . . . . Understand Multiplying Fractions82 . . . . . . . . Multiply Mixed Numbers83 . . . . . . . . Divide Fractions84 . . . . . . . . Divide Mixed Numbers85 . . . . . . . . Multiply and Divide Positive and . . . . . . . . . . Negative Fractions

86 . . . . . . . . Solve Word Problems87 . . . . . . . . Solve Word Problems88 . . . . . . . . Review Fractions89 . . . . . . . . Review Fractions

Unit 5 . . . . Equations and Graphs90 . . . . . . . . Use Order of Operations91 . . . . . . . . Write Equations92 . . . . . . . . Solve Equations93 . . . . . . . . Solve Equations94 . . . . . . . . Understand Functions95 . . . . . . . . Graph Functions96 . . . . . . . . Graph Functions97 . . . . . . . . Graph Functions98 . . . . . . . . Graph Rates99 . . . . . . . . Graph Rates100 . . . . . . . Review Equations and Inequalities101 . . . . . . . Review Equations and Inequalities102 . . . . . . . Review Graphing Functions

Unit 6 . . . . Measurement103 . . . . . . . Use Time Measurements104 . . . . . . . Convert Temperatures105 . . . . . . . Use Weight Measurements106 . . . . . . . Identify Angles107 . . . . . . . Find Angles108 . . . . . . . Find and Convert Customary Lengths109 . . . . . . . Find and Convert Metric Lengths110 . . . . . . . Convert Customary to Metric111 . . . . . . . Convert Metric to Customary112 . . . . . . . Solve Word Problems113 . . . . . . . Solve Word Problems114 . . . . . . . Review Measurement115 . . . . . . . Review Measurement

Unit 7 . . . . Geometry116 . . . . . . . Find Perimeters117 . . . . . . . Use the Pythagorean Theorem118 . . . . . . . Find Circumferences119 . . . . . . . Find Area of Parallelograms120 . . . . . . . Find Area of Triangles121 . . . . . . . Find Area of Circles122 . . . . . . . Find Area of Irregular Figures123 . . . . . . . Find Surface Area124 . . . . . . . Find Volume125 . . . . . . . Solve Word Problems126 . . . . . . . Solve Word Problems127 . . . . . . . Review Geometry128 . . . . . . . Review Geometry

Table of Contents

Unit 8 . . . . Probability129 . . . . . . . Find Averages130 . . . . . . . Figure Probability131 . . . . . . . Understand Odds132 . . . . . . . Identify Mean, Median & Mode133 . . . . . . . Solve Word Problems134 . . . . . . . Solve Word Problems135 . . . . . . . Review Probability136 . . . . . . . Review Probability

137 . . . . . . . Scope and Sequence138 . . . . . . . Answer Key139 . . . . . . . Answer Key140 . . . . . . . Answer Key141 . . . . . . . Answer Key142 . . . . . . . Answer Key143 . . . . . . . Answer Key144 . . . . . . . Answer Key

About This Series

This series was created by Saddleback Educational Publishing to provideextensive math practice as a supplement to in-class instruction. MathComputation Skills and Strategies can easily be integrated into mathcurricula to reinforce basic skills.The lessons focus on practice, with upto 70 items a page. In addition, the lessons are designed to challengestudents as their skills grow stronger.As the students progress throughthe individual lessons, the degree of difficulty increases.

Closely adhering to state standards, this series provides grade-levelappropriate lessons that are approachable for students at a range ofabilities. Review lessons are interspersed throughout the book to allowstudents to reinforce their skills. Furthermore, the Scope and Sequencechart at the back of the book will help you choose lessons that areapplicable to your curriculum.This series covers a range of topics,allowing students to build skills in multiple areas.Additionally, the lessonsprovide a variety of approaches, including word problems that emulatereal-life situations.

Each book is designed to challenge students who are learning skills atthe corresponding grade level. However, the lessons were created notjust for younger children, but for students of all ages.

Saddleback Educational Publishing believes in allowing students tostrengthen their skills with fun and exciting practice lessons.We hopeyou enjoy using this series to supplement class instruction and helpstudents gain skills for proficiency in math computation.

1 . - 3 5 0 . 5 1 2 0 0 - 7 0 9 - 1 0 . 6

2 . 1 8 - 2 5 , 9 7 6 5 . 7 2

3 . 9 7 - 6 2 0 . 3 5 9 9 6 0 , 4 4 8 1 1 2 1

4 . 5 7 3 , 0 6 8 - 5 7 1 - 6 . 0 0 3 2 8 0

5 . - 3 9 6 0 4 0 2 . 5 4 - 2 9 8 61 0

6Math Computation Skills and Strategies, Level 7Saddleback Educational Publishing ©2006

Integers can be positive, negative, or zero.

Understand Integers

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

Name Date3 Watson, Irvine, CA 92618

Phone (888) SDL-BACK www.sdlback.com

a b c d

413

e

34

910

1719

310

f

2

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

0-2 2 4 6 8-4-6-8

1 . - 4 + - 8 =

2 . 5 + - 9 =

3 . 13 - - 8 =

4 . - 6 - - 4 =

-12 -13 =

5 - 9 =

-7 + 13 =

10 - 15 =

-10 +15 =

-7 - 8 =

- 20 - - 40 =

500 + - 600 =


When you add or subtract integers, pay close attention to whether they arepositive or negative. This will affect the sum or difference.

Add and Subtract Integers



Subtracting a negative integer is like adding its opposite.3- -4 = 7

Adding a positive number and a negative number is like subtractingtwo 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

a b c d

5 .

6 .

7 .

80

+ 240

2200

+ 1900

340

+ 50

306

+ 204

130

+ 450600

+ 700

950

+ 951

532

+ 472

25

7568

+ 32

653

+ 500

871

+ 13

e

27

+ 62

130

+ 900

75

+ 33


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

Find Absolute Values



Directions: Solve.

1 . | 9 |

2 . | - 1 7 |

3 . | - 3 7 8 |

4 . | - 1 / 5 |

5 . | - 9 4 |

6 . |7 - 9|

7 . - | 1 3 - 5 |

8 . |-3 + 2|

| - 5 7 |

-|57|

| 4 . 5 |

- | - 4 9 2 7 |

- |-3 + 2|

- | 32|

| - 32|

( - | - 3 | )2

| - 2 . 3 |

| 5 7 0 5 |

|-3 1/3|

-|- 489|

| 0 - 1 4 |

|13 - 7|

-|35 ÷ 5|

|9 - 15|

a b c

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

9 . |-7| 7

1 0 . |3-4| - |3-4 |

-|5-2| | - 3 |

-|-25| - 5 2

-|-5| | - 5 |

|7-9| (-|7-4|) +4

a b c

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 )


Plotting points on a coordinate graph is easy. Just remember that the distancealong the horizontal x-axis, is listed first.

Read Coordinate Graphs



Directions: Name each point.The first one is done for you.

Directions: Plot the point at the correct place.

1 . A (2,7)

B

C

D

E

F

G

H

•A

• B

• C• D

• E• F

• G

• H

1 . 52

2 . 1 52

3 .

4 .

5 . 92

6 .

7 .

8 . 1 12

9 . 3 02

1 0 . 2 52

1 22

1 52

62

1 42

22

12

72

2 52

1 62

1 02

2 02

4 02

1 32

2 02

5 02

42

1 0Math Computation Skills and Strategies, Level 7Saddleback Educational Publishing ©2006

If you know your squares, it’s easy to find square roots.32 = 9 9 = 3

Find Squares and Square Roots



Directions: Find the square or the square root.

a b c d

121 16

625

225 64

36 81

4

100 196 900

400 49

2500 256

25 289

324


Using exponents can save time and space. For example 106 is the same as1,000,000, or one million.

Express Powers of Ten



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

1 . 100 = 1,o n e

2 . 101 = 10, t e n

3 . 102 =

4 . 103 =

5 . 104 =

105 =

106 =

107 =

108 =

109 =

a b

Directions: Write the number using powers of ten.

6 . 100 =

7 . 11 =

8 . 11,000 =

9 . 110 =

1 0 . 110,000 =

1,000,000 =

100,000,000 =

10,000,000 =

1,000,000,000 =

100,000 =

a b


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

Use Exponents



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 =

2 . 26 =

3 . 33 =

4 . 61 =

5 . 92 =

54 =

23 =

74 =

45 =

07 =

63 =

1 10 =

84 =

38 =

93 =

Directions: Write the exponent, then solve.

a b

6 . 2 x 2 x 2 =

7 . 4 x 4 x 4 x 4 x 4 =

8 . 7 x 7 x 7 x 7 x 7 x 7 x 7 =

9 . 8 x 8 =

1 0 . 5 x 5 x 5 =

6 x 6 x 6 x 6 =

9 x 9

3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 =

10 x 10 x 10 =

1 x 1 x 1 x 1 x 1 x 1 =

5 .

6 .

7 .

8 .

9 .

1 0 .

1 1 .


Remember: Equivalent means equal.

Identify Equivalent Fractions



a b c

34

___78

68

___1216

23

___45

13

___26

14

___212

28

___416

48

___12

Directions: Complete each number sentence with = or .

39

___13

214

___17

1012

___23

13

___312

1 .

2 .

3 .

4 . 912

___56

78=

16=

1112

=

510

=14=

35=

13=

816

=39=

34=

27=

48=

310

=79=

4

5=

12=

58=

2

4=

23=

56=

1012

=

Directions: Write equivalent fractions.

a b c


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

Convert Decimals and Fractions



Directions: Write the equivalent fraction or decimal.

1 .

2 .

3 . 0.75 =

4 . .4 =

5 .

6 . 0.125 =

7 . 0.09 =

8 .

0.1 =

.25 =

0.80 =

.66 =

0.5 =

0.60 =

.9 =

0.90 =

0.003 =

a b c

14=

34=

12=

1920

=310

=

25=

12=

15=

1100

=35=

59100

=

45= 0.8 = .8

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

9 .

1 0 .

1 1 .

a b c

14

___13

58

___ 0.579

___34

14

___ 0.2 0.9 ___910

12

___ 0.5

0.75 ___75100

13

___ 0.4 0.3 ___13

1 .

2 .

3 .

4 .

5 .

6 .

7 .

8 .


Some decimal numbers just never end! Here are some ways to deal withnon-terminating decimals.

Work with Non-Terminating Decimals



a b

2 = 6 =

18= 13 =

17=

1

18=

8 = 11=

19=

37=

5 =1112

=

56= 7 =

3 =211=

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

Round to the nearest tenth.

Put a bar over the digits that repeat.

Use an established number. = 3.14159265358979323846264338 =3.1416

7 = 2.6457513 = 2.6

1

6= 0.166666666 = 0.16


To compare integers, first look at the signs, then look at digits in the sameplace value.

Compare Integers



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

38 < 41 - 256 > -276

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 >.

5 . 175 178

6 . 23 23.4

7 . 643 633

8 . -97 -96

9 . 2576 2476

1 0 . -5.3 -5.2

1 1 . 809 798

1 2 . 609 690

8.13 8.14

-8 -9

7061 7062

4231 4321

-52 -50

0.51 0.5

6498 6488

757 758

-1 0

-0.3 -0.31

1081 1180

354 345

2675 3675

4873 -4872

31,568 31,468

-697 698

a b c


The sign can make all the difference.

Order Integers



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

1 0 . 5230, 5320, 5302

1 1 . -58, -59, 60

1 2 . 2.5, 2.4, 2.45

1 . 14 10 14 15 20

2 . 37 30 35 40 50

3 . 50 40 50 55 60

88 80 85 90 100

96 80 90 95 100

121 100 110 120 130


Sometimes you don't need to use exact numbers.You can round a number tothe nearest ten or hundred, for example.

Rounding



To round a number, look at the digit in the place to theright of the place you are rounding to. Round up if it is 5 orgreater. Round down if it is 4 or less.

Directions: Look at the number in dark print. Circle the number next to itthat is the same number rounded to the nearest ten.

Directions: Round the decimal to the nearest whole number.

a b

4 . 0.3 3.09 72.25

5 . 2.8 1.46 58.82

6 . 4.04 9.5 416.707

a b c

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

nearest ten nearest hundred nearest thousand

7 . 737.5

8 . 1,154

9 . 2,608.06

1 0 . 4,380.3


Rounding and estimating can help you check your answers.

Rounding and Estimating



76 + 31 80 + 30 = 110The 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 theexact answer.

a b

1 . 89 + 19 =

2 . 54 + 77 =

3 . 452 + 36 =

4 . 607 + 528 =

5 . 3,121 + 4,094 =

6 . 94 + 45 =

56 + 2 =

423 + 160 =

807 + 998 =

5,352 + 736 =

62 + 80 =

109 + 583 =


Percent means “out of each hundred.”

Find Percentages



Directions: Solve.

a b

1 . 60% of 80 =

2 . 50% of 90 =

3 . 90% of 30 =

4 . 70% of 200 =

5 . 25% of 4000 =

6 . 65% of 20 =

88% of 100 =

75% of 150 =

200% of 6 =

35% of 50 =

10% of 30 =

150% of 8 =

a b

7 . 20 out of 80 =

8 . 9 out of 15 =

9 . 6 out of 54 =

1 0 . 5 out of 75 =

1 1 . 11 out of 110 =

1 2 . 50 out of 200 =

9 out of 9 =

3 out of 300 =

12 out of 8 =

6 out of 12 =

12 out of 6 =

5 out of 500 =

Directions: Find the percentage for each set of numbers.


Working with percentages is like working with decimals.You may need toround percentages to the nearest whole number.

Find Percentages



4 out of 12 = 33.333333...% round to 33%

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

a b

1 . 2 out of 7 =

2 . 400 out of 900 =

3 . 5 out of 6 =

4 . 1 out of 30 =

5 . 50 out of 30 =

6 . 0.5 out of 1 =

7 . 18 out of 24 =

8 . 60 out of 45 =

9 . 700 out of 800 =

1 0 . 30 out of 200 =

10 out of 60 =

25 out of 20 =

1 out of 3 =

22 out of 24 =

17 out of 20 =

17 out of 19 =

400 out of 600 =

3 out of 4 =

28 out of 30 =

1 out of 12 =

1 1 . 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?

1 2 . The next night,Tanner spent 80 minutes doing homework. Of that time, he spentabout 45 minutes on math.What percentage of his time did Tanner spend doingmath homework?


Percents and decimals are very similar to each other.

Convert Percents and Decimals



Directions: Convert each decimal to a percent and eachpercent to a decimal.

1 . 85% =

2 . 0.47 =

3 . .72 =

4 . 29% =

5 . 50% =

6 . 0.9 =

7 . 0.06 =

8 . 3% =

200% =

.34 =

98% =

1.0 =

15% =

0.56 =

99% =

0.835 =

1.5 =

10% =

40% =

0.001 =

0.8 =

82% =

132% =

2.5 =

a b c

Directions: Write =, <, or > to compare the numbers.

9 . 0.4 0.39

1 0 . 37% 0.4

1 1 . 0.9 90%

1 2 . 0.05 50%

130% 1.3

0.7 75%

2.1 21%

0.61 62%

0.19 20%

0.5 50%

200% 0.2

4% 0.4

a b c


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

Convert Fractions and Percents



To convert a fraction to a percent: Divide the numerator by thedenominator, multiply by 100, and add the percent sign.

To convert a percent to a fraction: Make the percent the numeratorwith a denominator of 100. Simplify.

Directions: Convert each fraction to a percent and each percent toa fraction.

1 .

2 . 40% =

3 .

4 .

30% =

110% =

1% =

99% =

a b c

12=

23=

59=

14=

78=

910

=

120

=

Directions: Write =, <, or > to compare the numbers.

5 .

6 .

7 .

8 .

a b c

13

___14

50% ___35

71000

___ 7%

35% ___13

310

___ 31% 99% ___99100

85% ___1720

9100

___ 9% 42% ___2150

15% ___18

110% ___54

34

___ 80%

34= 3 ÷ 4 = 0.75 100 = 75%

80% =80100

=45


A ratio compares two amounts. A ratio can be expressed using a fraction, andcan be simplified, or reduced to lowest terms.

Understand Ratios



In the 2000 census, the U.S. Government counted 96 men for every 100women in the country.

The ratio of men to women was 96 out of 100, or 24 to 25.The ratiocan also be expressed in these ways:

or 24:25.

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

1 0 . girls in volleyball to students in the program

1 1 . boys in the program to students in the program

1 2 . girls in the program to boys in the program

2425


Setting up a ratio can help you find a number.

Find Ratios



The ratio of men to women is .

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

Directions: Complete the ratio.

1 .

2 . 5 to 9 = 10 to ?

3 . 1:3 = 9:?

4 .

5 .

6 . 1:6 = ? :18

1:4 = ?:44

15 to 18 = 5 to ?

7:10 = ?:40

24 to 26 = 12 to ?

4:5 = 16:?

18 to 27 = ? to 3

80:1000 = 8:?

a b c

34=

?16

310

=6?

153=

?1

29=6?

32=6?

57= ? to 35

1920

=?100

56=

?18

2425

2425

=m

200025m= 24 2,000 = 48,000

m=1,920


An irrational number is a decimal that doesn't repeat or end and isn't afraction. Other numbers are rational.

Understand Irrational Numbers



is the ratio of the circumference of a circle to its diameter.This ratiois the same for all circles.

= 3.1415926535897932384626433832795028841971...

The points after the 1 at the right (... ) mean that the number continueson without repeating or terminating.

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

1 .

2 .

3 .

4 .

5 . e = 2.718281...

6 .

7 . 0.573

8 . 0.33333333...

321.321321321...

2.673473

a b

2 =1.4142135K3

4= 0.75

2

9= 0.222222K 9.3 = 3.04959K

11

12= 0.9166K

2

3= 0.6666K

3 =1.732050K 6.5 = 2.5495K

5

8= 0.625

3

7= 0.42857K 7 = 2.64575K


Use what you know about numbers and number sense to solve these wordproblems.

Solve 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 andusing an exponent.

2 . After his daily run, Gabe is only 50% done with his workout. Some days helifts weights next. He met his friend Sabrina in the gym one day. She said that

she was done with her workout.Who was further along?

Show your conversion.

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

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

23


Use what you know about numbers and number sense to solve these wordproblems.

Solve Word Problems



Directions: Solve.

1 . Julia scrapbooked her pictures. She bought special paper in squares to glueher photos onto.The area of the square was 49 square inches.What sizewas the paper?

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

3 . Julia realized that two pictures were too big for her scrapbook. She wanted toscale them down by half. She wrote ratios to compare width and length.Complete the ratios.

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

810

=4?

610

=?5


You already have the skills — now practice applying them.

Solve Word Problems



Directions: Solve.

1 . Scientists have measured extremely cold liquids.Which of the followingreadings is the coldest?-7°, -26°, 32°, 0°

2 . Scientists have weighed seeds.Write these weights in order from lightest toheaviest, 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.

Write three fractions equivalent to .

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

2432

2432


Now you have the chance to show what you know!

Review Numbers and Number Sense



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

1 . -27

2 . 1,400

3 .

0.5

0

-439

-2.7

60,571

a b c d

3

2

4 .

5 . 6 x 6 x 6 x 6 =

6 . -40 + 70 =

7 . 83 =

8 . -|-7| =

9 . 95

1.09

3:4 = 15:

108 =

36 to 9 = 8 to

13 - -8 =

a b

81=

121=

Directions: Solve. Show all your work.

1 0 . Callie did an experiment with plants.At the end of the experiment shemeasured the height of the plants to see which grew the tallest.Write theheights 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

18

1112


Here’s another chance to show what you know.

Review Numbers and Number Sense



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

1 .

2 .

3 . 50% ___ 0.05

4 .

5 .

6 .

7 .

8 . -15 ___ -16

-0.34 ___ -0.23

15% ___ 1.5

0.8 ___ .80

10% ___0.2

200% ___ 2.0

0.4 ___ 4%

30%___

0.33 ___

a b c

45

___810

13% ___17

2 ___1.5718

___1436

56

___ 0.85

0.6 ___61100

25

___ 45%

18

___ 0.125

3 ___1.75 15

___ 21%9100

___ 9%

1720

___ 85%

34

___ 75%

0.1___19

9 . ABCDE

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

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

13

14

•A

• B

• C

• D

• E

Learn the properties of addition below to help you add more quickly andeasily.

Use Addition Properties




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

The Identity Property says that the sum of any number and zero isthat number.

The Commutative Property says that you can add two numbersin either order and get the same sum.

The Associative Property says that you can group three or morenumbers in any way and get the same sum.

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

a b

Directions: Write two examples to demonstrate each property.

8 . Identity

9 . Commutative

1 0 . Associative




Always start by adding the ones column. Remember to regroup into the nextgreater place value, if needed.

Add Two Digits

Directions: Add.

1 .

2 .

3 .

4 .

5 .

a

35

+ 24

b

68

+ 71

c

76

+ 76

d

89

+ 9

e

75

+ 65

16

+ 43

49

+ 38

38

+ 25

52

+ 37

49

+ 47

58

+ 60

92

+ 40

47

+ 58

64

+ 18

38

+ 63

84

+ 54

53

+ 47

22

+ 67

40

+ 46

72

+ 28

8

+ 85

16

+ 94

96

+ 81

58

+ 23

37

+ 28


Try adding numbers in the thousands.



Add Up to Four Digits

Directions: Add.

1 .

2 .

3 .

4 .

a

573

+ 425

b

284

+ 76

c

697

+ 328

d

837

+ 629

e

508

+ 757

962

+ 468

537

+ 829

5228

+ 554

3041

+ 748

653

+ 2346

2512

+ 4396

6683

+ 741

7052

+ 8353

7236

+ 4543

2834

+ 2834

5485

+ 3333

3691

+ 6317

4493

+ 1857

3958

+ 4062

8751

+ 6352

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

5 . 475 + 366 = 598 + 3702 =

6 . 7086 + 3259 = 6113 + 987 =

a b

3 5Math Computation Skills and Strategies, Level 7Saddleback Publishing, Inc. ©2006

Tip

Add Up to Seven Digits



Adding numbers in the millions is the same as adding other numbers.Youmay need to regroup more than once.




Directions: Add.

1 .

2 .

3 .

4 .

a

7390

+ 4386

b

52,174

+ 2,583

c

84,528

+ 3,471

d

58,496

+ 785

33,673

+ 26,325

38,209

+ 43,35262,630

+ 584

95,332

+ 22,257

461,037

+ 32,843

249,426

+ 75,185

326,124

+ 173,859

608,892

+ 372,209

876,958

+ 98,167

735,245

+ 466,729

2,093,461

+ 1,357,477

6,738,745

+ 3,017,283

a b

5 . 93,158 + 46,873

6 . 843,420 + 750,985

698,543 + 56,781

4,256,329 + 327,466

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


Tip



When adding decimals, line up the numbers on the decimal points. Regroupas you would other numbers.

Add Decimals




Directions: Add.

1 .

2 .

3 .

4 .

a

5.3

+ 6.4

b

4.8

+ 3.7

c

5.5

+ 7.9

d

12.8

+ 3.6

e

3.2

+ 6

6.21

+ 2.36

3.25

+ 6.33

8.47

+ 3.26

2.4

+ 6.03

21.34

+ 0.25

0.336

+ 0.283

1.803

+ 0.089

0.521

+ 0.359

2.1

+ 0.683

0.685

+ 2.37

41.3

+ 3.76

7.75

+ 0.98

23

+ 0.23

4.5

+ 0.45

7.02

+ 2.98

Directions: Rewrite in vertical form, then add. Remember to line up thedecimal points.

5 . 3.5 + 2.6 6.3 + 9

6 . 10.22 + 3.79 3.04 + 0.974

a b


See how quickly — and accurately — you can complete these additionequations.

Practice Addition



Directions: Add.

1 .

2 .

3 .

a

597

+ 23

b

3489

+ 504

c

9.35

+ 7.19

d

684

+ 97

e

96

+ 345

672

+ 934

96.7

+ 82.7

854

+ 3986

81.76

+ 57.79

7.39

+ 68.71

8143

+ 5589

6235

+ 4745

338

+ 572

59

+ 33

853

+ 276

4 .

5 .

a

7,671

+ 26,286

b

21,680

+ 74,532

c

852,873

+ 464,566

d

407,325

+ 3,598,633

93,507

+ 46,868368,192

+ 485

283,938

+ 62,338

567,433

+ 3,557,942


Always remember to line up the numbers on the ones or on the decimalpoints.

Practice Addition



Directions: Rewrite the equations vertically, then add.

1 . 47 + 58

2 . 2398 + 4871

3 . 2.5 + 3.7

4 . 3673 + 5436

5 . 52,370 + 36,389

6 . 45.35 + 75.25

3,672 + 362,759

8.037 + 2.58

76,521 + 8,797

968 + 786

25,300 + 30,435

6,543,219 + 876,123

a b

Directions: Subtract.

1 . 86 - 35

2 . 97 - 34

3 . 56 - 38

4 . 60 - 47

5 . 83 - 43

6 . 75 - 16

13 - 8

29 - 18

64 - 34

85 - 37

51 - 40

21 - 8

39 - 18

82 - 73

78 - 39

93 - 46

33 - 27

46 - 38

44 - 21

90 - 56

32 - 4

87 - 38

62 - 35

73 - 44

71 - 59

47 - 18

64 - 37

38 - 6

94 - 35

50 - 23


Start subtracting at the ones place. Regroup as needed.

Subtract Two Digits



a b c d e


You might have to borrow more than once. Remember to keep track eachtime.

Subtract Up to Four Digits




1 .

2 .

3 .

4 .

a

657

452

b

934

733

c

688

471

d

590

322

e

365

49

684

277

805

74

427

359

4726

624

6738

514

3986

1122

5139

3621

9455

7440

6107

328

8265

931

2835

2826

6928

4717

7863

3598

9072

7203

4120

1517

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

5 . 475 - 389 = 682 - 590 =

6 . 6851 - 3632 = 9332 - 782 =

a b



Subtracting in the millions is just like subtracting other numbers.

Subtract Up to Seven Digits



1 .

2 .

3 .

4 .

a

5,876

4,766

b

67,745

53,224

c

38,696

15,473

d

72,457

69,342

93,067

72,749

85,436

8,732

77,512

46,331

544,680

321,547

476,375

259,260

700,000

351,289

517,289

366,198

270,834

9,851

2,483,599

1,352,479

4,325,928

627,635

6,817,500

3,921,622

8,351,701

7,892,663

a b

5 . 65,723 - 27,641

6 . 380,452 - 276,368

875,400 - 6,785

5,423,167 - 3,246,897

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


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

Subtract Decimals



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

1 .

2 .

3 .

4 .

a

8.9

4.5

b

6.9

2.8

c

5.24

3.33

d

7.577

4.034

e

9.346

4.394

3.57

2.2

12.5

3.4

4.6

0.75

8

0.5

10.63

3.07

1

0.001

5.75

2.28

6.203

3.4

7.36

5.36

15

0.15

14.43

8.702

3

1.75

7.1

2.68

8.9

0.89

2.48

1.09

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

5 . 7.2 - 5.6 6 - 3.17

6 . 5 - 2.25 2.1 - 0.308

a b



The biggest mistake people make is regrouping when it's not needed orforgetting to borrow when it is.

Practice Subtraction



1 .

2 .

3 .

a

85

62

b

157

39

c

623

476

d

582

93

e

73

18

367

285

2361

487

5932

89

7184

377

85

62

4759

2892

5000

2541

6079

2184

9645

2763

4540

3636

4 .

5 .

a

46,300

18,596

b

583,256

34,164

c

920,157

6,221

d

632,700

270,070

721,361

719,275

867,073

668,069

7,834,603

6,934,747

3,525,400

1,287,364


Always remember to line up the numbers on the ones or on the decimalpoints.

Practice Subtraction



Directions: Rewrite the equations in vertical form, then subtract.

1 . 87 - 35

2 . 7436 - 279

3 . 5 - 3.75

4 . 31,455 - 28,364

5 . 570 - 248

6 . 671,388 - 87,500

9216 - 4775

4.523 - 0.36

76,921 - 6,877

600 - 147

5,432,198 - 1,234,567

59,723 - 6,894

a b


Apply the same rules for adding and subtracting greater integers.You maywish to change the order of some problems for easier computation.

Add and Subtract Greater Integers



17

+ 35

18

35

+ 17

18

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

1 . - 4385 + -5927

2 . 508 - -926

3 . 67,293 + -36,198

4 . 7.6 + -1.9

5 . -2364 - -6374

6 . 1615 - 2739

-23.6 + - 33.27

-5281 + 6572

-485 - 672

-83,436 - 24,754

75 - 6308

1268 + - 3522

a b


Because addition and subtraction are inverse operations, you can use one tocheck the other.

Check Addition and Subtraction



Directions: Write and solve a subtraction problem to checkeach sum, and an addition problem to check each difference.Circle correct answers.

9114 - 2477 = 7637

8675 + 7863 = 16,538

61,300 - 39,282 = 21,018

5768 + 5789 = 11,557

1 . 435 + 627 = 1162

2 . 3379 - 2859 = 620

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

4 . 4663 - 2738 = 1935

74,331 + 25,388 = 100,291

971 - 795 = 166

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

8405 - 2377 = 5028

5 . Adrian once counted 77 steps from the street to his locker.Today he'salready 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.

a b c


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

Solve Word Problems



Addition word problems often involve putting sets of numberstogether or gaining a certain amount. Clue words that may indicateaddition include altogether, total, or in all.

Subtraction word problems often involve comparing sets of numbersor losing a certain amount. Clue words that may indicate subtractioninclude difference, more, or borrow.

Directions: Write the letter of the expression that matches each wordproblem.Then solve.

1 . Most of the year, the town of Sagebrush has a population of 475. During thehot summer, 104 people leave for cooler areas. How many people live therein the summer?

2 . Stony Mountain path goes to where the mountain is 475 feet tall.The last104 feet of the mountain is a sheer rock wall that no one can climb. How tallis the mountain altogether?

3 . Little Canyon is 475 below sea level. If one climbs from the bottom to thefirst overlook, you will have climbed 104 feet. How far below sea level willyou be now?

4 . You can take a whitewater rafting trip starting in Little Canyon.The canyon isat 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?

A 475 + 104 B 475 - 104 C -475 + -104 D -475 + 104

Directions: Write the equation and solve.

5 . One night, the temperature on Stony Mountain got down to -20.Thetemperature rose by 47 degrees the next day. How warm did it get that day?


If you're not sure of an answer, you can always use the inverse operation tocheck yourself.

Solve Word Problems



Directions: Write an equation, then solve. Show your work.Remember to line up the numbers in the equation correctlyand to label your answers.

1 . Luke was learning a new card game. His score the first hand was -243 and thesecond 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 itin 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, sheonly 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 pageshad he read in all?

5 . At the football game, 34,264 people sat on one side of the stadium and33,987 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 footballstadium?

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 checkhis subtraction.


Be careful to watch the signs!

Review Addition and Subtraction



Directions: Add or subtract.

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

1 .

2 .

3 .

a

682

+ 739

b

836

556

c

4597

+ 8384

d

5701

2342

9056

+ 8477

7039

4254

52.3

26.35

846,213

+ 352,749

42,963

35,9564.367

+ 7.88

92,461

+ 356,8783567

2438

a b

4 . 4183 + 2877

5 . 9216 - 6636

8500 - 3423

76,309 + 8,931

c

55,576 - 29,048

6718 + 7894


You have all the information you need to solve them all!

Review Addition and Subtraction



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

1 . 10 - 0.503 =

2 . 68 + 735 =

3 . 6829 - 3144 =

4 . 72,038 + 57,358 =

5 . 852,316 - 39,427 =

4.8 + 5.94 =

941 - 736 =

54,328 + 97,143 =

9633 - 5727 =

845,365 + 2,635,354 =

a b

6 . Dylan bought a new shirt for $29 and new pants for $37. How much did hisnew 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 equationyou can use to check it.

Directions: Write the equation and solve it.

When you multiply any integer by 1, 2, 3, and so on, the product is a multipleof the first number:

Find Multiples

Directions: Fill in the blank with the correct number.




6 x 1 = 6; 6 x 2 = 12; 6 x 3 = 184 x 5 = 20; 4 x 6 = 24; 4 x 7 = 286, 12, and 18 are multiples of 6.20, 24, and 28 are multiples of 4.

1 . 6, 9, and 12 are multiples of .




a b

4, 10, 14, and 18 are multiples of .

28, 35, 42, and 56 are multiples of .

12, 18, and 24 are multiples of both and .

16, 24, and 32 are multiples of , , and .

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

5 . 5 22 16 20

6 . 9 54 19 39

7 . 3 23 31 21

8 . 6 58 42 16

9 . 8 18 42 24

a b

11 21 22 23

4 34 43 64

7 70 27 17

14 34 42 45

19 119 91 114


Numbers that you multiply together to get a product are called the factors ofthat number.



List Factors

Directions: Circle the one or more numbers that are factors of thefirst number.

1 x 12 = 12 12 x 1 = 12 2 x 6 = 12 6 x 2 = 123 x 4 = 12 4 x 3 = 12

1, 2, 3, 4, 6, and 12 are the factors of 12.

1 . 16 32 2 8 6

2 . 20 5 2 10 9

3 . 9 3 4 5 6

4 . 30 5 6 3 10

5 . 5 25 15 5 1

14 1 2 4 7

18 4 8 12 18

48 2 6 8 24

90 6 11 15 45

55 25 20 11 6

a b

Directions: List all the factors of each number.

6 . 8

7 . 15

8 . 16

9 . 19

1 0 . 24

56

22

35

4

28

a b


Name Date

All positive integers greater than 1 are either prime numbers or compositenumbers.

Identify Prime and Composite Numbers

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

Directions: Circle the number in each group that is a prime number.

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.

1 . 6 11 9

2 . 5 8 14

3 . 16 18 19

4 . 29 39 49

5 . 17 170 54

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:

1 0 . 51 Factors:

1 1 . 65 Factors:

1 2 . 77 Factors:

21 12 31

34 43 44

16 13 25

73 15 35

51 72 37

a b

Composite numbers are the products of factors other than 1 and the numberitself.

Identify Prime and Composite Numbers




Directions: Write the factors of each number.Then, if the number isprime, write a P in the blank next to the number. If the number iscomposite, write a C in the blank next to the number.

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.

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:

1 0 . 81 Factors:

1 1 . 105 Factors:

1 2 . 125 Factors:

Directions: Write the first ten prime numbers.

1 3 .

Just as addition and subtraction are inverse operations, so are multiplicationand division. Use one to check the other.

Check Multiplication and Division




Directions: Write an inverse problem to check each equation, thensolve it.

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.

1 . 8 x 14 = 112

2 . 67 x 3 = 204

3 . 34 ÷ 11 = 3

4 . 234 ÷ 9 = 26

5 . 94 ÷ 6 = 16

6 . 4 x 24 = 71

6 x 19 = 106

76 ÷ 4 = 19

9 x 18 = 166

45 ÷ 3 = 15

6 x 71 = 426

144 ÷ 18 = 6

a b

7 . Kaylee scored 5 goals for her lacrosse team in one game. She hoped to dothis in each of her team’s 16 games. If she did, she said that she would reach84 goals and set the team record. Is her multiplication correct? WriteKaylee's equation.Then write a division equation to check it.




You’ll solve problems like this in real life all the time. Remember to regroup asneeded.

Multiply 2 Digits by 1 Digit

24

5

20

10

120

65

9

45

54

585

87

6

42

48

522

1 .

2 .

3 .

4 .

5 .

a

59

6

b

83

3

c

48

9

d

92

3

e

36

5

42

3

14

8

97

5

84

6

58

2

60

2

91

9

62

5

29

9

70

7

37

7

52

8

51

9

17

4

39

9

75

2

73

4

73

4

40

8

56

4

Directions: Multiply.




Multiply numbers in the thousands just as you would other numbers.Remember to regroup as needed.



1 .

2 .

3 .

4 .

5 .

6 .

a

9,021

7

b

6,490

6

c

3,964

6

d

6,423

3

e

4,849

9

5,386

2

4,371

4

5,803

2

5,510

8

9,321

2

2,974

9

5,575

9

9,182

9

9,893

4

8,456

8

3,002

5

9,007

8

7,105

4

7,370

7

7,789

3

8,853

6

7,201

3

4,484

7

2,445

6

5,413

7

7,979

8

2,376

5

7,290

8

5,509

5

6,094

5




Multiply numbers with seven digits (millions) just as you would othernumbers. Remember to regroup as needed.



1 .

2 .

3 .

4 .

5 .

6 .

a

7,348,901

4

b

1,722,300

8

c

9,947,983

2

d

2,556,998

5

2,955,571

7

4,412,939

6

5,736,029

4

4,567,212

8

5,711,904

9

8,809,942

5

8,637,782

6

7,224,228

4

3,600,518

3

3,556,669

7

3,399,574

7

2,434,871

7

9,957,382

2

7,820,625

3

1,145,669

9

5,014,484

6

6,948,226

5

6,822,245

9

6,366,105

3

3,409,970

3




If both factors have a decimal, count the places in both and move thedecimal in the product from the right that amount.

Multiply Decimals

6.92

0.8

5.536

1 .

2 .

3 .

4 .

5 .

a

2.6

5

b

59

0.9

c

4.57

0.3

d

71.19

8

e

715

0.6

8.7

6

8.6

0.3

45.7

0.3

3.37

5

31

0.05

57

0.3

0.38

0.8

4.57

3

0.392

0.6

9.63

0.6

32

0.8

0.44

0.6

45.7

3

45.29

0.4

90.9

0.9

7.3

4.6

4.76

7

457

3

66.5

8

23.7

0.004


Multiply 2 Digits by 2 Digits




To multiply a number by a two-digit number, first multiply by the digit in theones place.Then multiply by the digit in the tens place.

1 .

2 .

3 .

4 .

5 .

a

62

93

b

76

32

c

35

75

d

27

54

88

12

51

27

98

17

52

98

37

33

93

62

44

68

31

41

48

74

71

91

82

45

72

38

29

58

42

56

64

69

70

23

57

23

171

114

1311



Multiplying four-digit numbers is the same as multiplying two-digit numbers.





1 .

2 .

3 .

4 .

5 .

a

4,959

25

b

7,202

16

c

8,498

49

d

5,029

27

9,938

49

5,832

54

1,832

35

3,845

53

1,245

93

3,445

78

4,771

61

9,541

88

8,285

37

2,948

39

2,257

14

5,748

17

6,031

65

9,788

22

6,003

70

7,226

94


Multiplying with seven digits may look complicated—but it’s not.




Multiplying numbers in the millions is the same as multiplyingother numbers. Start by multiplying the ones place.

1 .

2 .

3 .

4 .

5 .

a

5,938,964

72

b

3,471,109

53

c

1,201,905

49

d

4,586,873

52

7,849,338

43

6,048,722

35

7,527,394

23

2,770,638

64

2,255,830

68

9,339,020

88

3,449,723

39

8,311,194

39

4,733,837

26

8,203,478

92

6,299,715

74

9,885,752

83

1,983,674

18

7,374,599

63

5,639,826

13

3,266,686

43



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

Multiply Decimals



Multiplying numbers with decimals is no different than withother numbers. Remember to put the decimal point in thecorrect place.

1 .

2 .

3 .

4 .

5 .

a

37

0.6

b

57

0.32

c

0.638

28

d

5.675

0.81

7.3

9

5.21

8.7

56.6

5.6

3.497

4.9

4.2

37

17.4

6.6

63.03

9

34.97

4.9

8.3

5.6

7.7

7.7

37.92

0.44

349.7

4.9

95.7

8.9

3.82

4.3

3.892

7.6

3,497

4.9



Don't let the numbers overwhelm you—take division one step at a time.

Divide 2 Digits by 1 Digit



Directions: Divide.

1 .

2 .

3 .

4 .

5 .

6 .

a

6 96)

b

3 60)

c

4 68)

d

9 54)

4 76) 4 78) 3 87) 4 84)

9 45) 2 56) 4 92) 3 69)

3 63) 4 96) 2 42) 6 78)

7 84) 6 66) 5 35) 8 96)

8 88) 5 70) 7 63) 6 84)


Practice dividing with some larger numbers.




Directions: Divide.

1 .

2 .

3 .

4 .

5 .

a

4 1, 908)

b

6 3,168)

c

5 9,735)

d

7 4,564)

5 4, 230) 9 6,156) 2 4,822) 6 3, 282)

8 2,936) 8 7,616) 6 2, 580) 8 6,104)

2 4, 428) 7 2,506) 5 8,860) 3 6, 768)

3 5,874) 4 2,564) 8 3,192) 4 2,332)


Is division getting easier for you? If you’ve been doing well, this page will be abreeze!




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 =

1 0 . 7,770,120 ÷ 5 =

1 1 . 6,536,470 ÷ 2 =

1 2 . 8,231,073 ÷ 3 =

1 3 . 6,508,308 ÷ 4 =

1 4 . 2,707,860 ÷ 5 =

1 5 . 4,241,970 ÷ 2 =


Sometimes a number does not divide another evenly.The letter R stands forremainder.

Divide With Remainders



4 133 R 1

1 .

2 .

3 .

4 .

5 .

a

8 42

b

5 326

c

6 2,476

d

8 265

7 87 4 1,380 3 1,557 6 1,284

9 245 7 7,077 2 115 7 349

5 8,304 2 3,471 5 3,297 4 1,618

6 7,738 5 1,050 9 349 3 2,164

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


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

Decimal Quotients



4 13.003.25

)

1 .

2 .

3 .

4 .

5 .

a

4 15

b

7 44

c

6 146

d

8 4,967

5 26 3 20 3 101 6 5,052

7 24 8 32 2 355 3 2,333

9 54 2 19 5 600 4 4,570

6 41 5 63 9 532 7 6,248

Directions: Divide.


To divide by two-digit numbers, use the same steps as dividing by one-digitnumbers.

Divide 2 Digits by 2 Digits



Directions: Divide.

1 .

2 .

3 .

4 .

5 .

a

21 63

b

17 85

c

24 86

d

15 90

12 88 35 95 45 90 23 86

38 76 22 66 14 84 37 71

40 90 11 74 19 95 26 98

13 91 39 99 30 85 18 24


Divide larger numbers using the usual strategy–do one step at a time.

Divide 4 Digits by 2 Digits



Directions: Divide.

1 .

2 .

3 .

4 .

5 .

a

71 4,402

b

57 4,617

c

63 3,848

72 2,808 45 2,020 72 4,680

14 1,442 36 5,112 90 1,269

66 6,470 87 4,528 17 4,307

43 3,526 29 1,824 74 6,808


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

Divide Decimals



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

5 50.5.

5 50.510.1

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

5.12 512 5.12 51200100

)

1 .

2 .

3 .

4 .

a

6 4.2

b

8 22.4

c

6 14.5

d

8 32.8

3 8.7 9 0.58) 0.04 92 0.5 510

0.2 68 0.03 64 0.7 273 0.2 0.0037

0.05 45 0.6 270 5 3.58 9 6.61

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


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

Solve Word Problems



Directions: Solve. Show your work.

1 . Maria worked at a summer camp. Each week she earned $95. If she workedfor 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?

3 . The lifeguard at the camp earned times as much for the summer as

Maria did. How much did she earn for the summer?

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

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

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

112


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

Solve Word Problems




1 . Maria’s friend Andy works in the camp kitchen. He is serving fruit cocktail to96 campers and 16 staff members. If each can of fruit cocktail contains 24servings, how many cans will he need?

2 . Andy is baking sheet cakes for dessert. Each sheet cake can be cut into 18pieces. 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 theflour per pound?

4 . The high diving board at the camp lake is 10 feet high. If 1 foot is .33 of ayard, 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. Howmany 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, andthird place 1 point. One team, the Dolphins, won 2 races.They finishedsecond in 3 races and third in six races. How many total points did theDolphins earn?


Use what you know about multiplication and division.

Review Multiplication and Division




1 .

2 .

3 .

4 .

5 .

6 .

a

126

2

b

45

71

c

0.4 147.4

d

0.64

23

6,203

5

5,331

635 41 0.65 128

4 84 7,942,735

243 90 1.47

3

6 1,068 78

1372 936 5.2 4.65

6 6,785,442 8 7,048 7 7,070 0.15 737.9

8,500,213

913 78 4 3,434 54.81

2.3


Look at how much you've learned!

Review Multiplication and Division




1 . 6,930,952 x 47 =

2 . 8,944,478 ÷ 7 =

3 . 82 x 76 =

4 . 97 ÷ 13 =

a b c d

Directions: Write the first 6 multiples of these numbers.

5 . 4 7 13

Directions: List all the factors of these numbers.

6 . 32 56 96

Directions: Circle the prime numbers in this list.

7 . 11 46 50 29 21 19 2 33 18 5 9 41

a b c

a b c

2,959 ÷ 62 =

67 x 5,919 =

7,553 ÷ 6 =

8 x 4,092 =

3 x 6,093,951 =

49 ÷ 6 =

34 x 8 =

56 ÷ 8 =

4.8 ÷ 0.7 =

7.72 x 4.2 =

73.68 ÷ 1.45 =

91.66 x 0.55 =

To add fractions with like denominators, simply add the numerators.To addmixed numbers, add fractions first, regroup if needed, then add the wholenumbers.

Add Fractions with Like Denominators




1 .

2 .

3 .

4 .

5 .

6 .

7 .

8 .

9 .

1 0 .

1 1 .

1 2 .

Directions: Add. Remember to reduce fractions tosimplest terms.

a b

38+18=

13+13=

710

+710

=34+14=

415+ 6 =

35+45=

716

+ 2916

=39+59=

523+123=1

13+23=

914+14=4

56+156=

37+57=3

15+ 235=

29+59=6

23+ 323=

711+111=6

38+ 378=

29+49=

2 + 214=

519+ 359=

112

+712

=

413+ 413=3

13+ 723=




To add fractions with unlike denominators, convert them to like fractions usingthe least common multiple of the denominators.

Add Fractions with Unlike Denominators

1 .

2 .

3 .

4 .

5 .

6 .

7 .

8 .

9 .

1 0 .

1 1 .

1 2 .

Directions: Add. Remember to reduce fractions tosimplest terms, if needed.

a b

3310

+12=

23+12=

14+ 223=

14+16=

7 + 614=

58+516

=

149+ 215=

23+37=

334+35=

56+49=

213+ 427=

67+16=

312+ 413=

14+23=

35+ 212=

25+47=

15+24=

14+58=

158+14=

79+23=

12+57=

234+ 235=

315+134=1

49+ 312=


To subtract fractions with like denominators, simply subtract the numerators.To subtract mixed numbers, subtract fractions first, borrowing from the wholenumber if needed.Then subtract the whole numbers.



Subtract Fractions with Like Denominators

Directions: Subtract. Remember to reduce fractions tosimplest terms.

a b c

1 .

2 .

3 .

4 .

5 .

6 .

1115

715

=511

111=

3414=

3717=

7858=

4515=

7959=

1313=

7838=

6123

5

12

635

215

213

113

613

123

427

167

558

238

815

345

6

13


Tip

Subtract Fractions with Unlike Denominators



To subtract fractions with unlike denominators, convert to like fractions usingthe least common multiple of the denominators.





a b c

1 .

2 .

3 .

4 .

5 .

6 .

7823=

710

17=

5735=

8914=

5619=

1214=

2312=

1516

23=

4523=

413

212

6

58

312

114

229

157

512

338

345

234

11423

323

135

679

223

35+14=

38+12=


Tip



Here are the rules for adding and subtracting positive and negative fractions.

Add and Subtract Positive and Negative Fractions




The sum of two negative fractions is always negative.

Adding a negative fraction to a positive is like subtracting.It will be positive or negative, depending on which addendis greater.

Subtracting a negative fraction is like adding.

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

34+12=54= 114

56+13=12

1

2

1

5=

7

10

a b

1 .

2 .

3 .

14

45=

5812=

Directions: Add or subtract.

a b

4 .

5 .

6 .

15

23=

5812=

35+38=

c

38

58=

57+12=

310

+45=

58+12=

3518=

34+13=

4517=

23+15=


When you multiply fractions, multiply the numerators and then thedenominators.

Understand Multiplying Fractions



1 .

2 .

3 .

4 .

5 .

6 .

7 .

8 .

9 .

1 0 .

a b

2312=

3423=

310

35=

3549=

1013=

4712=

23910

=1314=

3513=

5814=

7814=

3558=

1856=4

13=

151011

=353 =

1227=

577 =

35710

=323=

c

5823=

4516

=

110

79=

934=

1357=

2545=

1412 =

2334=

3714 =

1212=

A shortcut when multiplying fractions is to cancel outcompatible numbers when they occur.

13

1551

15 6=15

Directions: Multiply. Remember to reduce or express products insimplest form.

5


When multiplying mixed numbers, convert them to improper fractions first.Remember to cancel out compatible numbers when you can.

Multiply Mixed Numbers



1 .

2 .

3 .

4 .

5 .

6 .

7 .

8 .

9 .

1 0 .

a b

4910

23=2

2312=

7452 =

34114=

37925=5

188 =

17212=12

23=

32358=12 2

34=

313335=

78213=

21223=3

1414=

5 334=3

13314=

2 412=6

153 =

12315=3

2334=

c

352110

=

27237=

3 213=

24549=

3 313=

1346 =

313316=

745267=

2710

5 =

6 413=



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

Divide Fractions



1 .

2 .

3 .

4 .

5 .

6 .

7 .

8 .

9 .

1 0 .

a b

15÷310

=12 ÷13=

79÷13=

13÷13=

710

÷12=7 ÷

12=

34÷13=9 ÷ 2 =

14÷14=8 ÷

14=

12÷23=

14÷ 8 =

34÷45=

37÷12=

59÷23=10 ÷

19=

56÷13=

34÷14=

45÷67=

34÷38=

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

12÷14=1241=42=21= 2


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

Divide Mixed Numbers



1 .

2 .

3 .

4 .

5 .

6 .

7 .

8 .

9 .

1 0 .

Directions: Divide.

a b

316÷ 6 =3

12÷ 3 =

815÷15=4 ÷ 2

13=

9 ÷ 413=7

35÷710

=

378÷27=3

2

3÷1

1

10=

334÷ 3 =

47÷117=

16÷ 3716

=18 ÷ 423=

4 ÷ 4112

=414÷12=

335÷ 225=

57÷23=

212÷ 615=1

15÷12=

613÷ 234=6 ÷ 4

13=


Here are the rules for multiplying and dividing positive and negative fractions.

Multiply and Divide Positive and Negative Fractions



When you multiply or divide two positive fractions, the answer isalways positive.

When you multiply or divide two negative fractions, the answer isalways positive.

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

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

a b

1 .

2 .

3 .

13

14=

3514=

9 ÷13=

c

16

14=

13÷25=

16

12=

310

÷ 6 =

23

15=

1423=

Directions: Multiply or divide.

a b

4 .

5 .

6 .

6 ÷23=

710

÷ 4 =

34÷23=

c

19÷23=

845=

13÷13=

56÷23=

38

57=8 ÷

27=


Multiplication word problems often involve putting together sets of equalnumbers. Division word problems often involve splitting up a group into equalparts.

Solve Word Problems



Directions: Solve.

1 . Jessie was studying for a big math test. One day she studied for 2 hours.

For of that time, Jessie studied fractions. How many hours did she work

on fractions?

2 . Jessie told a friend that she spent hours studying. of that time was

spent on math. How many hours did Jessie spend on subjects other

than math?

3 . Jessie decided she needed to study history for hours. If she

divided her history studying over days, how long would she

spend studying history each day?

4 . Jessie’s friend Rex spent hours working on his project for history class.

Jessie spent hours on hers. How many hours did they spend together on

their projects?

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

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

23

813

25

613

412

515

334

134

12

Directions: Write the letter of the equation that matcheseach word problem.Then solve. Remember to label youranswers.


Now for some real-world fraction problems.

Solve Word Problems



11445

13

4÷

4

5

1312÷34

131234

96411

A .

B.

C.

D.

E .

1 . Li and Genna are painting Li’s bedroom.The longest wall is feet long.The

roller they are using is foot wide. How many passes with the roller will

they need to paint the entire wall?

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

the wall they need to paint is 96 square feet, how much of the wall is taken

up by the window?

3 . Li mixed up gallons of wall paint. But the girls used only of what

Li mixed. How much paint was used?

4 . It took the girls hours to paint the entire room. If they finished of

the job on a Saturday, how many hours did they work?

5 . A big brush they used is of a foot wide. How many brush strokes would it

take to make a brush mark 1 feet wide?

13123

4

411

114

45

1312

34

45 34


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

Review Fractions



Directions: Solve.

a b c

1 .

2 .

3 .

4 .

5 .

6 .

7 .

8 .

11545=

1215=

13+13=

4712= 2

3435=

45+35=

27+45=

58÷23=

58+178=

3413=

34÷12=

35+13=

2514= 2

23÷16=

8959=

214÷ 5 =

2358=

3447=

114

+ 513

323

+ 145

415

+ 435

647

267

825

638

4

114


Now you can solve fraction problems in half the time.

Review Fractions



Directions: Solve.

a b c

1 .

2 .

3 .

4 .

5 .

14÷57=

58÷ 5 =

34+14=

34

34= 6 1

23=

13+23=

47+13=

4915=

35+13=

14

16=

7878=

37+13=

2 3310

=710

÷1310

=245158=

Directions:Write the letter of the matching equation, then solve.Remember to label your answers and show all your work.

A . B. C.13÷12=

3423= 1

12÷ 3 =

6 . Li used of a small can of paint. It took of what she used to paint a

stool for her room. How much of the paint did it take to paint the stool?

7 . Genna wants to mix up some wallpaper paste to use for Li’s room. She

only has enough paste mix to make of a bucket, the amount she

wants to make. How much wallpaper paste does she want to make?

8 . Li has quarts of varnish. If she wants to finish 3 end tables for her

room, how much varnish can she use on each table?

23

34

13

12

112

To solve any equation, always perform the operations in the order givenbelow.

Use Order of Operations




3 (4 + 6) + 2 – 3 = ?

operations in parenthesis 3 (10) + 2 – 3 = ?multiplication, then division from left to right 30 + 2 – 3 = ?addition or subtraction from left to right 32 – 3 = 29

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

1 . 2 x 4 + (6 + 1) – 4 =

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

3 . 8 – 4 ÷ 3 – 2 =

4 . 5 + 2 x 5 + 2 =

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

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

7 . 72 ÷ 9 + 6 + 2 + 5 =

64 ÷ (8 + 6 + 1 + 8) =

64 ÷ 8 + (6 + 1 + 8) =

(5 x 30) + 40 =

5 x (30 + 40) =

5 x 30 + 40 =

4 x 15 + 3 x 15 =

4 x (15 + 3) x 15 =

(4 x 15 + 3) x 15 =

4 x 8 – 4 x 3 =

4 x (8 – 4) x 3 =

4 x (8 – 4 x 3) =

(5 + 1) x 3 + 7 =

5 + (1 x 3) + 7 =

5 + 1 x (3 + 7) =

a b c




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

Write Equations

Francis has a radio-controlled (R/C) monster truck that isthe size of a real truck. If the headlights on the actual carare 3 inches tall, how tall are they on the R/C car?

h stands for the height of the headlight

The headlights on the R/C car are

inch tall.

Directions: Solve. Use a variable that makes sense to you.

124

3124

= h

324

= h

18= h1

8

49

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, howlarge is its rudder?

2 . To run his R/C cars and boats, Francis charges his batteries for 30 minutes toget 20 minutes of running time.About how much charging time does it taketo make a minute of running time?

3 . Francis added up the value of the R/C cars and boats he owned. He owned4 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/Cvehicles worth together?

4 . For his birthday Francis's parents gave him $25. His grandmother gave him

$20. Francis used of his birthday money to buy parts for his R/C vehicles.

How much did he spend on parts?


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.



Solve Equations

5x – 1 = 295x –1 + 1 = 29 + 15x = 305x ÷ 5 = 30 ÷ 5x = 6

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

1 . 4n = 24

2 . x – 3 = 4

3 .

4 . 4 + z = 0

5 . 3k = 24

6 . m + 4 = 17

7 . 2x + 2 = 16

8 .

j + j + 3 = 15

5 + n = 18

6f – 2 = 5f

11 = 2t + 3

y ÷ 8 = 9

4 = 9 – k

72 ÷ r = 24

h – 9 = 14

70 ÷ p = 5

3q – q = 12

c2 – 3 = 46

5t – 2t = 21

13 – m = m + 7

2x = x + 3

y

3= 5

n

5+ 2 = 5

f12= 7

12z = 9 z

a b c


Tip

Solve Equations



Here’s more practice in solving equations.




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

1 . x + x – 5 = 27

2 . y – 2 = 9

3 . 3f + 2 = 4f

4 . 4 + z = 1

5 . 3k = 15

6 . 56 ÷ r = 8

7 . 2x – 2 = 16

8 .

4n = 8

5 + n = 11

19 = 2t + 3

y ÷ 4 = 9

14 = 9 + k

m + 4 = 10

h – 9 = 22

75 ÷ p = 15

5q – q = 12

c2 – 3 = 33

7x – 2x = 30

16 – n = n + 10

3x = x + 16

a b c

z12= 8

y

3= 30

n

6+ 2 = 5

12z= z 30


Tip



A function is a special kind of equation with two variables.

Understand Functions




In a function, there is only one value of x for each value of y, and vice versa.

x = y + 3 When x is 4, y can only be 1.x = y – 5 When x is 7, y can only be 2.x = 3y When x is 6, y can only be 2.

When x is 2, y can only be 8.x =y

4

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 .



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 .

1 0 . In the function x = 3y + 2 , if x is 14, then y is .

1 1 . In the function x = y/4 – 2, if y is 12, then x is .

1 2 . In the function x = y/4 – 2, if y is 16, then x is .

1 3 . In the function x = 3y + 1, if x is 7, then y is .

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

1 5 . In the function x = 3y + 1, if y is 4, then y is .


It’s easy to graph a function.

Graph Functions



To graph a function, plot two pairs of points on the x(horizontal) and y (vertical) axis.Then draw a straight linethrough both points. Put an arrowhead at the end of the lineto show that it continues off the graph.

To graph the function x = y + 1, find and plot any two pairs ofvalues of x and y.

x y2 13 24 35 46 5

x = y + 1

Directions: Complete the tables and graph each function.

x y23456

x = y + 2x y01234

x = y -1

1 . a b


Here’s more practice in graphing functions.

Graph Functions




x y246

x = 2yx y123

1 . a b

x y357

x = 2y + 1x y357

x = 2y – 1

2 .

x =y

3


Here’s more practice in graphing functions.

Graph Functions




x y246

x y123

1 . a b

x y368

x y123

x = 2y – 1

2 .

x

3= yx =

y

2

x 1=y

3


A rate is a special kind of function or ratio.

Graph Rates



A rate compares different units. Forexample, a car gets 25 miles to a gallonof 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 yougraph a function.With a rate, however, theaxes are labeled differently.

Directions: Read the description. Label the axes and mark the scale.Then graph each rate.

1 . A 5-pound bag offlour costs 3dollars.


Now try these.

Graph Rates



Directions: Read the description. Label the axes and mark thescale.Then graph each rate.

1 . For each half-hour Martinexercises, he burns 300 calories.

2 . Jerome has two plants. For eachinch his jade plant grows, thesnake plant grows 2 inches.

1 0 0Math Computation Skills and Strategies, Level 7Saddleback Educational Publishing ©2006

Graphs can be used to display inequalities.

Graph Equations and Inequalities



Directions: Match the inequality with its graph.

All points in the shaded area are solutions to the inequality.

x y0 21 32 43 5

x y – 2

1 .

2 .

3 .

4 .

A. x < y + 3

B. y > 2x

C. x < 3y - 2

D. y < 2x + 2



Use what you know about equations to solve these.

Review Equations and Inequalities



1 . x + x – 1 = 15

2 . 2 – -y = 4

3 . 3a + 3 = 4a

4 . 3 + z = 11

5 . 4k = 20

6 . 45 ÷ r = 5

7 . 5x – 3 = 12

8 .

4n = 12

6 + n = 17

15 = 2t + 3

y ÷ 3 = 9

27 = 9 + k

m + 4 = 16

4x = x + 27

h – 8 = 0

60 ÷ p = 15

5q – q = 16

b2 – 22 = 42

7x – 2x = 35

12 – n = n + n

a b c

y

3=15

n

4+ 2 = 6

12z = z 10

z12= 9


Here’s a chance to use what you learned about functions, rates, inequalities,and graphs.

Review Graphing Functions



Directions: Graph each function.

x y

1 .y 1=

x

2x y

2 .

x y + 1

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

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

Use Time Measurements




Directions: Fill in the blank. Show your work.

Directions: Write the equation, then add or subtract.

1 . A quarter of a day is hours.

2 . A quarter hour is minutes.

3 . A half day is hours.

4 . A half hour is minutes.

5 . 4 hours = minutes

6 . 3 days = hours

7 . hours = minutes

8 . 6 days = hours

9 . hours = 325 minutes

hours = minutes

days = 52 hours

166 hours = days

hour = minutes

days = hours

190 min = hours

min = hours

7 days = hours

minutes = 164 hours

a b

1 0 . A group’s hike lasted five hours, forty minutes from start to finish.They restedfor fifteen minutes once and ten minutes another time. How long were theyactually walking?

512

23

314

512

412


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



Convert Temperatures

Directions: Convert the temperature to the nearest degree.

To convert Fahrenheit to Celsius, use this formula:

To convert Celsius to Fahrenheit, use this formula:

Hint:To multiply a number by , you can multiply using the fraction, you

can multiply by the decimal (1.8), or you can multiply by 9 then divide by 5.

1 . 92°F = °C

2 . 21°C = °F

3 . 80°F = °C

4 . –15°C = °F

5 . 4°C = °F

60°F = °C

–2°C = °F

8°F = °C

0°C = °F

92°C = °F

19°F = °C

4°C = °F

–15°F = °C

40°F = °C

–78°C = °F

a b c

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

6 . 100°F 100°C

7 . 32°C 32°F

8 . 12°F 12°C

9 . 6°C 48°F

1 0 . 32°F 0°C

22°C 57°F

–15°F –15°C

25°C 77°F

–100°C –30°F

125°F 45°C

85°C 185°F

212°F 100°C

–95°C -–175°F

0°F –16°C

15°C 60°F

a b c

59

(F 32) = C

95

C + 32 = F

95




In the Customary System, weight is measured in ounces, pounds, and tons.Tofind part of a unit of weight, divide.To find multiples of a unit of weight,multiply.

Use Weight Measurements

Directions: Solve.

oz = ouncelb = poundT = ton

16 oz = 1 lb2000 lbs = 1 T

1 . lb = oz

2 . 32 oz = lb

3 . T = 1000 lb

4 . 5 lb = oz

5 . 52 oz = lb

3 T = lb

lb = T

4.5 lb = oz

2 oz = lb

1 lb = oz

T = lb

oz = 3 lb

T = lb

12 oz = lb

oz = lb

a b c

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

6 . lb 36 oz

7 . 6000 lb T

8 . 6 oz lb

6 T 12,000 lb

8 oz lb

T 800 lb

lb 25 oz

9000 oz T

64 oz 3 lb

a b c

12

212

T

14

514

T

12

12

212

134

212

23

14

34

12

Angles are the measure of turning where two lines meet.

Identify Angles




Directions: Answer the questions.

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.

A . B. C. D.

Two angles whose sum is 90° are called complementary.Two angles whosesum is 180° are called supplementary.

Find Angles




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?

1 0 . What is the measure of angle B?

1 1 . Draw a set of supplementary angles and a set of complementary

angles below and label each.




The U.S. Customary System measures length using inches, feet, yards, andmiles.

Find and Convert Customary Lengths

Directions: Solve.

inch = infoot = ftyard =ydmile = mi

12 in = 1 ft3 ft = 1 yd5280 ft = 1 mi

1 . 1 mi = yd

2 . 36 in = ft

3 . 36 in = yd

4 . ft = in

5 . mi = ft

in = ft

mi = ft

9240 ft = mi

11 ft = yd

ft = mi

20 ft = yd

32 in = ft

5280 ft = yd

2 mi = yd

mi = yd

a b c

23

13

81214

35

12

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

6 . 36 in ft

7 . 9 ft 3 yd

8 . 3 mi 15,000 ft

9 . yd 5 ft

1 0 . 75 in 2 yd

20 yd 20 ft

mi 13,000 ft

21 in ft

16 in yd

27 in ft

mi 7000 ft

10 yd 30 ft

2200 yd mi

6 mi 30,000 ft

9 in ft

a b c

312

112

212

113

213

34

_134

112

13




In many places, people measure length with the Metric System instead of theCustomary System.A centimeter is shorter than an inch and a kilometer isshorter than a mile.A meter is a little longer than a yard.

Find and Convert Metric Lengths

1 . a pencil

2 . a woman

3 . a mouse

4 . a car trip

a paper clip

a flagpole

the distance to the moon

a basketball player

centimeter = cmmeter = mkilometer = km

100 cm = 1 m1000 m = 1 km

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

a b

Directions: Solve.

5 . 10 cm = m

6 . 10 m = cm

7 . 10 m = km

8 . km = m

9 . m= cm

cm = 2 m

3000 m = km

500 m = km

80 cm = m

km = 15,000 m

7 m = cm

km = m

km = m

50 cm = km

km = cm

a b c

34

1212

113

45


1 0 . 1 m 100 cm 10 cm 1 m m 500 cm

a b c

12

12




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

Convert Customary to Metric

1 in = 2.54 cm1 ft = 0.3048 m1 yd = 0.9144 m1 mi = 1609 m

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

1 . 4 in = cm

2 . 6 ft = m

3 . 10 in = cm

4 . mi = m

200 yd = km

48 in = m

7 ft = m

18 mi = km

18 in = cm

20 in = m

ft = m

mi = km

a b c

12

212


5 . 40 in 40 cm

6 . 30 in 3 m

7 . 3 mi 3000 m

8 . 2 yd 2 m

9 . 1 mi 2 km

1 m 40 in

804 m mi

6 cm 2 in

3 m = 90 in

70 cm 7 in

8 m 8 ft

4 yd 4 m

10 km 5 mi

15 in 15 cm

10 m 11 yd

a b c

13

13

12


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

Convert Metric to Customary



1 cm = 0.3937 in1 m = 39.37 in1 km = 0.621 mi

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

1 . 4 cm = in

2 . 2 km = mi

3 . 50 cm = ft

4 . km = mi

1200 m = ft

12 cm = in

2 m = in

100 km = mi

4000 m = mi

m = in

200 m = yd

1 km = yd

a b c

34


5 . 22 km 18 mi

6 . 2 m 6 ft

7 . 1 km 3270 ft

8 . 621 m 1 mi

9 . 2 m 72 in

1 km 621 ft

39 m 3937 in

6 m 3 yd

1 cm 2.54 in

1609 m 1 mi

m in

km 5280 ft

161 km 100 mi

50 cm yd

50 cm 17 in

a b c

110

39

1012

12

12

y


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

Solve Word Problems



Directions: Write the equation, then solve. Remember to labelyour answers and show all your work.

1 . The movie Shauna is watching is 130 minutes long. How many hours andminutes is that?

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

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

4 . Shauna helped Darcie heat a pot of water until it boiled. On the Fahrenheitscale, 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-one-fourth foot long. Her friend's is fourteen inches long.Whose is longer?

7 . Shauna bought pounds of apples at the store. How many ounces is that?

8 . One bag of grapes was pounds, another was 20 ounces.Which bagwas heavier?

113

134


Sarah wrote her pen pal Mia in Sweden.When Mia replied, Sarah had toconvert the measurements to understand how they compared.

Solve Word Problems



Directions: Read the letters.Then answer the questionsby converting the measurements in the letters.

Hi Mia,

We're fine here in Ohio.Today it was 89°F at 9:00 in the morning.Yow! I had to walk mileto 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 havegourds in Sweden?

I think about what you are doing when I am writing.You’re six hours ahead of us. So, when I’meating 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 andcold does it get where you live?

The lake where we swim is two km away. Sometimes I walk there, and sometimes my motherdrops 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 havevegetables 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 inSweden 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)?

113


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

Review Measurement



Directions: Use what you have learned to answer thequestions.

1 . hours = minutes

2 . days = 78 hours

3 . 144 hours = days

4 . hour = minutes

5 . hours = minutes

6 . days = 156 hours

7 . 120 hours = days

8 . hour = days

65°F = °C

28°C = °F

82°F = °C

–36°C = °F

115°F = °C

37°C = °F

380°F = °C

–2°C = °F

6 T = lb

lb = T

2.2 lb = oz

4 oz = lb

lb = oz

T = lb

oz = 4 lb

T = lb

a b c

34

313

225

712

34

3110

23

1514

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

1 . in = ft

2 . mi = ft

3 . 13,200 ft = mi

4 . 14 ft = yd

5 . ft = mi

6 . 40 ft = yd

7 . 28 in = ft

8 . 10560 ft = yd

9 . 2 in = ft

1 0 . yd = in

cm = 3 m

5000 m = km

km = 750 m

75 cm = m

km = 11,000 m

7 1/2 m= cm

m = km

km = m

500 cm = km

cm = km

800 m = ft

mi = 100 km

22 mi = km

21 in = cm

m = 21 in

1 1/2 m = in

m = ft

mi = km

in = 16 cm

36 m = ft


Did you know you’ve learned so much?

Review Measurement



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

a b c

25

34

18

58

123

14

23

1112

15

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

Find Perimeters




4 + 6 + 6 + 2 = 18 ft

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

1 .

4 x 4 in 5 + 5 + 3 ft

2 .

6 + 6 + 6 + 6 + 6 m8 + 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 andbottom are 4, sides are 3

a b




The PythagoreanTheorem helps you find the lengths of the sides of a righttriangle.

Use the Pythagorean Theorem

a2 + b2 = c2

32 + 42 = 52

9 + 16 = 25

Directions: Find the length of the unlabeled side.

1 .

2 .

3 .

a b

x10 in

9 in15 in

8 in

x

15 in


Circumference is the distance around a circle.



Find Circumferences

Directions: Find the circumference.

Pi ( ) is often used when measuring circles. Use the number 3.14 for .

To find circumference use the formula: C = d

a b

1 .

2 .

3 .

4 .

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

If the four-sided figure has all right angles, simply multiply the lengthtimes 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.

1 1 9Math Computation Skills and Strategies, Level 7Saddleback Publishing, Inc. ©2006

Tip

Find Area of Parallelograms



Area is the space inside a figure.




1 .

Perimeter: Area: Perimeter: Area:

2 .

Perimeter: Area: Perimeter: Area:

a b

1 2 0Math Computation Skills and Strategies, Level 7Saddleback Publishing, Inc. ©2006

Tip



To find the area of any triangle, multiply length by height and then divide inhalf.

Find Area of Triangles




Directions: Find the area for each triangle.

a b

1 .

2 .

3 .

4 .


To find the area of a circle, use the formula: A = r2

Find Area of Circles



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

The radius (r) is a line from any point on a circle to its center.

The radius is half the length of its diameter.

a b

1 .

2 .

3 .

4 .


Wondering how to find the area of irregular figures?

Find Area of Irregular Figures



Directions: Find the area.

1 .

2 .

3 .

To find the area of an irregular figure, divide it up into regular figures, such assquares, triangles, rectangles, parallelograms, and circles.Then find the areas ofthe regular figures and add them together.

For this figure, find the area of part A,a square with sides 2 in.Then find thearea 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

a b


Surface area is all the outside area of a three-dimensional figure.Tofind surface area, find the area of each face, then add to get the total.Remember that some faces may be hidden from view!

Find Surface Area



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:


Volume is how much space is inside a three-dimensional figure. Find volumeby multiplying the area of the base times height.

Find Volumes



Directions: Find the volume for each figure.

1 .

Volume: Volume:

2 .

Volume: Volume:

3 .

Volume: Volume:

a b


Real people use real geometry.

Solve Word Problems



Directions: Solve the word problems.

1 . Robert is wrapping a gift. Find the circumference to find the length of ribbonhe should use to wrap around the gift, find the surface area to find how muchwrapping paper he needs, and find the volume to find the amount ofStyrofoam peanuts he needs for inside the gift. (Hint: to find the area of thelong part of the cylinder, use the circumference of the circle as two sides andthe 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 dimensionsfrom the perimeter given. Find the surface area to know how much paintthey'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 convertthe feet to inches, then back again when working with volume and surfacearea.)

Height: 2 in

Perimeter: 44 ft Missing side length:

Area to be painted: Amount of concrete:


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

Solve Word Problems



Directions: Solve the word problems.

1 . Drake and his friends are building a skateboard ramp. It will look like thedrawing below and be made of plywood. Plywood comes in sheets that arefour feet by eight feet. How many sheets of plywood will they need to buy tomake sure they have enough to build the ramp? (Hint:The ramp has nobottom.)

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

5 ft

5 ft

3 ft

4 ft


You may have to work backwards to find an answer.

Review Geometry



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:


Here are some more review problems.

Review Geometry



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 .

When most people think of an average, they think of a mean.To find themean, add to find the total, then divide by the number of addends.

Find Averages




Directions: Find the average for each set of numbers. Showall 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 scaleof 1 to 10, 10 being the best. Find the average score of the reviewers.

7, 7, 9, 5, 3, 6, 7, 9, 10, 6

1 0 . Marlie kept track of her math quiz scores for four weeks. Help her find heraverage for that time.

86%, 90 %, 79%, 82%, 88%, 86%, 91%, 91%, 96%, 89%


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



Figure Probability

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 gettinga 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 pullingout another one?

1 0 . What is the probability for pulling out a green button, keeping it out and pullingout a blue one?

1 1 . What is the probability for pulling out a blue button, putting it back and pullingout a red button again?

1 2 . What is the probability for pulling out three blue buttons in a row, keeping eachof them out?

16

outcome of a 1possible outcomes




Odds compare the possibility of an event happening to the event nothappening. Just as in fractions, you can simplify odds.The odds againstspinning an even number on this spinner are 2 to 2 or 1 to 1.

Understand Odds

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 ora 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?

1 0 . What are the odds against pulling out a green button?

1 1 . What are the odds for pulling out a red button, keeping it, then pulling anotherred button?

1 2 . What are the odds against pulling out a red button, putting it back, and pulling ared button?

Directions: Write the odds for each situation. Simplify, if needed.

number of number ofways to ways to spinspin a 3 anything else

1 to 31 : 3

Odds of spinning a 3

You found the mean earlier. Here’s how to find two other types of averages.

Identify Mean, Median, and Mode




The median is the “middle value” of a set of numbers. Half the numbersare 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 thenumbers 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 familieshad 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 thecost from several builders:

$22,500 $20,100 $18,000$20,100 $17,800 $22,100$19,999 $21,850 $24, 575

Mean: Median: Mode:

You know how to solve these now.

Solve Word Problems




Directions: Solve. Use the space below the problems to workout the answers.

1 . Jason made a spinner for his little sister’s board game. It is a circle dividedinto eight equal parts. Four of them are red, four are yellow.What is theprobability 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 adrawer, what are the odds that you would pull out a blue shirt withoutlooking?

3 . Imagine you pulled a blue shirt out of your drawer. Now what is theprobability 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 beingpaired with a Sarah for a partner project are 1 to 6. How many kids are inyour math class?

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


Now try these.

Solve Word Problems



Directions: Solve. Use the space below the problems to workout the answers.

1 . Five friends decided to pool all the money they had in their pockets to buysome pizza. Here’s what they pooled: $2.35, $1.70, $.90, $1.25, and $1.55. Findthe 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 themean?

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

4 . Donnell hopes to get a 90, or B+, quiz average for this grading period inmath. 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 witha 90 mean average?

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


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

Review Probability



Directions: Look at the spinner and write the odds for eachsituation. 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?


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

Review 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 evennumber?



Scope and Sequence

Students

I NI I NI I NI2. NI I NI I NI NI3. I I NI I NI I4. I NI I NI I I5. NI I I NI I I

An integer can be a positive wholenumber, its opposite, or zero.

PAGE 71. -12 -25 52. -4 -4 -153. 21 6 204. -2 -5 -1005. -320 300 290 -510 356. 320 -1300 -1 60 -7707. -50 36 -153 -884 -42

PAGE 81. 9 57 2.32. 17 -57 5,7053. 378 4.5 3 1/34. 1/5 -4,927 -4895. 94 -1 146. 2 -9 67. -8 9 -78. 1 9 69. = < <

10. > > >

PAGE 91. B (3,6) F (8,7)

C (2,4) G (8,4)D (4,3) H (9,0)E (6,6)

2.

PAGE 101. 2.5 11 4 1692. 225 144 49 253. 15 9 8 2254. 6 36 625 95. 81 2 256 2,5006. 10 196 14 307. 20 7 100 168. 121 4 50 169. 900 5 400 17

10. 625 1 1,600 18



Answer Key

PAGE 111. 1 or one

100,000 or one hundred thousand2. 10 or ten 1,000,000 or one million3. 100 or one hundred

10,000,000 or ten million4. 1,000 or one thousand

100,000,000 or one hundred million5. 10,000 or ten thousand

1,000,000,000 or one billion6. 102 106

7. 101 + 100 108

8. 104 + 103 107

9. 102 + 101 109

10. 105 + 104 105

PAGE 121. 64 626 2162. 64 8 13. 27 2,401 4,0964. 6 1,024 6,5615. 81 0 7296. 9 1,2967. 1,024 818. 77 59,0499. 64 1,000

10. 125 1

PAGE 131. =2. = =3. = = =4.

Answers for items 5-11 may vary. Sampleanswers are listed.

5. 14/16 2/12 22/246. 1/2 2/8 6/107. 2/6 1/2 1/38. 9/12 4/14 1/29. 6/20 14/18 8/10

10. 4/8 10/16 1/211. 4/6 25/30 5/6

PAGE 141. 0.5 0.75 0.252. 0.33 0.95 1/23. 3/4 1/10 3/54. 2/5 0.5 0.45. 0.20 1/4 9/106. 1/8 0.6 0.017. 9/100 4/5 9/108. 0.59 2/3 3/1,0009. < > >

10. > = =11. = < =

PAGE 151. 1.4 2.42. 0.125 3.63. 0.142857

0.054. 2.8 3.35. 0.11 0.46. 2.2 0.9167. 0.833 2.68. 1.7 0.18

PAGE 161. 55 7. > < <2. 480 8. < < >3. -60 9. > < <4. -298 10. < > >5. < < < 11. > > >6. < > > 12. < < <

PAGE 171. -51 52 3572. -76 68 753. -8 0.8 84. 3,157 3,298 3,300 3,5365. 0.236 0.326 0.6336. -51 -5.1 -5 5 5.1 517. 40,569 40,579 41,5598. 0.001 0.01 0.1 19. 0.7 0.07 -7

10. 5,320 5,302 5,23011. 60 -58 -5912. 2.5 2.45 2.4

PAGE 181. 10 902. 40 1003. 50 1204. 0 3 725. 3 1 596. 4 10 4177. 740 700 10008. 1,150 1,200 1,0009. 2,610 2,600 3,000

10. 4,380 4.400 4,000

PAGE 191. 110, 108 60, 582. 130, 131 580, 5833. 490, 488 1,810, 1,8054. 1,140, 1135 6,090, 6,0885. 7,220, 7,215 140, 1426. 140, 139 690, 692

•M

•T•R

•V•S •N

•O

•P



PAGE 201. 48 88 7. 25% 100%2. 45 112.5 8. 60% 1%3. 27 12 9. 11% 150%4. 140 17.5 10. 6.66% 50%5. 1,000 3 11. 10% 200%6. 13 12 12. 25% 1%

PAGE 211. 29% 17% 7. 75% 67%2. 44% 125% 8. 133% 75%3. 83% 33% 9. 88% 93%4. 3% 33% 10. 15% 8%5. 166% 92% 11. 80%6. 50% 89% 12. 56%

PAGE 221. 0.85 2.00 150%2. 47% 34% 0.13. 72% 0.98 0.44. 0.29 100% 0.1%5. 0.5 0.15 80%6. 90% 56% 0.827. 6% 0.99 1.328. 0.03 83.5% 250%9. > = < 11. = > >

10. > < = 12. < < <

PAGE 231. 50% 87.5 0.01 5. > < <2. 2/5 3/10 0.05 6. > < =3. 61% 90% 99/100 7. = = =4. 56% 1.10% 25% 8. > < <

PAGE 241. 4 to 11 7. 4/82. 7:4 8. 8 to 343. 7/5 9. 5:154. 11 to 7 10. 8/395. 7:39 11. 20 to 396. 8 to 8 12. 20:19

PAGE 251. 12 11 27 4. 20 28 52. 18 6 20 5. 25 13 1003. 27 4 2 6. 3 95 15

PAGE 261. I R 5. I R2. R R 6. R R3. R R 7. R I4. I R 8. I R

PAGE 271. 49, 72 3. 1002. 1/2 4. 80

PAGE 281. 7 x 72. 8 x 83. 8/10 = 4/5, 6/10 = 3/54. 25%

PAGE 291. -26˚2. 0.1237 0.1273 0.1327 0.13723. 12/16 6/8 3/44. Rational. It is nonrepeating.

PAGE 301. IN R IR IR2. IN IR IN IN3. R IN R IR4. 11 1.15. 1,296 206. 30 100,000,0007. 512 28 -7 219. 100 9

10. 2.09 in., 2.9 in., 3.24 in.,3.42 in., 3.5 in., 3.6 in.

PAGE 311. = < = 5. < = <2. < < > 6. < < =3. > < < 7. = = >4. = < < 8. > < =9. A(1,5) D(6,6)

B(2,9) E(7,10)C(2,2)

PAGE 321. C C 5. A A2. I I 6. I I3. A A 7. C C4. C C

Answers for items 8-10 may vary.Sample answers are listed.

8. 100 + 0 = 0 + 100 5 + 0 = 0 + 59. 1 + 2 = 3 2 + 1 = 3

10. 5 + (7 + 3) = 15 7 + (5 + 3) = 15

PAGE 331. 59 139 152 98 1402. 59 87 63 89 963. 118 132 105 82 1014. 138 100 89 86 1005. 93 110 177 81 65

PAGE 341. 998 350 1,025 1,466 1,2652. 1,430 1,366 5,782 3,789 2,999

3. 6,908 7,424 15,405 11,779 5,6684. 8,818 9,908 6,350 8,020 15,1035. 841 4,300 6. 10,345 7,100

PAGE 351. 11,796 54,757 87,999 59,2812. 59,998 81,561 63,214 117,7893. 493,870 324,611 499,973 981,1014. 975,125 1,201,974

3,450,938 9,756,0285. 140,031 755,3246. 1,594,405 458,795

PAGE 361. 11.7 8.5 13.4 16.4 9.22. 8.57 4.58 11.75 8.43 21.593. 0.619 1.892 0.880 2.783 3.0554. 44.06 8.73 23.23 4.95 10.005. 6.1 15.36. 14.01 4.014

PAGE 371 . 5 2 0 3 , 9 9 3 1 6 . 5 4 7 8 1 4 4 12 . 1 , 6 0 6 1 7 9 . 4 3 , 8 4 0 1 3 9 . 5 5 7 6 . 0 03 . 1 3 , 6 3 2 1 0 , 9 8 0 9 1 0 9 2 1 , 1 2 94 . 3 3 , 9 5 7 1 0 6 , 2 1 2 1 , 3 1 7 , 4 3 9 4 , 0 0 5 , 9 5 85 . 1 4 0 , 3 6 5 3 6 8 , 6 7 7 3 4 6 , 2 6 6 4 , 1 1 5 , 3 7 5

PAGE 381. 105 366,4312. 7,269 10.6173. 6.2 85,3184. 9,109 1,7545. 88,759 283,4356. 120.6 7,419,342

PAGE 391. 51 5 21 23 122. 63 11 9 34 293. 18 30 39 28 274. 13 48 47 49 325. 40 11 6 27 596. 59 13 8 29 27

PAGE 401 . 2 0 5 2 0 1 2 1 7 2 6 8 3 1 62 . 4 0 7 7 3 1 6 8 4 , 1 0 2 6 , 2 2 43 . 2 , 8 6 4 1 , 5 1 8 2 , 0 1 5 5 , 7 7 9 7 , 3 3 44 . 9 2 , 2 1 1 4 , 2 6 5 1 , 8 6 9 2 , 6 0 35 . 8 6 9 26 . 3 , 2 1 9 8 , 5 5 0

PAGE 411. 1,110 14,521 23,223 3,1152. 20,318 76,704 31,181 223,1333. 217,115 348,711 151,091 260,9834. 1,113,120 3,698,293

2,895,8878 459,0385. 38,082 868,6156. 104.084 2,176,270

•A

•C

•B

•J

•I

•D

•H

•F

•E

•G



Answer Key

PAGE 421. 4.4 4.1 1.91 3.543 4.9522. 1.37 9.1 3.85 7.5 7.563. 0.999 3.47 2.803 2 14.854. 5.728 1.25 442 8.01 1.395. 1.6 2.836. 2.75 1.792

PAGE 431. 23 118 247 489 552. 82 1,874 5,843 6,807 233. 1,867 2,459 3,895 6,882 9044. 27,704 549,092 913,936 362,6305. 2,086 199,004 899,856 2,238,036

PAGE 441. 52 4,441 4. 3,091 4532. 7,157 4.163 5. 322 4,197,6313. 1.25 70,044 6. 583,888 52,829

PAGE 451. -10312 -56.87 4. 5.7 108,1902. 1,434 1,291 5. 4,010 -6,2333. 31,095 -1157 6. -1,124 -2,254

PAGE 461. 1,062 6,637 99,7192. 520 correct 1763. correct 22,018 1,183,6474. 1,925 correct 6,0285. No, he has 48 to go.

PAGE 471. B 371 3. D 371 5. 27˚2. A 579 feet 4. C 579

PAGE 481. 1252. 0.09 seconds3. 75 pages4. 211 pages5. 68,251 people6. 277 people7. No, there are 7,552 more people

where he lives.

PAGE 491. 1,421 280 12,981 3,3592. 17,533 2,765 25.95 1,198,9623. 7,007 12.247 449,339 1,1294. 7,060 5,077 26,5285. 2,580 85,240 14,612

PAGE 501. 9.494 10.742. 803 2053. 3,685 151,4714. 129,396 3,9065. 812,889 3,480,7196. $66 7. $62 8. $77

PAGE 511. 3 22. 7 73. 5 3 and 64. 9 2,4, and 85. 20 226. 54 647. 21 708. 42 429. 24 114

PAGE 521. 2, 8 1,2,72. 5,2,10 183. 3 2,6,8,244. 5,6,3,10 6,15,455. 5,1 116. 1,2,4,8 1,2,4,7,8,14,28,567. 1,3,5,15 1,2,11,228. 1,2,4,8,16 1,5,7,359. 1,19 1,2,4

10. 1,2,3,4,6,8,12,24 1,2,4,7,14,28

PAGE 531. 11 31 7. 1,2,19,382. 5 43 8. 1,2,3,6,7,14,21,423. 19 13 9. (prime) 1,194. 29 73 10. 1,3,175. 17 37 11. 1,5,13,656. (prime) 1,47 12. 1,7,11,77

PAGE 541. C 1,2,3,6,9,182. C 1,3,9,273. C 1,3,7,9,21,634. P 1,415. C 1,7,496. C 1,2,5,6,10,14,35,707. P 1,978. P 1,299. C 1,2,29,58

10. C 1,3,9,8111. C 1,3,5,7,15,21,35,10512. C 1,5,25,12513. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

PAGE 551. correct 1142. 201 correct3. 33 1624. correct correct5. 96 correct6. 9.6 87. 80

PAGE 561. 354 249 432 276 1802. 126 112 485 504 1163. 120 819 310 261 4904. 259 416 459 68 3515. 140 292 511 320 224

PAGE 571 . 63,147 38,940 23,784 19,269 43,6612 . 10,772 17,484 11,626 44,080 18,6423 . 18,766 50,175 82,638 39,572 67,6484 . 15,010 72,056 28,420 51,590 23,3675 . 53,118 21,603 31,388 12,670 37,8916 . 63,832 10,880 58,320 27,545 30,450

PAGE 581. 29,395,604 13,378,400

19,895,966 12,784,9902. 20,688,997 26,477,634

22,944,116 36,537,6963. 51,407,136 44,049,710

51,826,692 28,896,9124. 10,801,554 24,896,683

23,797,018 17,044,0975. 19,914,764 23,461,875

10,311,021 30,086,9046. 34,741,130 21,400,205

19,098,315 10,229,910

PAGE 591. 13 53.1 1.371 569.52 4292. 52.2 2.58 13.71 16.85 1.553. 17.1 .304 13.71 .2352 5.7784. 25.6 .264 137.1 18.116 81.815. 33.58 33.32 1.371 532 .0948

PAGE 601. 5,766 2,432 2,625 1,4582. 1,056 1,377 1,666 5,0963. 1,221 5,766 2,292 1,2714. 3,552 6,461 3,690 2,7365. 1,682 2,352 4,416 1,610

PAGE 611. 123,975 115,232 416,102 135,7832. 486,962 314,928 64,120 203,7853. 115,785 268,710 291,031 839,6084. 306,545 114,972 31,598 97,7165. 392,015 215,336 420,210 679,244

PAGE 621. 427,605,408 183,968,777

58,893,345 238,517,3962. 337,521,534 211,705,270

173,130,062 177,320,8323. 153,396,440 821,833,760

134,539,197 324,136,5664. 123,079,762 754,719,976

466,178,910 820,517,4165. 35,706,132 464,599,737

73,317,738 140,467,498

PAGE 631. 22.2 18.24 17.864 4.596752. 65.7 45.327 316.96 17.13533. 155.4 114.84 567.27 171.3534. 46.48 59.29 16.6848 1713.535. 851.73 16.426 29.5792 17,135.3



PAGE 641. 16 20 17 62. 19 19.5 29 213. 5 28 23 234. 21 24 21 135. 12 11 7 126. 11 14 9 14

PAGE 651. 477 528 1,947 6522. 846 684 2,411 5473. 367 952 430 7634. 1,107 358 1,772 2,2565. 1,958 641 399 583

PAGE 661. 2,168,093 9. 350,0302. 577,558 10. 154,0243. 1,332,600 11. 3,268,2354. 3,251,105 12. 2,743,6915. 472,368 13. 1,627,0776. 1,627,003 14. 541,5727. 1,873,979 15. 2,120,9858. 919,620

PAGE 671. 5 R2 65 R1 412 R4 33 R12. 12 R3 345 519 7,7043. 27 R2 1,011 57 R1 49 R64. 1,660 R4 1,735 R1 659 R2 404 R25. 1,289 R4 210 38 R7 721 R1

PAGE 681. 3.75 6.29 24.33 620.8752. 5.2 6.667 33.667 8423. 3.43 4 177.5 777.6674. 6 9.5 120 1,142.55. 6.83 12.6 59.11 892.57

PAGE 691. 3 5 3.58 62. 7.33 2.714 2 3.743. 2 3 6 1.924. 2.25 6.72 5 3.775. 7 2.54 2.838 1.33

PAGE 701. 62 81 61.082. 39 44.88 653. 103 142 14.14. 98.03 52.05 253.355. 82 62.90 92

PAGE 711. 0.7 2.8 2.42 4.12. 2.9 0.064 2,300 1,0203. 340 2,133.33 390 0.01854. 900 450 0.716 0.734

PAGE 721. $855 4. $3.322. $2.38 5. 12 campers per cabin3. $1,282.50 6. 6 tents

PAGE 731. 5 4. 3.39 yards2. No, there will be 5. 6 teams

4 too few. 6. 8 teams3. 2.5 yards 7. 27 points

PAGE 741 . 252 3,195 368.5 1 4 . 7 22 . 31,015 3 3 5 , 8 5 3 8 . 2 1 9 6 . 93 . 21 190,625,640 30 4 . 4 14 . 178 1,014 13 0 . 8 95 . 1 , 1 3 0 , 9 0 7 881 1,010 4 , 9 1 9 . 3 36 . 76,501,917 6 858.5 1 2 6 . 0 6 3

PAGE 751. 325,754,744 47.73

18,281,853 6.862. 1,277,782.57 396,573

8.1667 32.4243. 6,232 45,318

272 50.814. 7.46 32,736

7 50.4135. 4,8,12,16,20,24 7,14,21,28,35,42

13,26,39,52,65,786. 1,2,4,8,16,32 1,2,4,7,8,14,28,56

1,2,3,4,6,8,12,16,24,32,48,967. 11,29,19,2,5,41

PAGE 761. 2/3 1/2 7. 5 4/5 1 1/72. 1 1 2/5 8. 10 1/3 7/93. 1 2/5 10 1/5 9. 10 1/4 8/114. 8/9 3 10. 8 2/3 2/35. 2 7 1/3 11. 2/3 4 1/46. 5 5/6 9 1/2 12. 11 8 2/3

PAGE 771 . 1 1/6 3 4/5 7 . 1 1 / 1 2 7 5/62 . 5 / 1 2 2 11/12 8 . 3 4 / 3 5 3 1/103 . 1 5 / 1 6 13 1/4 9 . 7 / 8 7 / 1 04 . 1 2/21 3 29/45 1 0 . 1 3/14 1 7/85 . 1 5/18 4 1/2 1 1 . 5 7/20 1 4/96 . 1 1/42 6 13/21 1 2 . 4 17/18 4 19/20

PAGE 781. 1/2 4/15 4/112. 3/5 2/7 1/43. 1/2 2/9 04. 4 2/5 3 1/2 4 1/25. 2 3/7 1 4 2/36. 5 2/3 3 2/8 4 2/5

PAGE 791. 4/35 5/24 39/702. 1/4 23/36 13/183. 2/15 1/6 13/484. 2 1/4 1 5/11 5 3/85. 1 3/5 32/63 2 1/46. 4 1/9 7/12 2 1/15

PAGE 801. P P2. N N3. N P4. 1/8 13/15 1/45. -1 1/8 -39/40 3/146. -5/12 19/40 -1 1/10

PAGE 811. 1/2 1/3 5/122. 4/15 9/50 1 1/43. 2/7 3 1/3 7/904. 1/12 3/5 6 3/45. 5/32 1/5 5/216. 3/8 7/32 8/257. 1 1/3 15 38. 1 4/5 2/11 1/29. 5 1/7 6

10. 2 21/50 1/4

PAGE 821. 1 1/3 3 4/15 1 13/502. 15/16 15 3/5 34/493. 41 1 23/45 74. 8 5/14 1 11/455. 33 2 7/24 106. 2 1/24 12 10 1/27. 13/16 1 2/3 10 5/98. 10 5/6 18 3/4 22 2/79. 18 3/5 9 13 1/2

10. 4 1/8 1/3 26

PAGE 831. 36 2/32. 1 2 1/33. 14 1 2/54. 4 1/2 2 1/45. 32 16. 1/32 3/47. 6/7 15/168. 90 5/69. 3 2 1/2

10. 2 14/15

PAGE 841. 1 1/6 19/362. 1 5/7 413. 10 6/9 2 1/134. 3 1/3 13 9/165. 1/2 1 1/46. 3 6/7 8/1657. 8 1/2 48/498. 1 1/14 1 1/29. 2 2/5 25/62

10. 1 5/13 2 10/33

PAGE 851. N P P 4. -7/40 -9 1/62. N N P 5. 1 1/4 -1 1/8 103. N P P 6. -28 -15/56 -1



Answer Key

PAGE 861. 1 2/3 hours 4. 8:572. 5 hours 5. 1 9/203. 1 11/27 6. 8 3/4

PAGE 871. C 182. D 34 10/113. A 1 gallon4. E 10 1/85. B 2 3/16

PAGE 881. 2/3 2/5 1/102. 1 2/5 1/14 1 13/203. 2 1/2 1 3/35 15/164. 14/15 5/12 1 1/25. 1/3 1/10 166. 3/7 9/20 5/127. 8 4/5 6 7/12 5 7/158. 2 3/4 3 5/7 2 1/40

PAGE 891. -1/2 7/20 -1/82. -1/3 -9/16 -103. 5/12 -5/21 4/154. -16/21 -29/45 49/645. 3 7/40 -1 3/10 -91/1006. B 1/27. A 2/38. C 1/2

PAGE 901. 11 2.78 9452. 28 23 203. 4.667 190 484. 17 350 -165. 36 190 256. 27 105 157. 21 1,080 50

PAGE 911. 52 inches 3. $3602. 1.5 minutes 4. $20

PAGE 921. 6 6 23 5. 8 72 72. 7 13 14 6. 13 5 73. 15 2 14 7. 7 6 34. 4 4 6 8. 15 3 3

PAGE 931. 11 2 31 5. 5 36 62. 11 6 5 6. 7 5 63. 2 90 16 7. 7 60 34. -3 8 2 8. 18 14 8

PAGE 941. 1 6. 32 11. 12. 10 7. 48 12. 23. 2 8. 3 13. 24. 3 9. 3 14. 15. 2 10. 4 15. 13

PAGE 951. 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)


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

(1,3) (2,6) (3,9)2. a. Plot these points:


(3,2) (5,3) (7,4)



(3,1) (6,2) (9,3)2. a. Plot these points:


(0,1) (3,2) (5,3)

PAGE 981.

PAGE 991.

2.

PAGE 1001. D 2. B 3. A 4. C

PAGE 1011. 8 3 9 5. 5 36 42. 2 11 8 6. 9 18 83. 3 45 4 7. 3 20 74. 8 6 18 8. 16 12 4

PAGE 1021. x: 2,4,6,8,10 y: 2,3,4,5,6

2. x: 1,2,3,4,5 y: 0,1,2,3,4

3.

3

6

9

12

15

18

21

24

27

5 10 15 20 25 30 35 40 45

pounds

••

••

••

••

•

100

200

300

400

500

600

700

800

900

1 2 3 4

hours of exercise

•

•

•

1

2

3

4

5

6

7

8

9

10 2 3 4 5 6 7 8 9

jade plant growth in inches

•

•

•

•

•

••

••

•

••

••

••

0

100

200

300

400

100 200 300 400

food in grams

••

••



PAGE 1031. 6 1952. 15 2 1/63. 12 6 11/124. 30 405. 240 1326. 72 3 1/67. 270 3308. 144 1689. 5.42 9,840

10. 5 hours 15 minutes

PAGE 1041. 33.33 15.5 -7.22. 69.8 28.4 39.23. 26.67 -13.3 -26.14. 5 32 4.445. 39.2 197.6 -108.46. < > =7. > < =8. < = >9. < < <

10. = > <

PAGE 1051. 8 6,000 5,0002. 2 500 483. 1/2 72 10,5004. 80 1/8 3/45. 3 1/4 24 1/326. > = >7. > < >8. < > >

PAGE 1061. A, D 3. C2. B, D 4. Answers will vary.

PAGE 1071. CD, MN 6. 120o

2. AB, JK 7. Right angle3. Acute 8. 90o

4. 45o 9. 45o

5. Obtuse 10. 60o

11. Answers will vary for item 11.

PAGE 1081. 1,760 8 6.67 6. < > >2. 3 1,760 2.67 7. = > =3. 1 1.75 1,760 8. > = <4. 102 3.67 3,520 9. < > >5. 1,320 3,168 880 10. > < =

PAGE 1091. cm cm 3. cm km2. m m 4. km m5. 0.1 200 7506. 1,000 3 7507. 0.01 0.5 1,333

8. 500 0.8 0.000059. 50 15 8,000

10. = < <

PAGE 1101. 10.16 0.18288 45.722. 1.8288 1.22 0.5083. 25.4 2.1336 0.15244. 4,023.36 28.96 0.5365. > > >6. < < <7. > > >8. < > >9. < > <

PAGE 1111. 1.57 3,937 249 5. < > =2. 1.24 4.72 29.53 6. > < <3. 1.64 78.74 218.72 7. > > =4. 0.31 62.14 1,093 8. < < >9. > = >

PAGE 1121. 2 hours 10 minutes2. 1 hour 15 minutes3. 24˚F4. 212˚F5. 100˚F 0˚F6. Darcie’s; by 1 inch7. 21.33 ounces8. 1.25 pounds

PAGE 1131. Ohio is warmer. 73.4˚F 89˚F2. Mia3. 68 kilograms

PAGE 1141. 144 18.33 12,0002. 3.25 82.4 1,5003. 6 27.7 35.24. 35 -32.8 0.255. 200 46.1 126. 6.5 98.6 6.2007. 5 193.3 648. .0277 28.4 30,5009. Answers will vary.

PAGE 1151. 9 300 2,624.672. 660 5 62.143. 2.5 0.75 35.414. 4.67 0.75 53.345. 2,112 11 0.5336. 13.33 750 59.17. 2.33 625 0.0768. 3,520 1,666.67 1.079. 0.167 0.005 6.3

10. 39 20,000 118.11

PAGE 1161. 16 inches 75 feet2. 30 meters 24 miles3. 22 inches 22 yards

PAGE 1171. 12 inches 20 inches2. 6 inches 28 inches3. 45 inches 24 inches

PAGE 1181. 6.28 inches 25.13 feet2. 12.6 yards 56.55 meters3. 11 inches 78.54 centimenters4. 0.94 inches 50.27 centimeters

PAGE 1191. 28 yd, 49 sq yd 10 ft, 6sq ft2. 44 in, 112 sq in 36 cm, 81 sq cm

PAGE 1201. 9 ft2 600 in2

2. 113.5 cm2 151.8 yd2

3. 48 in2 144 ft2

4. 6 m2 170 in2

PAGE 1211. 3.14 in2 201.06 ft2

2. 63.6 yd2 346.4 m2

3. 16 in2 113.1 cm2

4. 0.13 in2 572.56 cm2

PAGE 1221. 25.94 in2 28 in2

2. 26 in2 13.57 in2

3. 15 in2 13.43 in2

PAGE 1231. 36,36,36,36,36,36,216 m2

2. 98,98,98,98,28,28,448 in2

3. 80,80,80,80,100,420 yd

PAGE 1241. 216 yd3 1,280 in3

2. 424.12 ft3 192 m3

3. 432 cm3 25,735 yd3

PAGE 1251. 43.98 13,541 in2 153 in3

2. 10 in 123.6674 ft 20.004 ft3

PAGE 1261. 3 sheets of plywood2. 121,918.93 ft3

PAGE 1271. 8 ft 2. 12 cm 3. 14 in4. 5 yd 5. 184 in2



Answer Key

PAGE 1291. 17.32. 55.63. 7.274. 2105. 1.366. 117. 3.88. 72.259. 6.9

10. 87.8%

PAGE 1301. 1/2 5. 6/6 9. 1/152. 1/6 6. 1/9 10. 1/53. 1/2 7. 1/10 11. 3/1004. 1/1296 8. 3/10 12. 1/120

PAGE 1311. 1:1 5. 1:3 9. 3:72. 0:4 6. 1:3 10. 4:13. 1:0 7. 3:1 11. 4:54. 1:1 8. 1:1 12. 1:1

PAGE 1321. 3.09 3 32. 89.3 89 873. 20,780.4 20,100 20,100

PAGE 1331. 1/22. 1/33. 3/11 5/114. green marbles5. 24 kids6. 2/425

PAGE 1341. 1.55 1.552. 19 22 233. Yes. By .574. 96%5. Carly

PAGE 1351. 1:1 5. 5:32. 1:1 6. 2:53. 1:8 7. even4. 3:4 8. 3:2

PAGE 1361. 3:7 5. 3:72. 4:7 6. 3:73. 1:7 7. even4. 0 8. even

PAGE 1281. 26 m 24 sq m2. 18 ft 14 sq ft3. 15.708 in 19.64 sq in4. 37.7 in 113.1 sq in5. 1485 cu ft 798 sq ft6. 1024 cu in 640 sq in

LEVEL

Operations

Fractions andDecimals

Whole Numbers

Perimeter and Area

Regrouping

Solving WordProblems

Money

Measurement

MATHCOMPUTATIONMATHCOMPUTATIONSKILLS & STRATEGIES

HIGH-INTEREST

7 100plus+ REPRODUCIBLE ACTIVITIES

HIG

H-IN

TE

RE

ST M

AT

H C

OM

PU

TAT

ION

SKIL

LS &

STR

AT

EG

IES •

LE

VE

L 7

Every book in the Math Computation Skills and Strategies series contains over 100 reproducible pages.These high-interest activities combine computation practice with strategyinstruction. Featuring a Scope and Sequence chart, the booksallow educators to supplement their math lessons with theextra math practice all students need. In addition, periodicreviews allow for reinforcement and assessment of skills.

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

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

MATH COMPUTATION SKILLS & STRATEGIESMATH COMPUTATION SKILLS & STRATEGIES

HIGH-INTEREST

SAD

DL

EB

AC

K E

DU

CA

TIO

NA

L P

UB

LISH

ING

Saddleback E-Book

Saddleback Math Covers 10/22/06 6:24 PM Page 5

math computation skills & strategies level 7 (math computation skills & strategies)

Documents