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Study Guide and
Intervention Workbook
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Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written permission of the publisher.
Send all inquiries to:
Glencoe/McGraw-Hill
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ISBN: 978-0-07-890739-5
MHID: 0-07-890739-X Study Guide and Intervention Workbook, Pre-Algebra
Printed in the United States of America.
1 2 3 4 5 6 7 8 9 10 066 14 13 12 11 10 09 08
To the Student
This Study Guide and Intervention Workbook gives you additional examples and problems for the concept exercises in each lesson. The exercises are designed to aid your study of mathematics by reinforcing important mathematical skills needed to succeed in the everyday world. The materials are organized by chapter and lesson, with two Study Guide and Intervention worksheets for every lesson in Glencoe Pre-Algebra. Always keep your workbook handy. Along with your textbook, daily homework, and class notes, the completed Study Guide and Intervention Workbook can help you in reviewing for quizzes and tests.
To the Teacher
These worksheets are the same ones found in the Chapter Resource Masters for Glencoe Pre-Algebra. The answers to these worksheets are available at the end of each Chapter Resource Masters booklet as well as in your Teacher Edition interleaf pages. ii_iv_PASGFM_890739.indd iiii_iv_PASGFM_890739.indd ii6/28/08 12:24:19 PM6/28/08 12:24:19 PM Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
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iii
Lesson/Title Page
1-1 Words and Expressions ............................1
1-2 Variables and Expressions .......................3
1-3 Properties .................................................5
1-4 Ordered Pairs and Relations ....................7
1-5 Words, Equations, Tables, and
Graphs ......................................................9
1-6 Scatter Plots ...........................................11
2-1 Integers and Absolute Value ..................13
2-2 Adding Integers ......................................15
2-3 Subtracting Integers ...............................17
2-4 Multiplying Integers .................................19
2-5 Dividing Integers .....................................21
2-6 Graphing in Four Quadrants ..................23
2-7 Translations and Re ections on
the Coordinate Plane ..............................25
3-1 Fractions and Decimals ..........................27
3-2 Rational Numbers ...................................29
3-3 Multiplying Rational Numbers .................31
3-4 Dividing Rational Numbers .....................33
3-5 Adding and Subtracting Like
Fractions .................................................35
3-6 Adding and Subtracting Unlike
Fractions .................................................37
4-1 The Distributive Property ........................39
4-2 Simplifying Algebraic Expressions ..........41
4-3 Solving Equations by Adding or
Subtracting ..............................................43
4-4 Solving Equations by Multiplying or
Dividing ...................................................45
4-5 Solving Two-Step Equations .................47
4-6 Writing Equations ...................................49
5-1 Perimeter and Area ................................51
5-2 Solving Equations with Variables
on Each Side ..........................................53
5-3 Inequalities ..............................................55
5-4 Solving Inequalities .................................57
5-5 Solving Multi-Step Equations and
Inequalities ..............................................59
6-1 Ratios ......................................................61
6-2 Unit Rates ...............................................63
6-3 Converting Rates and
Measurements ........................................65
6-4 Proportional and Nonproportional
Relationships ..........................................67
6-5 Solving Proportions ................................69
6-6 Scale Drawings and Models ...................71
Lesson/Title Page
6-7 Similar Figures ........................................73
6-8 Dilations ..................................................75
6-9 Indirect Measurement .............................77
7-1 Fractions and Percents ...........................79
7-2 Fractions, Decimals, and Percents .........81
7-3 Using the Percent Proportion .................83
7-4 Find Percent of a Number Mentally ........85
7-5 Using Percent Equations ........................87
7-6 Percent of Change ..................................89
7-7 Simple and Compound Interest ..............91
7-8 Circle Graphs ..........................................93
8-1 Functions ................................................95
8-2 Sequences and Equations ......................97
8-3 Representing Linear Functions .............99
8-4 Rate of Change ....................................101
8-5 Constant Rate of Change and
Direct Variation .....................................103
8-6 Slope .....................................................105
8-7 Slope-Intercept Form ............................107
8-8 Writing Linear Equations ......................109
8-9 Prediction Equations .............................111
8-10 Systems of Equations ...........................113
9-1 Powers and Exponents .........................115
9-2 Prime Factorization ...............................117
9-3 Multiplying and Dividing
Monomials ............................................119
9-4 Negative Exponents .............................121
9-5 Scienti c Notation .................................123
9-6 Powers of Monomials ...........................125
9-7 Linear and Nonlinear Functions ...........127
9-8 Quadratic Functions .............................129
9-9 Cubic and Exponential Functions .........131
10-1 Squares and Square Roots ................133
10-2 The Real Number System ..................135
10-3 Triangles .............................................137
10-4 The Pythagorean Theorem .................139
10-5 The Distance Formula ........................141
10-6 Special Right Triangles .......................143
11-1 Angle and Line Relationships .............145
11-2 Congruent Triangles ...........................147
11-3 Rotations .............................................149
11-4 Quadrilaterals .....................................151
11-5 Polygons .............................................153
11-6 Area of Parallelograms, Triangles,
and Trapezoids ...................................155
11-7 Circles and Circumference .................157
Contents
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Lesson/Title Page
11-8 Area of Circles ....................................159
11-9 Area of Composite Figures .................161
12-1 Three-Dimensional Figures ................163
12-2 Volume of Prisms ...............................165
12-3 Volume of Cylinders ...........................167
12-4 Volume of Pyramids, Cones and
Spheres ..............................................169
12-5 Surface Area of Prisms ......................171
12-6 Surface Area of Cylinders ..................173
12-7 Surface Area of Pyramids and
Cones .................................................175
12-8 Similar Solids ......................................177
Lesson/Title Page
13-1 Measures of Central Tendency ..........179
13-2 Stem-and-Leaf Plots ...........................181
13-3 Measures of Variation .........................183
13-4 Box-and-Whisker Plots .......................185
13-5 Histograms ..........................................187
13-6 Theoretical and Experimental
Probability ...........................................189
13-7 Using Sampling to Predict ..................191
13-8 Counting Outcomes ............................193
13-9 Permutations and Combinations ........195
13-10 Probability of Compound Events ........197
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
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Chapter 1 1 Glencoe Pre-Algebra
Study Guide and Intervention
Words and Expressions
1-1 Translate Verbal Phrases into Expressions A numerical expression contains a combination of numbers and operations such as addition, subtraction, multiplication, and division. Verbal phrases can be translated into numerical expressions by replacing words with operations and numbers.
Example
plus the sum of increased by more than minus the difference of decreased by less than times the product of of divide the quotient of divided by among
Phrase the product of seventeen and three
Expression 17 × 3
Write a numerical expression for each verbal phrase. a. the product of seventeen and three
Exercises
Write a numerical expression for each verbal phrase.
1. eleven less than twenty 2. twenty-five increased by six
3. sixty-four divided by eight 4. the product of seven and twelve
5. the quotient of forty and eight 6. sixteen more than fifty...four
7. six groups of twelve 8. eighty...one decreased by nine
9. the sum of thirteen and eighteen 10. three times seventeen
b. the total number of pencils given to each student if 18 pencils are shared among 6 students
Phrase 18 shared among 6
Expression 18 ÷ 6
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Chapter 1 2 Glencoe Pre-Algebra
1-1Study Guide and Intervention (continued)
Words and Expressions
Example Evaluate each expression.
b. 4(3 + 6) + 2 11
4(3 + 6) + 2
11 = 4(9) + 2
11 = 36 + 22 = 58
Evaluate (3 + 6).
Multiply 4 and 9, and 2 and 11.
Add 36 and 22.
Multiply 6 and 5.
Divide 10 by 2.
Subtract 5 from 30.
a. 6
5 - 10 ÷ 2
6
5 - 10 ÷ 2 = 30 - 10 ÷ 2
= 30 - 5 = 25
Exercises
Evaluate each expression.
1. 6 + 3 9 2. 7 + 7 3 3. 14 - 6 + 8
4. 26 - 4 + 9 5. 10 ÷ 5
3 6. 22 ÷ 11
6
7. 2(6 + 2) - 4
3 8. 5(6 + 1) - 3
3 9. 2[(13 - 4) + 2(2)]
10. 4[(10 - 6) + 6(2)] 11.
(67 + 13)
34 - 29
12. 6(4 - 2) + 8
13. 3[(2 + 7) ÷ 9] - 3 14. (8
7) ÷ 14 - 1 15.
4 18 2 9
16. (9
8) - (100 ÷ 5)
Order of Operations Evaluate, or find the numerical value of, expressions with more than one operation by following the order of operations. Step 1 Evaluate the expressions inside grouping symbols.
Step 2 Multiply and/or divide from left to right.
Step 3 Add and/or subtract from left to right.
c. 3[(7 + 5) ÷ 4 - 1]
3[(7 + 5) ÷ 4 - 1] = 3[12 ÷ 4 - 1]
= 3(3 - 1) = 3(2) = 6
Evaluate (7 + 5) first.
Divide 12 by 4.
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