California math triumphs the core processes of mathematics, volume 4b

295AF1.2, 6AF1.2, 7AF1.3 5AF1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution.. 7AF1.1 Use variables and a

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Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber

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California Math Triumphs

2A Chapter 2 Equivalence of Fractions

2B Chapter 3 Operations with Fractions

2B Chapter 4 Positive and Negative Fractions and Decimals

Volume 3 Ratios, Rates, and Percents 3A Chapter 1 Ratios and Rates

3A Chapter 2 Percents, Fractions, and Decimals

3B Chapter 3 Using Percents

3B Chapter 4 Rates and Proportional Reasoning

Volume 4 The Core Processes of Mathematics 4A Chapter 1 Operations and Equality

4A Chapter 2 Math Fundamentals

4B Chapter 3 Math Expressions

4B Chapter 4 Linear Equations

4B Chapter 5 Inequalities

Volume 5 Functions and Equations 5A Chapter 1 Patterns and Relationships

5A Chapter 2 Graphing

5B Chapter 3 Proportional Relationships

5B Chapter 4 The Relationship Between

Graphs and Functions

Volume 6 Measurement 6A Chapter 1 How Measurements Are Made 6A Chapter 2 Length and Area in the Real World 6B Chapter 3 Exact Measures in Geometry

6B Chapter 4 Angles and Circles

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Authors and Consultants

AUTHORS

Frances Basich Whitney

Project Director, Mathematics K–12

Santa Cruz County Offi ce of Education

Capitola, California

Kathleen M Brown

Math Curriculum Staff Developer Washington Middle School Long Beach, California

Dixie Dawson

Math Curriculum Leader Long Beach Unifi ed Long Beach, California

CONSULTANTS

Assessment

Donna M Kopenski, Ed.D.

Math Coordinator K–5

City Heights Educational Collaborative

San Diego, California

Instructional Planning and Support

Beatrice Luchin

Mathematics Consultant League City, Texas

ELL Support and Vocabulary

ReLeah Cossett Lent

Author/Educational Consultant Alford, Florida

Dinah-Might Activities, Inc.

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California Advisory Board

Carol Cronk

Mathematics Program Specialist

San Bernardino City Unifi ed

School District

San Bernardino, California

Audrey M Day

Classroom Teacher Rosa Parks Elementary School San Diego, California

Jill Fetters

Math Teacher Tevis Jr High School Bakersfi eld, California

Grant A Fraser, Ph.D.

Professor of Mathematics California State University, Los Angeles

Los Angeles, California

Eric Kimmel

Mathematics Department Chair

Frontier High School

Bakersfi eld, California

Donna M Kopenski, Ed.D.

Math Coordinator K–5 City Heights Educational Collaborative San Diego, California

Michael A Pease

Instructional Math Coach Aspire Public Schools Oakland, California

Chuck Podhorsky, Ph.D.

Math Director City Heights Educational Collaborative San Diego, California

Arthur K Wayman, Ph.D.

Professor Emeritus

California State University, Long

Beach

Long Beach, California

Frances Basich Whitney

Project Director, Mathematics K–12 Santa Cruz County Offi ce of Education

Capitola, CA

Mario Borrayo

Teacher Rosa Parks Elementary San Diego, California

Melissa Bray

K–8 Math Resource Teacher Modesto City Schools Modesto, California

CALIFORNIA ADVISORY BOARD

Glencoe wishes to thank the following professionals for their invaluable

feedback during the development of the program They reviewed

the table of contents, the prototype of the Student Study Guide, the

prototype of the Teacher Wraparound Edition, and the professional

Bonnie Awes

Teacher, 6th Grade Math Monroe Clark Middle School San Diego, California

Kathleen M Brown

Math Curriculum Staff Developer Washington Middle School Long Beach, California

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California Reviewers

CALIFORNIA REVIEWERS

Each California Reviewer reviewed at least two chapters of the Student

Study Guides, providing feedback and suggestions for improving the

effectiveness of the mathematics instruction

Bobbi Anne Barnowsky

Monica S Patterson

Educator Aspire Public Schools Modesto, California

Rechelle Pearlman

4th Grade Teacher Wanda Hirsch Elementary School Tracy, California

Armida Picon

5th Grade Teacher Mineral King School Visalia, California

Anthony J Solina

Lead Educator Aspire Public Schools Stockton, California

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Volume 4A The Core Processes of Mathematics

4AF1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use

of the concept of a variable).

4AF2.1 Know and understand that equals added to equals are equal.

4AF2.2 Know and understand that equals multiplied by equals are equal

Chapters 1 and 2 are contained in Volume 4A Chapters 3, 4, and 5 are contained in Volume 4B.

Chapter

Point Lobos State Park

Standards Addressed

in This Chapter

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3AF1.5 Recognize and use the commutative and associative properties of multiplication (e.g., if 5 × 7 = 35, then what is 7 × 5? and if 5 × 7 × 3 = 105, then what is 7 × 3 × 5?).

5AF1.3 Know and use the distributive property in equations and expressions with variables.

7AF1.2 Use the correct order

of operations to evaluate algebraic

Mustard plants in Napa Valley

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3-4 Evaluate Variable Expressions 29

5AF1.2, 6AF1.2, 7AF1.3

5AF1.2 Use a letter to represent

an unknown number; write and evaluate simple algebraic expressions in one variable by substitution.

6AF1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables.

7AF1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).

7AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used.

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7AF4.0 Students solve simple linear equations and inequalities over the rational numbers.

Alabama Hills, Owens Valley

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7AF4.0 Students solve simple linear equations and inequalities over the rational numbers.

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Chapter

The Transamerica Pyramid in San Francisco

is 248 meters lower than the Taipei 101 building in Taiwan To

find the height of the Transamerica Pyramid,

let x equal the height

of the Taipei 101 The

expression x – 248

represents the height

of the Transamerica Pyramid.

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3

You know how to translate certain phrases into math symbols

Example:

I have 5 more dollars than Teresa

So, the money you have is:

Teresa’s amount of money + 5

2 Harold ate 2 of my brownies

So, the brownies I have left are:

the brownies I had - 2 .

When you do not know a number,

you use a variable, such as x, in place

STEP 2 Preview Get ready for Chapter 3 Review these skills and compare

them with what you’ll learn in this chapter

STEP 1 Quiz Are you ready for Chapter 3? Take the Online Readiness

Quiz at ca.mathtriumphs.com to find out

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coefficient

a number that is multiplied by the variable

in a term

algebraic expression

a combination of numbers, variables, and

at least one operation

KEY Concept

7AF1.1 Use variables and appropriate operations to write

an expression, an equation, an

inequality, or a system of equations or

inequalities that represents a verbal description.

variable a, b, x

constant -5, 8, 10 term 2x, 7, 5x2, _ 8z

coefficient 5 is the coefficient in 5y

algebraic expression 3z + 4, 7x

term

Terms are separated by + or – signs Constants are terms that

do not have a variable A constant includes the sign that is

written before it

Example 1

Name the variable, constant, and coefficient

in 8t + 2.

1 The variable is the letter t.

2 The constant is the number 2

3 The coefficient is the number 8 because it

is multiplied by the variable t.

YOUR TURN!

Name the variable, constant, and

coefficient in 7x - 5.

1 What is the variable?

The variable is the letter x

2 What is the constant?

The constant is the number -5

3 What is the coefficient?

The coefficient is the number multiplied

by the variable It is the number 7

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Lesson 3-1 Algebraic Expressions 5

Example 2

Write an algebraic expression that has the

constant term 9 and the variable h.

1 Write the term with the variable Follow it

with a + or - sign h +

2 Write the constant term before or after the

variable and operation symbol h + 9

There is more than one expression that has a

constant term 9 and a variable h.

Write an algebraic expression that has the

constant term 5 and the variable a.

1 Write the term with the variable Follow

or precede it with a + or - sign

Sample answer: + 4a

2 Write the constant term before or after the variable and operation symbol

Write three other expressions that have a

constant term 5 and a variable a

Sample answers:

a + 5, 3/a + 5, 5 + 2a,

5 - 2a, 5 - a.

Who is Correct?

Write an algebraic expression that has the constant term 2, a variable

n, and the coefficient 8.

1 Write three different algebraic expressions that have the constant

term 1 and the variable h.

Answers will vary Sample answer: h + 1, 5h + 1, 7 _ h + 1, 1 - h.

2 Write three different algebraic expressions that have the constant

term 5 and the variable a.

Answers will vary Sample answer: a + 5, 8a + 5, a _ 9 + 5, 5 - a

Remember that constant terms do not have a variable

Their values do not change.

Remember that constant terms do not have a variable

Their values do not change.

GO ON

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3 Name the variable, constant, and coefficient in –12 + k

6

Step 1 Determine the variable

The variable is the letter k

Step 2 Determine the constant

The constant is the number - 12

Step 3 Determine the coefficient

The coefficient is the number mutiplied by the variable The term k

6 can be written as 1

6 k The coefficient is 1 _ 6

Step by Step Practice

Name the variable, constant, and coefficient in each expression.

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Solve.

12 HEIGHT Doris was 42 inches tall on her birthday She

grew the next year Write an expression for Doris’s new

height in inches

Understand Read the problem Write what you know

Doris’s height is expressed by the constant term

Doris’s height should be greater after one year

Select a variable to represent the number of inches that Doris grew Sample answer: h

Solve Write the expression

42 + h

Check Does the expression make sense? Doris’s height will

be greater than the height on her birthday

13 MONEY Naveen saved $86 He spent some of the money on comic

books Write an expression for the amount of money Naveen has

left Check off each step 86 - m

✔ Understand

✔ Plan

✔ Solve

✔ Check

14 PETS Akiko feeds her fish x teaspoons of fish food each day

Write an expression for the amount of food, in teaspoons,

Akiko feeds her fish in 7 days

7x

Problem-Solving Strategies

✓

Draw a diagram.

Look for a pattern.

Guess and check.

Use logical reasoning.

Solve a simpler problem.

✓

GO ON

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EATING OUT Dustin took his friend out for lunch

He ordered the soup and salad special His

friend ordered a turkey sandwich They both

ordered regular milkshakes

15 Dustin could not read the cost of a regular

milkshake Write an expression for the total

price of the meal

Sample answer: 6 + 5 + 2m

or 6 + 5 + m + m

16 Write an expression for the total cost of

t sandwiches and two large milkshakes.

Sample answer: 5t + 2(4)

17 List key words that tell you which

operation to use when writing an expression

Answers may vary Sample answer: more than means to add, less than means

to subtract, times means to multiply, divided by means to divide

Skills, Concepts, and Problem Solving

18 Write three different expressions that have the constant term –15

and the variable d.

Answers will vary Sample answer: –15 + d, –15 + 7d, –15 + d _ 2 , d - 15.

19 Write three different expressions that have the constant term 6 and

the variable q.

Answers will vary Sample answer: q + 6, 3q + 6, 1 _ q + 6, 6 - q

Name the variable, constant, and coefficient in each expression.

F

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28 PRODUCE Akshi’s orange tree has 72 oranges She gave an equal

number of oranges to each of her cousins Write an expression for

the number of oranges Akshi gave each cousin

Sample answer: 72 ÷ c or 72 _ c

29 MOVIES Lamar had 48 DVDs in his collection He bought more

DVDs Write an expression for the total number of DVDs in

Lamar’s collection

Sample answer: 48 + d

30 BAKING Gavin promised to bring cupcakes for April’s party April

wants to have enough cupcakes so each party guest can eat two

Write an expression for the number of cupcakes Gavin must bring

Sample answer: 2p

31 MOVIES Carlos and Lucas (both 14 years old) are

taking their younger sisters (who are under 13)

to a movie They have x younger sisters Write an

expression for the total cost of admission

.PWJF5IFBUFS"ENJTTJPO

Sample answer: 2 · 8 + 5x or 8 + 8 + 5x GO ON

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Vocabulary Check Write the vocabulary word that completes each

sentence.

32 A(n) variable is a symbol, usually a letter, that can

have different values

33 A(n) coefficient is a number that is multiplied by the

variable in a term

34 A value that does not change is a constant

35 A(n) algebraic expression is a combination of numbers, variables,

and at least one operation

36 Writing in Math What is the coefficient in the expression y + 14?

Explain

1; the term y can also be written as 1y.

Spiral Review

Solve (Lesson 2-4, p xx)

37 SHOPPING Zola bought 4 packs of pencils with 5 pencils each

She gave 4 pencils to Clara Then Zola bought 2 packs of pencils

with 8 pencils each How many pencils does Zola have now?

32

38 SHOPPING Janet bought 5 packs of erasers with 10 erasers each

Jorge gave Janet 2 erasers Then Janet gave 9 erasers to each of

3 friends How many erasers does Janet have now? 25

Use the Distributive Property and a model to find each product Show

your work (Lesson 2-3, p xx)

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Lesson 3-2 Translating Verbal Phrases into Mathematical Symbols 11

Lesson

3-2 Translating Verbal Phrases

into Mathematical Symbols

(Lesson 3-1, p 4)

coefficient

a number that is multiplied by the variable

algebraic expression

(Lesson 3-1, p 4)

KEY Concept

You can look for certain words in problems to help you

determine which operations to use Below are the most

common of these words

Addition Subtraction Multiplication Division

increased by decreased by twice separate into

equal groups

If none of these words are in your problem, the

circumstances in the situation will help you decide

which operation to use

Example 1

Translate “seven more than a number n” to an expression.

1 The words “more than” tell you to use

2 What is the constant term? 5

3 What is the variable? x

5AF1.2 Use a letter to represent

an unknown number; write and evaluate simple algebraic expressions in one variable by substitution.

7AF1.1 Use variables and appropriate operations to write an expression, an

equation, an inequality, or a system of

equations or inequalities that represent a verbal description.

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3 The “same number of fish as Arturo” is a

variable Choose the letter f as the variable

three times as many fish

1 What operation does the word

“separating” tell you to use?

division

2 What is the constant term? four or 4

3 What is the variable? b

separating all of her books into four piles

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GO ON

4 twice the amount of y multiplication

6 the quotient of s and 9 division

Translate each phrase to an expression.

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Write an expression to represent the following situation.

17 Niles has four fewer magazines than Wilma

Step 1 Decide the operation to use in the expression The word “fewer” tells you to

subtract

Step 2 The constant term is 4

Step 3 Choose a letter for the variable The number of magazines Wilma has is

Step 4 Write the expression m - 4

Write an expression to represent each situation.

18 Denise separated her postcards into 3 equal stacks

Which word(s) tell you the operation to use?

separated into equal stacks

Choose a letter for the variable Sample answer: p

19 Joe’s puppy weighed 3 pounds more than it did last month

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GO ON

Solve.

23 GEOMETRY The perimeter of a triangle is the sum of the

lengths of its sides One side length is 12 feet Another side

length is 9 feet Write an expression for the perimeter of

the triangle

The perimeter of a triangle is the sum of the lengths of 3 sides

One side is 12 feet

One side is 9 feet

One side is unknown

Plan Pick a strategy One strategy is to draw a diagram

Sketch the triangle Choose a variable for the length

of the unknown side

Check Does the expression make sense? The perimeter of

the triangle should be greater than the length of the two known sides combined

24 FITNESS Tyrus runs 4 miles each day Write an expression for the

number of miles Tyrus runs in d days Check off each step 4d

Look for a pattern.

Guess and check.

Solve a simpler problem Work backward.

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25 RIDES Ruben’s dad is taking Ruben and his friends on a hot-air

balloon ride The weight limit is 900 pounds Ruben’s dad weighs

250 pounds Ruben weighs 74 pounds Nathaniel weighs 87 pounds

Belinda weighs b pounds Write an expression for their combined

weights in pounds 250 + 74 + 87 + b

26 FAMILY Paul is 23 years younger than his mother Write an

expression for Paul’s age a - 23

27 Do the expressions 5 – r and r – 5 have the same value?

Explain and give an example

No; the order in which you subtract affects the answer The Commutative

Property does not hold true for subtraction Let r = 1 5 - 1 = 4 and 1 - 5 = -4

For each phrase, name the operation.

36 45 minus x⎭ ⎬ ⎫ ⎭ ⎬ ⎫ ⎭ ⎬ ⎫ 37 a number plus 61⎭ ⎬ ⎫ ⎭ ⎬ ⎫ ⎭ ⎬ ⎫

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GO ON

Write an expression to represent each situation.

52 FOOD A party-sized sandwich feeds 18 students Write an

expression for the number of sandwiches needed for s students.

s ÷ 18

53 ANIMALS Read the photo caption to the right Write an expression

for the speed of the antelope

c - 9

54 GAMES Sabrina scored 63 points less than Aailiyah playing a

board game Aailiyah scored p points Write an expression for the

number of points Sabrina scored

p - 63

55 MONEY Xavier has $18, Anton has $24, and Len has d dollars

Write an expression for the sum of money Xavier, Anton, and Len

have altogether

18 + 24 + d

ANIMALS A cheetah can run 9 miles per hour faster than an antelope.

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56 GEOMETRY The area of a rectangle is 6 times the area of a square

The area of the square is x square units Write an expression for the

area of the rectangle

6 × x or 6x

57 SCHOOL Last year the number of students at Central High was

425 students This year the number increased Write an expression

to show the increase in students from last year to this year

425 + n

58 REAL WORLD Write three real-world examples of variables and

constants in the table

Answers will vary Answers will vary

Sample answers: age,

height, length of a movie

Sample answers: the year you were born, days in a year, length of a wall

In Exercises 59–64, match the expressions on the left with the phrases on the right.

Vocabulary Check Write the vocabulary word that completes each

sentence.

65 Terms are each of the quantities connected by plus

or minus signs in an algebraic expression

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66 A constant is a value that does not change

67 A combination of numbers, variables , and at least one

operation is an algebraic expression

68 Writing in Math How do you know when to use a variable when

writing an expression?

Answers will vary Sample answer: Use a variable when one of the terms can

have different values (or the value is unknown).

71 FOOTBALL A football team scored 4 touchdowns (each worth 6

points) and 2 extra points (each worth 1 point) How many points

did the football team score? (Lesson 2-3, p 57)

26

72 STAMP COLLECTING Hogan has 140 stamps in his stamp

collection He put the stamps in 2 albums Each album has the

same number of stamps How many stamps are in each album?

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3

Progress Check 1 (Lessons 3-1 and 3-2)

1 Write three different expressions that have the constant term 7 and

the variable f 7AF1.1

Answers will vary Sample answer: f + 7, 2f + 7, f _ 8 + 7, 7 - f

For each phrase, name the operation 7AF1.1

Name the variable, constant, and coefficient in each expression 7AF1.1

Translate each phrase to an expression 7AF1.1

n ÷ 9 or n _ 9 h - 13

Write an expression to represent each situation 5AF1.2

8 Lizzie has 6 times as many pencils as Betty 6p

Solve 7AF1.1, 5AF1.2

10 BUSINESS Trina made 47 glasses of lemonade She sold

x glasses of lemonade Write an expression to find how many

glasses of lemonade Trina has left

47 - x

11 CRAFTS Daja made 28 bracelets She separated the bracelets

into p piles Write an expression to find the number of bracelets

in each pile

28 ÷ p or 28 _ p

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Lesson 3-3 Simplify Expressions 21

(Lesson 3-1, p 4)

like terms

terms that have the same variables to the same powers

simplify

to combine like terms

KEY Concept

Recall that terms can be a number, a variable, or a

combination of numbers and variables Terms can be positive

or negative, and they can have exponents

Examples of

6 and 13 They are both constants

-x and 3x Both contain the

variable x and the exponent 1

2x2 and 5x2 Both contain the variable x and the

Like terms can be combined, or simplified

-x + 3x = -1x + 3x Add the coefficients of terms with like

variables.

Unlike terms cannot be combined For example, in 2y + 4x the

terms cannot be combined because the variables are different

Simplify Expressions

When grouping and simplifying like terms, use the Associative and

Commutative Properties of Addition and the Distributive Property of

Multiplication

Example 1

Simplify 3x + 2y + 2x by using a model.

1 Let represent x and represent y.

2 Draw a model to represent the expression

Simplify c + 3t + 2c by using a model.

1 Let represent c and represent t.

2 Draw a model to represent the expression

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3 Add the like terms

= (12 + 13 + 61) + 9r + 17r Add the constant terms

YOUR TURN!

Simplify 13p + 13 - 5p + 5.

1 Find the like terms

What are the constant terms? 13 and 5

2 Rearrange to group the constant terms together and the p terms

together using the Commutative and Associative Properties

Circle correct answer(s) Cross out incorrect answer(s)

Remember that the Commutative Property states that the order in which two numbers are added or multiplied does not change the answer.

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Step 3 Combine the u2 terms

There is only one term with variable u and exponent 2

So there are no like terms to combine

Step 4 The simplified expression is 6u2 + 16u + 21

GO ON

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Solve.

14 MONEY Rashin bought 4 hair clips for x dollars each She

also bought shampoo for $5 and a hairbrush for $4 In the

checkout lane, she decided to buy 2 ponytail holders that

each cost the same as a hair clip

The expression 4x + 5 + 4 + 2x represents the total cost

Simplify the expression to see how much Rashin spent

The expression that needs to be simplified is

4x + 5 + 4 + 2x

Plan Pick a strategy One strategy is to use a model

Solve You can use a model to find the answer

Let represent x and represent the constant terms

Combine the constant terms and the variable terms

4x + 5 + 4 + 2x = (4x + 2x ) + ( 5 + 4)

Rashin spent 6x + 9 dollars

Check You can circle one set of like terms and box in

another set of like terms to check your answer

Look for a pattern.

Guess and check.

Use a model.

Solve a simpler problem.

Work backward.

GO ON

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15 MOWING Over the summer, Zakir, Deltric, and Rafael mowed

yards Each day, Zakir mowed 2 yards, Deltric mowed 3 yards, and

Rafael mowed 1 yard The expression 2d + 3d + d represents the

number of yards they mowed in d days Simplify the expression

Check off each step 6d

✔ Understand

✔ Plan

✔ Solve

✔ Check

16 AGES Laurita is n years old Elisa is 2 years older than Laurita

Esteban is 3 years older than Elisa Represent the sum of their ages

with the expression n + (n + 2) + (n + 2 + 3) Simplify the

expression

3n + 7

17 Are 5h2 and -9h2 like terms? Explain

Yes; both terms have the same variable and same exponent

Name the like terms in each expression.

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Simplify each expression Show your work.

32 MONEY Mrs Clark gives her four children an allowance each

week Jodi gets n dollars Brooke gets twice as much as Jodi Mark

gets $3 less than Brooke Katrina gets twice as much as Mark The

expression n + 2n + (2n − 3) + 2(2n − 3) represents the total of the

four allowances Simplify the expression

(Hint: Use the Distributive Property.) 9n - 9

33 SCHOOL In Mrs Garcia’s class, students can earn points for

free books Mrs Garcia’s bulletin board shows how many points

a student can earn Sergio earned some As and some Bs He had

perfect attendance for the same number of weeks as he earned

As The expression 20a + 15b + 2(20a) represents the number of

points that Sergio earned Simplify the expression

1OINTS:OU$AN&ARN

"POINTS

#POINTS

$POINTS 1ERFECT"TTENDANCEINAWEEK 5WICEASMANYPOINTSASAN"

GO ON

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35 To simplify means to combine like terms

36 Writing in Math Explain how to combine the like terms in the

expression 7x + 5 + 4x using the Associative Property and the

Commutative Property

Answers will vary Sample answer: Use the Commutative Property to switch the

addends: 7x + 4x + 5 Use the Associative Property to group like terms:

(7x + 4x) + 5 Then add the like terms to get 11x + 5.

41 FOOD Julio cooked 34 hot dogs He sold 18 hot dogs Julio then

cooked 6 more hot dogs How many hot dogs does Julio have

ready to sell? 22

42 SHOPPING Dawn bought 3 packages of paper clips There were

4 boxes of paper clips in each package There were 50 paper clips in

each box How many paper clips did Dawn buy? 600

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Lesson 3-4 Evaluate Variable Expressions 29

algebraic expression (Lesson 3-1, p 4)

value

the amount of a number

order of operations

(Lesson 2-4, p 63)

rules that tell what order

to use when evaluating expressions

symbols.

(2) Simplify exponents.

order from left to right.

KEY Concept

Evaluate Variable Expressions

To evaluate an algebraic expression , substitute a value for a

variable Then perform the operations

Remember to use the order of operations after substituting, or

replacing, the variables with numbers

Evaluate 2 2 + 4 when = 2 and = 3

1 Replace with 2 in the expression

by substitution.

6AF1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables.

7AF1.3 Simplify numerical expressions

by applying properties of rational numbers and justify the process used.

Simplify grouping symbols

Add

GO ON

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1 Replace y with 2 and x with 4

Write the expression

3(2)2 + 4 · 3 - 2

2 Simplify using the order of operations

3(2)2 + 4 · 3 - 2 = 3(4) + 4 · 3 - 2

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