Name Daily Spiral Review 6-1 - Wikispaces - owlsharenestgrade+topic+6.pdf · 18.03.2008 · Inc. 5...

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Topic 6 19

Daily Spiral Review

6-1

1. Celia has listened to 5 __ 14 of the songs on her new CD. Which equation could Celia use to ! nd s, the fraction of the songs she has left to listen to?

A 5 ___ 14 ! s " 9 ___ 14

B 5 ___ 14 ! s " 14 ___ 14

C 9 ___ 14 ! s " 14 ___ 14

D 14 ___ 14 ! s " 5 ___ 14

2. The table below shows how far each skater in a 1-mile race has traveled.

Skating Race

Skater Ray Scott Theo Walt

Distance (miles) 2 __ 5 3 ___ 10 1 __ 2 1 ___ 10

If none of the skaters pass each other, which skater will win the race?A Ray B Scott C Theo D Walt

3. A dolphin swims 26 miles per hour. How far could a dolphin swim in 9 hours?A 125 miles B 184 milesC 234 miles D 269 miles

4. Jack needs to ! nish 5 _ 8 of a school project by Monday. So far he has done 3 _ 8 of the project.a. Draw a rectangle to show

Jack’s project. Shade the fraction that Jack has ! nished so far.

b. What fraction of the project does Jack have left to do by Monday? Write your answer in simplest form.

5. The giant tortoise can move at speeds of up to 0.17 miles per hour. The top speed for a greyhound is 39.35 miles per hour. How much greater is the greyhound’s speed than the tortoise’s?

6. A school needs 75 light bulbs. Bulbs come in packages of 8. How many packages should the school order?

Daily Spiral Review

6-1

30428_T06__19 19 1/16/08 5:11:38 PM

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Topic 6 19

Daily Spiral Review

6-1

1. Celia has listened to 5 __ 14 of the songs on her new CD. Which equation could Celia use to ! nd s, the fraction of the songs she has left to listen to?

A 5 ___ 14 ! s " 9 ___ 14

B 5 ___ 14 ! s " 14 ___ 14

C 9 ___ 14 ! s " 14 ___ 14

D 14 ___ 14 ! s " 5 ___ 14

2. The table below shows how far each skater in a 1-mile race has traveled.

Skating Race

Skater Ray Scott Theo Walt

Distance (miles) 2 __ 5 3 ___ 10 1 __ 2 1 ___ 10

If none of the skaters pass each other, which skater will win the race?A Ray B Scott C Theo D Walt

3. A dolphin swims 26 miles per hour. How far could a dolphin swim in 9 hours?A 125 miles B 184 milesC 234 miles D 269 miles

4. Jack needs to ! nish 5 _ 8 of a school project by Monday. So far he has done 3 _ 8 of the project.a. Draw a rectangle to show

Jack’s project. Shade the fraction that Jack has ! nished so far.

b. What fraction of the project does Jack have left to do by Monday? Write your answer in simplest form.

5. The giant tortoise can move at speeds of up to 0.17 miles per hour. The top speed for a greyhound is 39.35 miles per hour. How much greater is the greyhound’s speed than the tortoise’s?

6. A school needs 75 light bulbs. Bulbs come in packages of 8. How many packages should the school order?

Daily Spiral Review

6-1

10

39.18 miles per hour

1 __ 4

30428_T06_019_19 19 3/18/08 2:10:15 PM

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6-1

Prob

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6-1

20 Topic 6

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30428_T06__20 20 1/16/08 5:11:47 PM

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1. Which shows the phrase “a number divided by 5” as an algebraic expression?

A x ! 5

B 5x

C 5 " x

D x " 5

2. A teacher needs 6 craft sticks for each student in a class for a project. Which algebraic expression shows this situation if s represents the number of students?

A 6s

B 6 " s

C s ! 6

D 6 # s

3. Writing to Explain There are p people in Susanna’s family (an even number). They went to an amusement park for the day.

a. Admission was $15.00 per person. Write an expression to show the cost of admission for all of them.

b. They split into two equal groups while they were at the park. Write an expression to show the number of people in each group.

c. All of them but three went on the rollercoaster. Write an expression to show the number of people that went on the rollercoaster.

d. They saw another family that had 4 more people in their family than Susanna’s family. Write an expression to show the number of people in that family.

Quick Check

6-1Q

uick Check 6

-1

Topic 6 21

30428_T06__21 21 1/16/08 5:11:49 PM

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1. Which shows the phrase “a number divided by 5” as an algebraic expression?

A x ! 5

B 5x

C 5 " x

D x " 5

2. A teacher needs 6 craft sticks for each student in a class for a project. Which algebraic expression shows this situation if s represents the number of students?

A 6s

B 6 " s

C s ! 6

D 6 # s

3. Writing to Explain There are p people in Susanna’s family (an even number). They went to an amusement park for the day.

a. Admission was $15.00 per person. Write an expression to show the cost of admission for all of them.

b. They split into two equal groups while they were at the park. Write an expression to show the number of people in each group.

c. All of them but three went on the rollercoaster. Write an expression to show the number of people that went on the rollercoaster.

d. They saw another family that had 4 more people in their family than Susanna’s family. Write an expression to show the number of people in that family.

Quick Check

6-1Q

uick Check 6

-1

Topic 6 21See student samples at the right.

30428_T06_020-024_21 21 3/18/08 2:10:31 PM

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Reteaching

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22 Topic 6

Variables and ExpressionsA variable is a letter or symbol. It represents an unknown amount that can change.

You can do mathematical operations with variables and numbers.

You can state these operations in word expressions. You can also state them in algebraic expressions.

Operation ! " # $

Word expression the sum of r and 3

the difference between r and 3

the product of r and 3

the quotient of r and 3

Algebraic expression r ! 3 r " 3 3r r $ 3

Other ways of saying the word

expression

3 added to r3 more than r

3 subtracted from r3 less than r

r multiplied by 33 times r

r divided by 33 equal parts of r

Complete the algebraic expression for each of the following word expressions.

Circle the letter of the correct word expression for each algebraic expression.

7. t " 13 a. 13 subtracted from t b. t subtracted from 13

8. 4n a. 4 more than n b. 4 times n

9. 11 ! s a. 11 more than s b. 11 less than s

10. 45a a. the product of a and 45 b. 45 more than a

11. y $ 6 a. y less 6 b. 6 equal parts of y

12. v " 5 a. 5 less than v b. v subtracted from 5

1. the sum of b and 8

b ____ 8

4. 7 less than z

z ____ 7

2. the difference between m and 6

m ____ 6

5. 2 more than d

d ____ 2

3. the quotient of k and 16

k ____ 16

6. j divided by 4

j ____ 4

30428_T06__22 22 1/16/08 5:11:52 PM

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Reteaching

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22 Topic 6

Variables and ExpressionsA variable is a letter or symbol. It represents an unknown amount that can change.

You can do mathematical operations with variables and numbers.

You can state these operations in word expressions. You can also state them in algebraic expressions.

Operation ! " # $

Word expression the sum of r and 3

the difference between r and 3

the product of r and 3

the quotient of r and 3

Algebraic expression r ! 3 r " 3 3r r $ 3

Other ways of saying the word

expression

3 added to r3 more than r

3 subtracted from r3 less than r

r multiplied by 33 times r

r divided by 33 equal parts of r

Complete the algebraic expression for each of the following word expressions.

Circle the letter of the correct word expression for each algebraic expression.

7. t " 13 a. 13 subtracted from t b. t subtracted from 13

8. 4n a. 4 more than n b. 4 times n

9. 11 ! s a. 11 more than s b. 11 less than s

10. 45a a. the product of a and 45 b. 45 more than a

11. y $ 6 a. y less 6 b. 6 equal parts of y

12. v " 5 a. 5 less than v b. v subtracted from 5

1. the sum of b and 8

b ____ 8

4. 7 less than z

z ____ 7

2. the difference between m and 6

m ____ 6

5. 2 more than d

d ____ 2

3. the quotient of k and 16

k ____ 16

6. j divided by 4

j ____ 4

!"

#

" ! #

30428_T06_020-024_22 22 3/18/08 2:10:34 PM

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Practice 6-1

Practice

6-1

Topic 6 23

Variables and ExpressionsFor questions 1 through 4, use a variable to write an algebraic expression that represents the word phrase.

1. a number of apples divided into 12 baskets

2. 5 more than s

3. three times the cost for one hat

4. nine fewer than the total number of people

For 5 through 7, translate each algebraic expression into words.

5. 3 ! w

6. 8x

7. 40 " p

8. Write two different word phrases for the expression t __ 30 .

9. Number Sense Do 5 ! x and x ! 5 represent the same expression? Explain.

10. Algebra Dan is 12 in. taller than Jay. Use x for Jay’s height. Which expression shows Dan’s height?

A x ! 12 B x " 12 C 12 x D x ___ 12

11. Explain It Explain what the expression 6x means.

30428_T06__23 23 1/16/08 5:11:54 PM

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Practice 6-1

Practice

6-1

Topic 6 23

Variables and ExpressionsFor questions 1 through 4, use a variable to write an algebraic expression that represents the word phrase.

1. a number of apples divided into 12 baskets 2. 5 more than s 3. three times the cost for one hat 4. nine fewer than the total number of people For 5 through 7, translate each algebraic expression into words.

5. 3 ! w 6. 8x 7. 40 " p

8. Write two different word phrases for the expression t __ 30 .

9. Number Sense Do 5 ! x and x ! 5 represent the same expression? Explain.

10. Algebra Dan is 12 in. taller than Jay. Use x for Jay’s height. Which expression shows Dan’s height?

A x ! 12 B x " 12 C 12 x D x ___ 12

11. Explain It Explain what the expression 6x means.

Samples: A number t divided by 30, a number t times 1 __ 30 , 30 equal parts of t

Yes, because of the Commutative Property of Addition

n ! 12 or n __ 12 s " 53 # h or 3ht $ 9

Three plus a number wEight times a number xp less than 40

Sample: A number x multiplied by 6

30428_T06_020-024_23 23 3/18/08 2:10:37 PM

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Algebra

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Enrichment

6-1

24 Topic 6

Log OnMel spends time each evening designing games on his computer. The number of minutes he spends can be represented by the variable c. Use the variable to complete the exercises below.

1. Write an algebraic expression to represent the number of minutes Mel’s friend Gina spends designing games on her computer if she designs 45 min more an evening than Mel.

2. Write an algebraic expression to represent the time Mel will spend designing games on his computer in 9 weeks. (Remember: there are 7 days in 1 week.)

3. Mel designs games on his computer for 58 min (c ! 58). Mel’s friend Lou spends half the amount of time designing games on his computer that Mel does. Write an algebraic expression to represent this, and solve for the value.

4. Mel spent c min designing games on his computer on Monday, 70 min designing games on Tuesday, and 92 min designing games on Wednesday. Wednesday’s time can be represented by the variable w. The time Mel spent designing games on his computer on Monday was 1 _ 4 the time spent on Wednesday (c ! w __ 4 ). How much time did Mel spend designing games on his computer in those 3 days?

30428_T06__24 24 1/16/08 5:11:56 PM

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Enrichment

6-1

24 Topic 6

Log OnMel spends time each evening designing games on his computer. The number of minutes he spends can be represented by the variable c. Use the variable to complete the exercises below.

1. Write an algebraic expression to represent the number of minutes Mel’s friend Gina spends designing games on her computer if she designs 45 min more an evening than Mel.

2. Write an algebraic expression to represent the time Mel will spend designing games on his computer in 9 weeks. (Remember: there are 7 days in 1 week.)

3. Mel designs games on his computer for 58 min (c ! 58). Mel’s friend Lou spends half the amount of time designing games on his computer that Mel does. Write an algebraic expression to represent this, and solve for the value.

4. Mel spent c min designing games on his computer on Monday, 70 min designing games on Tuesday, and 92 min designing games on Wednesday. Wednesday’s time can be represented by the variable w. The time Mel spent designing games on his computer on Monday was 1 _ 4 the time spent on Wednesday (c ! w __ 4 ). How much time did Mel spend designing games on his computer in those 3 days?

c + 45

63c

185 min

c __ 2 , 58 ___ 2 , 29 min

30428_T06_020-024_24 24 3/18/08 2:10:40 PM

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Topic 6 25

Daily Spiral Review

6-2

1. Derrick is 13 inches taller than his little brother Cedric. Let c be Cedric’s height. Which gives Derrick’s height? A c ! 13 B c " 13 C 13 " c D 13 # c

2. Mr. Alvarez buys a table, 4 chairs, and a china cabinet for his dining room. What fraction of these pieces of furniture are chairs?

A 1 __ 4

B 1 __ 3

C 2 __ 3

D 3 __ 4

3. Shante and Dawn go out for dinner. Shante’s meal costs $12.45, and Dawn’s meal costs $13.29. What is the cost of the two meals together?A $25.64 B $25.74 C $35.64 D $36.74

4. Marnie’s score on a test is s. Lisa’s score is 7 points less than Marnie’s score. Write an expression that gives Lisa’s score.

5. A rocket travels 147,098,074 kilometers from Planet A to Planet B. Another rocket travels 152,097,701 kilometers from Planet A to Planet C. How much farther did the second rocket travel?

6. Sarah chooses 3 of these cards.

1 2 3 4 5

List all the different groups of 3 cards that Sarah could choose.

Daily Spiral Review

6-2

30428_T06__25 25 1/16/08 5:12:03 PM

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Topic 6 25

Daily Spiral Review

6-2

1. Derrick is 13 inches taller than his little brother Cedric. Let c be Cedric’s height. Which gives Derrick’s height? A c ! 13 B c " 13 C 13 " c D 13 # c

2. Mr. Alvarez buys a table, 4 chairs, and a china cabinet for his dining room. What fraction of these pieces of furniture are chairs?

A 1 __ 4

B 1 __ 3

C 2 __ 3

D 3 __ 4

3. Shante and Dawn go out for dinner. Shante’s meal costs $12.45, and Dawn’s meal costs $13.29. What is the cost of the two meals together?A $25.64 B $25.74 C $35.64 D $36.74

4. Marnie’s score on a test is s. Lisa’s score is 7 points less than Marnie’s score. Write an expression that gives Lisa’s score.

5. A rocket travels 147,098,074 kilometers from Planet A to Planet B. Another rocket travels 152,097,701 kilometers from Planet A to Planet C. How much farther did the second rocket travel?

6. Sarah chooses 3 of these cards.

1 2 3 4 5

List all the different groups of 3 cards that Sarah could choose.

Daily Spiral Review

6-2

s ! 7

4,999,627 kilometers

1, 2, 3; 1, 2, 4; 1, 2, 5; 1, 3 ,4; 1, 3, 5; 1, 4, 5; 2, 3, 4; 2, 3, 5; 2, 4, 5; 3, 4, 5

30428_T06_025_25 25 3/18/08 2:10:50 PM

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Problem of the Day 6-2

6-2Problem of the DayProblem

of the Day

6-2

26

Topic 6

Alberto and Toshi are on a 7-day hike. They hike 10 miles on the first day, 12 miles on the second day, 14 miles on the third day, and 16 miles on the fourth day. If this pattern continues, how many miles will they hike on the seventh day?

30428_T06__26 26

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Topic 6 27

Interactive Learning Recording Sheet

10

Interactive Learning Recording Sheet 1

0

1.

2.

3.

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Topic 6 27


10


0

1.

2.

3.

Number of Friends

Number of Favors

1 3

2 6

3 9

4 12

Number of Packages

Number of Muffins

1 4

2 8

3 12

4 16

Number of Cartons

Number of Eggs

1 6

2 12

3 18

4 24

n ! 4; 4n

n ! 3; 3n

n ! 6; 6n

Sam

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Name Quick Check

6-2Q

uick

Che

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28 Topic 6

1. Derek is 5 inches taller than Erin. Evaluateh ! 5 for h " 52 inches to find out how tall Derek is if Erin is 52 inches tall.

A 47 inches

B 52 inches

C 57 inches

D 62 inches

2. Evaluate the expression for n " 8. 35.6 # n

A 30.6

B 29.6

C 28.6

D 27.6

3. Writing to Explain Larry and Martha each planted the same number of carrot seeds in their gardens. After 4 weeks, Larry had c carrots and Martha had 6 more than Larry.

a. Write an algebraic expression for the number of carrots Martha had after 4 weeks.

b. Evaluate the expression for c " 15, 20, and 25.

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30428_T06__28 28 1/16/08 5:12:23 PM

Name Quick Check

6-2Q

uick

Che

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28 Topic 6

1. Derek is 5 inches taller than Erin. Evaluateh ! 5 for h " 52 inches to find out how tall Derek is if Erin is 52 inches tall.

A 47 inches

B 52 inches

C 57 inches

D 62 inches

2. Evaluate the expression for n " 8. 35.6 # n

A 30.6

B 29.6

C 28.6

D 27.6

3. Writing to Explain Larry and Martha each planted the same number of carrot seeds in their gardens. After 4 weeks, Larry had c carrots and Martha had 6 more than Larry.

a. Write an algebraic expression for the number of carrots Martha had after 4 weeks.

b. Evaluate the expression for c " 15, 20, and 25.

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See student samples at the right.

30428_T06_028-031_28 28 3/18/08 2:11:27 PM

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Patterns and ExpressionsChan makes beaded necklaces for gifts. To make a necklace, he strings beads onto thin ribbon. To tie the necklace, he cuts the ribbon 10 inches longer than the length he wants to bead. The chart shows the length of the ribbon for different beaded lengths.

Word Expression NumberExpression

Algebraic Expression

10 inches longer than 11-inch beaded section11 ! 10


10 inches longer than z-inch beaded sectionz ! 10

Zoe is going to use Chan’s algebraic expression to make two necklaces. She wants to make one with a 10-inch beaded section. The other necklace will have a 12-inch beaded section. Here is how she evaluated the expression.


Number Expression Word Expression Evaluated

Expression

z ! 10 10 ! 1010 inches longer than 10-inch beaded section

20


22

Chan also makes beaded bracelets. The chart shows the length of the beaded part of the bracelet. The second column shows the length of the ribbon he uses to make it.

1. Write a word expression that describes the pattern of the relationship.

Reteaching 6-2

Reteaching

6-2

BeadedLength (in.)

RibbonLength (in.)

5 5 ! 76 6 ! 78 8 ! 7

Topic 6 29

30428_T06__29 29 1/16/08 5:12:25 PM

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Patterns and ExpressionsChan makes beaded necklaces for gifts. To make a necklace, he strings beads onto thin ribbon. To tie the necklace, he cuts the ribbon 10 inches longer than the length he wants to bead. The chart shows the length of the ribbon for different beaded lengths.

Word Expression NumberExpression




10 inches longer than z-inch beaded sectionz ! 10

Zoe is going to use Chan’s algebraic expression to make two necklaces. She wants to make one with a 10-inch beaded section. The other necklace will have a 12-inch beaded section. Here is how she evaluated the expression.


Number Expression Word Expression Evaluated

Expression


20


22

Chan also makes beaded bracelets. The chart shows the length of the beaded part of the bracelet. The second column shows the length of the ribbon he uses to make it.

1. Write a word expression that describes the pattern of the relationship.

Reteaching 6-2

Reteaching

6-2

BeadedLength (in.)

RibbonLength (in.)

5 5 ! 76 6 ! 78 8 ! 7

Topic 6 29

The ribbon length is 7 inches longer than the beaded section.

30428_T06_028-031_29 29 3/18/08 2:11:29 PM

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Practice

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30 Topic 6

Patterns and ExpressionsIn 1 through 4, evaluate each expression for n ! 3 and n ! 8.

1. n " 10 2. 24 ___ n

3. n # 5 4. 36 $ n

Complete each table.

5. 6.

7. Write a Problem Write a situation that can be represented by the algebraic expression $3.50t.

8. Algebra If a ! 10, which of the following is the correct solution for a # 0.1?

A 0.01 B 0.1 C 1 D 10

9. Explain It Write one numerical expression and one algebraic expression. Then explain what the difference between a numerical and algebraic expression is.

n 0.9 + n0.5

0.2

0.15

0.1

n 96 ! n1

2

3

4

30428_T06__30 30 1/16/08 5:12:27 PM

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Practice

6-2Pr

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30 Topic 6

Patterns and ExpressionsIn 1 through 4, evaluate each expression for n ! 3 and n ! 8.

1. n " 10 2. 24 ___ n

3. n # 5 4. 36 $ n


5. 6.

7. Write a Problem Write a situation that can be represented by the algebraic expression $3.50t.

8. Algebra If a ! 10, which of the following is the correct solution for a # 0.1?

A 0.01 B 0.1 C 1 D 10

9. Explain It Write one numerical expression and one algebraic expression. Then explain what the difference between a numerical and algebraic expression is.

n 0.9 + n0.5

0.2

0.15

0.1

n 96 ! n1

2

3

4

13; 18 8; 3

15; 40 33; 28

Check students’ work.

Check students’ work. An algebraicexpression has a variable.

1.4 1.1 1.05 1.0

96 48 32 24

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Algebra

Enrichment

6-2Enrichm

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Topic 6 31

Family FunRon has 4 more sisters than he has brothers, and he has 2 brothers. He is one-third the age of his eldest brother. He is three times the age of his youngest sister. For the exercises below, tell if the statement about Ron’s family is true or false and explain why.

1. If Ron’s brothers are represented by the variable b, and his sisters are represented by the variable s, the algebraic expression b ! 4 " s represents the number of sisters he has.

2. If the age of Ron’s youngest sister is represented by the variable y, and Ron’s age is represented as r, his youngest sister’s age can be represented as y _ r " 3.

3. If the age of Ron’s oldest brother is represented by the variable x and Ron’s age is represented as r, Ron’s age can be represented as x _ 3 " r.

4. If the number of sisters Ron has is represented by the variable s, then the number of brothers he has can be represented as s # 4.

5. There are 8 children in Ron’s family.

30428_T06__31 31 1/16/08 5:12:29 PM

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Algebra

Enrichment

6-2Enrichm

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Topic 6 31

Family FunRon has 4 more sisters than he has brothers, and he has 2 brothers. He is one-third the age of his eldest brother. He is three times the age of his youngest sister. For the exercises below, tell if the statement about Ron’s family is true or false and explain why.

1. If Ron’s brothers are represented by the variable b, and his sisters are represented by the variable s, the algebraic expression b ! 4 " s represents the number of sisters he has.

2. If the age of Ron’s youngest sister is represented by the variable y, and Ron’s age is represented as r, his youngest sister’s age can be represented as y _ r " 3.

3. If the age of Ron’s oldest brother is represented by the variable x and Ron’s age is represented as r, Ron’s age can be represented as x _ 3 " r.

4. If the number of sisters Ron has is represented by the variable s, then the number of brothers he has can be represented as s # 4.

5. There are 8 children in Ron’s family.

False. b ! 4 " s representsthe number of sisters.

False. r _ 3 " y is the correct expression.

True x _ 3 " r is the correct expression.

False. s # 4 represents the number of brothers Ron has.

False. Ron has 2 brothers ! 4 moresisters than brothers " 6 sisters.2 ! 6 ! Ron " 9 children

30428_T06_028-031_31 31 3/18/08 2:11:35 PM

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32 Topic 6

Daily

Spi

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-3

1. Kayla plays a game with colored cards. She gets 4 points for each blue card. Which expression tells her total points when she has b blue cards? A b B 4b C 4 ! b D 4b " b

2. The map shows bike paths through a city park.

ShortcutPath

HillPath

Speed Path

RockyPath

Which two paths appear to be parallel?A Hill and Rocky B Speed and Hill C Shortcut and Speed D Rocky and Shortcut

3. A town charges a sales tax of $0.0825 for every dollar spent. What is this amount rounded to the nearest hundredth?A $0.09 B $0.08 C $0.03 D $0.01

4. A farmer has a apples. She puts them in 36 baskets. Each basket has the same number of apples. Write an expression that gives the number of apples in 1 basket.

5. The thermometer shows the temperature at noon. The temperature drops 19°F by midnight. What is the temperature at midnight?

70

80

60

50

#F

6. Last year, Alvin worked 12 hours each week for 50 weeks. How many hours did Alvin work last year?

Daily Spiral Review

6-3

30428_T06__32 32 1/16/08 5:12:35 PM

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32 Topic 6

Daily

Spi

ral R

evie

w 6

-3

1. Kayla plays a game with colored cards. She gets 4 points for each blue card. Which expression tells her total points when she has b blue cards? A b B 4b C 4 ! b D 4b " b

2. The map shows bike paths through a city park.

ShortcutPath

HillPath

Speed Path

RockyPath

Which two paths appear to be parallel?A Hill and Rocky B Speed and Hill C Shortcut and Speed D Rocky and Shortcut

3. A town charges a sales tax of $0.0825 for every dollar spent. What is this amount rounded to the nearest hundredth?A $0.09 B $0.08 C $0.03 D $0.01

4. A farmer has a apples. She puts them in 36 baskets. Each basket has the same number of apples. Write an expression that gives the number of apples in 1 basket.

5. The thermometer shows the temperature at noon. The temperature drops 19°F by midnight. What is the temperature at midnight?

70

80

60

50

#F

6. Last year, Alvin worked 12 hours each week for 50 weeks. How many hours did Alvin work last year?

Daily Spiral Review

6-3

a ! 36

600 hours

58ºF

30428_T06_032_32 32 3/18/08 2:11:47 PM


Topic 6 3

3


6-3Problem of the Day

Problem of the Day

6-3

Mary is older than Henry and younger than Jean. Mary is younger than Karen. Jean is older than Tom and younger than Mark. Tom is older than Mary. Who is the youngest?

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11

Miles DrivenCost for Miles Driven Final Cost

30

40

75

100

125

250

34 Topic 6

Inte

ract

ive

Lear

ning

Re

cord

ing

Shee

t 11

30428_T06__34 34 1/16/08 5:12:51 PM

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11

Miles DrivenCost for Miles Driven Final Cost

30

40

75

100

125

250

34 Topic 6

Inte

ract

ive

Lear

ning

Re

cord

ing

Shee

t 11

$2n 40 ! 2n

$2 " 30

$2 " 40

$2 " 75

$2 " 100

$2 " 125

$2 " 250

40 ! (2 " 30) # $100

40 ! (2 " 40) # $120

40 ! (2 " 75) # $190

40 ! (2 " 100) # $240

40 ! (2 " 125) # $290

40 ! (2 " 250) # $540

Molly

30428_T06_034-034_34 34 3/18/08 2:12:14 PM

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Topic 6 35

Quick Check

6-3

1. Which algebraic expression correctly represents the phrase: thirteen times a number, minus 8? Let x represent the number.

A 13(x ! 8)

B 13(x) ! 13(8)

C 13x ! 8

D 13 ! 8x

2. Which expression represents the phrase: 6 less than a number, times 5?

A (6 ! n) " 5

B (n ! 6) " 5

C 6 ! 5n

D 5n ! 6

3. Micah started an exercise program. The first day, he walked 20 minutes. Each day after that, he added 4 minutes to his walking time the previous day. Which expression shows how far Micah walked n days after he started?

A 4n # 20

B 20n # 4

C 4(n # 20)

D 20(n ! 4)

4. Your monthly phone bill is $18 plus $2.50 for each optional service. Which expression represents a bill including s optional services?

A $18 " $2.50 " s

B $18 # $2.50 " s

C $18 # $2.50 # s

D $18 " s # $2.50

5. Writing to Explain A carpet installer charges $75 for each room to cover supplies, plus $55 an hour for his labor. Write an expression for the cost of a one-room installation that requires x hours to complete. Then calculate the total charge if the job takes 4 hours and the total charge if it takes 6 hours.

Quick C

heck 6-3

30428_T06__35 35 1/16/08 5:12:58 PM

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Topic 6 35

Quick Check

6-3

1. Which algebraic expression correctly represents the phrase: thirteen times a number, minus 8? Let x represent the number.

A 13(x ! 8)

B 13(x) ! 13(8)

C 13x ! 8

D 13 ! 8x

2. Which expression represents the phrase: 6 less than a number, times 5?

A (6 ! n) " 5

B (n ! 6) " 5

C 6 ! 5n

D 5n ! 6

3. Micah started an exercise program. The first day, he walked 20 minutes. Each day after that, he added 4 minutes to his walking time the previous day. Which expression shows how far Micah walked n days after he started?

A 4n # 20

B 20n # 4

C 4(n # 20)

D 20(n ! 4)

4. Your monthly phone bill is $18 plus $2.50 for each optional service. Which expression represents a bill including s optional services?

A $18 " $2.50 " s

B $18 # $2.50 " s

C $18 # $2.50 # s

D $18 " s # $2.50

5. Writing to Explain A carpet installer charges $75 for each room to cover supplies, plus $55 an hour for his labor. Write an expression for the cost of a one-room installation that requires x hours to complete. Then calculate the total charge if the job takes 4 hours and the total charge if it takes 6 hours.

Quick C

heck 6-3


30428_T06_035_035_35 35 3/18/08 2:12:28 PM

Cleaning fee 2-day rental 3-day rental 5-day rental

$12 $35

$35

$35

$35 $35

$35 $35

$35 $35 $35

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36 Topic 6

Reteaching

6-3Re

teac

hing

6-3

More Patterns and ExpressionsYou can use variables to write and evaluate expressions.

Sunny Rent-A-Car rents cars for $35 per day plus a $12 fee for cleaning the car when you return it. Write an algebraic expression for the total cost of a car rental. Evaluate the expression for a 2-day car rental; for a 3-day car rental; for a 5-day car rental.

Step 1. The total cost is the cleaning fee plus the cost per day times the number of days. Since the number of days can change, it is your variable. Use d for the number of days.

Step 2. To evaluate the expression, think about counting out the money to pay for the car rental. Each rental will have a stack of $12 for the cleaning fee. Then, each rental will have a stack of $35 for each day. A 2-day rental will have 2 stacks of $35. A 3-day rental will have 3 stacks of $35. A 5-day rental will have 5 stacks of $35.

Step 3. To solve for the total cost of the car rentals, multiply the number of stacks by $35. Then, add the $12 stack.

2-day rental (2 ! 35) " 12 # 82 A 2-day rental will cost $82.3-day rental (3 ! 35) " 12 # 117 A 3-day rental will cost $117.5-day rental (5 ! 35) " 12 # 187 A 5-day rental will cost $187.

Write an algebraic expression for each phrase. Let n stand for the number. Evaluate each expression for n # 4. 1. 3 plus 4 times a

number 2. 7 times a number,

minus 2 3. 6 less than a number

times 15

30428_T06__36 36 1/16/08 5:13:06 PM

Cleaning fee 2-day rental 3-day rental 5-day rental

$12 $35

$35

$35

$35 $35

$35 $35

$35 $35 $35

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36 Topic 6

Reteaching

6-3Re

teac

hing

6-3

More Patterns and ExpressionsYou can use variables to write and evaluate expressions.

Sunny Rent-A-Car rents cars for $35 per day plus a $12 fee for cleaning the car when you return it. Write an algebraic expression for the total cost of a car rental. Evaluate the expression for a 2-day car rental; for a 3-day car rental; for a 5-day car rental.

Step 1. The total cost is the cleaning fee plus the cost per day times the number of days. Since the number of days can change, it is your variable. Use d for the number of days.

Step 2. To evaluate the expression, think about counting out the money to pay for the car rental. Each rental will have a stack of $12 for the cleaning fee. Then, each rental will have a stack of $35 for each day. A 2-day rental will have 2 stacks of $35. A 3-day rental will have 3 stacks of $35. A 5-day rental will have 5 stacks of $35.

Step 3. To solve for the total cost of the car rentals, multiply the number of stacks by $35. Then, add the $12 stack.

2-day rental (2 ! 35) " 12 # 82 A 2-day rental will cost $82.3-day rental (3 ! 35) " 12 # 117 A 3-day rental will cost $117.5-day rental (5 ! 35) " 12 # 187 A 5-day rental will cost $187.

Write an algebraic expression for each phrase. Let n stand for the number. Evaluate each expression for n # 4. 1. 3 plus 4 times a

number 2. 7 times a number,

minus 2 3. 6 less than a number

times 15

35d ! 12

3 ! 4n; 19 7n " 2; 26 15n " 6; 54

30428_T06_036_036_36 36 3/18/08 2:12:42 PM

n 60 ! n

1

2

3

4

n 0.7 " n

0.5

0.2

0.15

0.1

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Topic 6 37

Practice

6-3More Patterns and Expressions 1. Write an algebraic expression to represent the cost of a

concert ticket, h, with a service charge of $6.75.

2. Write an algebraic expression to represent the cost of m gallons of gasoline if each gallon costs $1.45.

Evaluate each expression for n ! 3 and n ! 6.

3. 0.2 " n 4. n # 2.1

5. 12 ___ n 6. 35 $ n


7. 8.

9. Explain It What is another way to write the expression 44n? What is another way to write the expression 44 % n?

10. Which is the correct product of n " 7 if n ! $0.25?

A $3.25 B $2.75 C $2.25 D $1.75

11. Write a Problem Write a situation that can be represented by the algebraic expression $3.25d.

Practice 6-3

30428_T06__37 37 1/16/08 5:13:13 PM

n 60 ! n

1

2

3

4

n 0.7 " n

0.5

0.2

0.15

0.1

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Topic 6 37

Practice

6-3More Patterns and Expressions 1. Write an algebraic expression to represent the cost of a

concert ticket, h, with a service charge of $6.75.

2. Write an algebraic expression to represent the cost of m gallons of gasoline if each gallon costs $1.45.

Evaluate each expression for n ! 3 and n ! 6.

3. 0.2 " n 4. n # 2.1

5. 12 ___ n 6. 35 $ n


7. 8.

9. Explain It What is another way to write the expression 44n? What is another way to write the expression 44 % n?

10. Which is the correct product of n " 7 if n ! $0.25?

A $3.25 B $2.75 C $2.25 D $1.75

11. Write a Problem Write a situation that can be represented by the algebraic expression $3.25d.

Practice 6-3

44 # n; 44 ___ n

0.6 1.2 0.9 3.9

Sample answer: Keri buys d candles at $3.25 each.

h " $6.75

m # $1.45 or $1.45m

4 2 38 41

60302015

1.2 .9 .85 .8

30428_T06_037_040_37 37 3/18/08 2:12:57 PM

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38 Topic 6

Enrichment

6-3

Algebra

Enric

hmen

t 6-3

Prime TimeBill spends time each evening watching television. This amount of time, in minutes, can be represented by the variable t. Use the variable to complete the exercises below.

1. Write an algebraic expression to represent the time Bill’s friend Jill spends watching television if she watches 30 min more an evening than Bill.

2. Write an algebraic expression to represent the time Bill will spend watching television in 8 weeks. (Remember: There are 7 days in 1 week.)

3. Bill watches television for 52 min (t ! 52). Bill’s friend Hilda watches half the amount of television that Bill does. Write an algebraic expression to represent this, and solve for the value.

4. Bill spent t min watching television on Monday, 60 min watching television on Tuesday, and 90 min watching television on Wednesday. Wednesday’s time can be represented by the variable w. The time Bill spent watching television on Monday was 1 _ 2 the time spent on Wednesday (t ! w __ 2 ). How much time did Bill spend watching television in those 3 days?

30428_T06__38 38 1/16/08 5:13:16 PM

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38 Topic 6

Enrichment

6-3

Algebra

Enric

hmen

t 6-3

Prime TimeBill spends time each evening watching television. This amount of time, in minutes, can be represented by the variable t. Use the variable to complete the exercises below.

1. Write an algebraic expression to represent the time Bill’s friend Jill spends watching television if she watches 30 min more an evening than Bill.

2. Write an algebraic expression to represent the time Bill will spend watching television in 8 weeks. (Remember: There are 7 days in 1 week.)

3. Bill watches television for 52 min (t ! 52). Bill’s friend Hilda watches half the amount of television that Bill does. Write an algebraic expression to represent this, and solve for the value.

4. Bill spent t min watching television on Monday, 60 min watching television on Tuesday, and 90 min watching television on Wednesday. Wednesday’s time can be represented by the variable w. The time Bill spent watching television on Monday was 1 _ 2 the time spent on Wednesday (t ! w __ 2 ). How much time did Bill spend watching television in those 3 days?

t ! 30

56t

t __ 2 , 52 __ 2 26 min

195 min

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Topic 6 39

1. Which answer shows the algebraic expression for the following phrase?

Five times a number plus three

A 5n ! 3B 5 ! 3nC 5 " 3 ! nD 5 ! n " 3

2. Evaluate the following expression.

(32 ! 12) # 17

A 37B 33C 28D 27

3. Evaluate the following expression for y $ 11.

63 # 4y

A 18B 19C 21D 29

4. To complete a project, Roshan must spend 3 hours on research and 2 hours writing each page. Write an expression for the total hours she needs.

Use the expression to evaluate for 12 pages.


5. Evaluate the following expressions for x $ 33.

288 # 4x

10x ! 17

8x # 201

Daily Spiral Review

6-4

Daily Spiral Review

6-4

30428_T06__39 39 1/16/08 5:13:17 PM

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Topic 6 39

1. Which answer shows the algebraic expression for the following phrase?

Five times a number plus three

A 5n ! 3B 5 ! 3nC 5 " 3 ! nD 5 ! n " 3

2. Evaluate the following expression.

(32 ! 12) # 17

A 37B 33C 28D 27

3. Evaluate the following expression for y $ 11.

63 # 4y

A 18B 19C 21D 29

4. To complete a project, Roshan must spend 3 hours on research and 2 hours writing each page. Write an expression for the total hours she needs.



5. Evaluate the following expressions for x $ 33.

288 # 4x

10x ! 17

8x # 201

Daily Spiral Review

6-4

Daily Spiral Review

6-4

3 ! 2p

27 hours

45 hours

156

347

63

30428_T06_037_040_39 39 3/18/08 2:13:02 PM


40

Topic 6


Every 42 minutes, a bell rings to indicate it is time to change classes. If the school day is 6 hours long, how many classes are held each day?

Problem of the Day

6-4


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Topic 6 41

8

10

4

1. !


12


2

30428_T06__41 41 1/16/08 5:13:25 PM

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42 Topic 6

1. Use the Distributive Property to rewrite the numeric expression: 307 ! 13.

A (300 ! 10) " (7 ! 3)B (300 ! 13 " (70 ! 13)C (300 ! 13) " (7 ! 13)D (3 ! 100) " (7 ! 13)

2. Which algebraic expression has the same value as 32x " 8?A 4(x + 2)B 8(4x + 1)C 4(8x + 1)D 8(4x + 8)

3. The perimeter of a rectangle can be calculated byperimeter = 2(length " width). What is the width of a rectangle

with a perimeter of 50 cm and a length of 20 cm?A 5 cmB 10 cmC 20 cmD 30 cm

4. Which expression shows the number of shaded squares?

A (20 ! 7) # (20 ! 6)B (20 ! 6) # (7 ! 6)C (20 ! 6) " (7 ! 6)D (20 ! 13) " (6 ! 7)

5. Writing to Explain The PTA gives Mr. Andrews some money to buy supplies for his class. There are 23 students in the class. Each kit of supplies costs $2.04. Use the Distributive Property to write an expression that shows how to calculate the total cost of Mr. Andrews’s purchase. Then evaluate the expression to determine the cost.

Quick Check

6-4Q

uick

Che

ck 6-4

30428_T06__42 42 1/16/08 5:13:33 PM

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42 Topic 6

1. Use the Distributive Property to rewrite the numeric expression: 307 ! 13.

A (300 ! 10) " (7 ! 3)B (300 ! 13 " (70 ! 13)C (300 ! 13) " (7 ! 13)D (3 ! 100) " (7 ! 13)

2. Which algebraic expression has the same value as 32x " 8?A 4(x + 2)B 8(4x + 1)C 4(8x + 1)D 8(4x + 8)

3. The perimeter of a rectangle can be calculated byperimeter = 2(length " width). What is the width of a rectangle

with a perimeter of 50 cm and a length of 20 cm?A 5 cmB 10 cmC 20 cmD 30 cm

4. Which expression shows the number of shaded squares?

A (20 ! 7) # (20 ! 6)B (20 ! 6) # (7 ! 6)C (20 ! 6) " (7 ! 6)D (20 ! 13) " (6 ! 7)

5. Writing to Explain The PTA gives Mr. Andrews some money to buy supplies for his class. There are 23 students in the class. Each kit of supplies costs $2.04. Use the Distributive Property to write an expression that shows how to calculate the total cost of Mr. Andrews’s purchase. Then evaluate the expression to determine the cost.

Quick Check

6-4Q

uick

Che

ck 6-4


30428_T06_042_051_42 42 3/18/08 2:13:26 PM

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Topic 6 43

Distributive PropertyHector’s rock collection is in 7 cases. Each case holds 28 rocks. How many rocks are in Hector’s collection? You can use the Distributive Property to find the product of 7 ! 28.

ORStep 1. Split 28 into 20 " 8.7 ! 28 # 7 ! (20 " 8)

Step 2. Multiply 7 times each part of the sum. (7 ! 20) " (7 ! 8)

140 " 56

Step 3. Use addition to find the sum.140 " 56 # 196

Step 1. Split 28 into 30 $ 2.7 ! 28 # 7 ! (30 $ 2)

Step 2. Multiply 7 times each part of the difference.(7 ! 30) $ (7 ! 2)

210 $ 14

Step 3. Use subtraction to find the difference.

210 $ 14 # 196So, 7 ! 28 # 196. Hector has 196 rocks in his collection.

Rewrite using the Distributive Property. Then find the product.

1. 3 ! 42 2. 39 ! 5 3. 6 ! 147 4. 19 ! 70

5. 54 ! 67 6. 90 ! 83 7. 364 ! 26 8. 45 ! 678

Algebra For questions 9 through 12, find the value of n.

9. 4 ! 62 # (4 ! n) " (4 ! 2)

10. 79 ! 20 # (80 ! 20) $ (n ! 20)

11. 53 ! 118 # (53 ! 100) " (n ! 18)

12. 352 ! 75 # (n ! 75) " (50 ! 75) " (2 ! 75)

13. Joey’s class is collecting food for the school canned food drive. There are 28 children in Joey’s class. Each child brought in 15 cans of food. Use the Distributive Property to find out how many cans of food Joey’s class collected.

Reteaching

6-4Reteaching 6

-4

30428_T06__43 43 1/16/08 5:13:34 PM

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Topic 6 43

Distributive PropertyHector’s rock collection is in 7 cases. Each case holds 28 rocks. How many rocks are in Hector’s collection? You can use the Distributive Property to find the product of 7 ! 28.

ORStep 1. Split 28 into 20 " 8.7 ! 28 # 7 ! (20 " 8)

Step 2. Multiply 7 times each part of the sum. (7 ! 20) " (7 ! 8)

140 " 56

Step 3. Use addition to find the sum.140 " 56 # 196

Step 1. Split 28 into 30 $ 2.7 ! 28 # 7 ! (30 $ 2)

Step 2. Multiply 7 times each part of the difference.(7 ! 30) $ (7 ! 2)

210 $ 14

Step 3. Use subtraction to find the difference.

210 $ 14 # 196So, 7 ! 28 # 196. Hector has 196 rocks in his collection.

Rewrite using the Distributive Property. Then find the product.

1. 3 ! 42 2. 39 ! 5 3. 6 ! 147 4. 19 ! 70

5. 54 ! 67 6. 90 ! 83 7. 364 ! 26 8. 45 ! 678

Algebra For questions 9 through 12, find the value of n.

9. 4 ! 62 # (4 ! n) " (4 ! 2)

10. 79 ! 20 # (80 ! 20) $ (n ! 20)

11. 53 ! 118 # (53 ! 100) " (n ! 18)

12. 352 ! 75 # (n ! 75) " (50 ! 75) " (2 ! 75)

13. Joey’s class is collecting food for the school canned food drive. There are 28 children in Joey’s class. Each child brought in 15 cans of food. Use the Distributive Property to find out how many cans of food Joey’s class collected.

Reteaching

6-4

Reteaching 6-4

126 195 882 1,330

3,618 7,470 9,464 30,510

601

53300

(15 ! 30 ) " (15 ! 2 ) # 450 " 30 # 420 cans

30428_T06_042_051_43 43 3/18/08 2:13:29 PM

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44 Topic 6

Distributive PropertyUse the Distributive Property to multiply mentally.

1. 5 ! 607 " 2. 16 ! 102 "

3. 7 ! 420 " 4. 265 ! 5 "

5. 44 ! 60 " 6. 220 ! 19 "

7. 45 ! 280 " 8. 341 ! 32 "

9. Number Sense Fill in the blanks to show how the Distributive Property can be used to find 10 ! 147.

10 ! (150 # 3) " (10 ! 150) # ( ! 3) "

1,500 # "

10. In 1990, there were 1,133 tornadoes in the U.S. If there were the same number of tornadoes for 10 years in a row, what would be the 10-year total?

11. There were 1,071 tornadoes in the U.S. in 2000. What is the number of tornadoes multiplied by 20?

12. If 4 ! 312 " 4 ! 300 $ n, which is the value of n?A 4 B 12 C 48 D 300

13. Explain It Margaret said that she used the Distributive Property to solve 4 ! 444. Is her answer shown below correct? Explain.

4 ! 444 " 4 ! (400 $ 40 $ 4) "(4 ! 400) $ (4 ! 40) $ (4 ! 4) "1,600 $ 160 $ 16 " 1,776

Practice

6-4Pr

actic

e 6-4

30428_T06__44 44 1/16/08 5:13:36 PM

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44 Topic 6

Distributive PropertyUse the Distributive Property to multiply mentally.

1. 5 ! 607 " 2. 16 ! 102 "

3. 7 ! 420 " 4. 265 ! 5 "

5. 44 ! 60 " 6. 220 ! 19 "

7. 45 ! 280 " 8. 341 ! 32 "

9. Number Sense Fill in the blanks to show how the Distributive Property can be used to find 10 ! 147.

10 ! (150 # 3) " (10 ! 150) # ( ! 3) "

1,500 # "

10. In 1990, there were 1,133 tornadoes in the U.S. If there were the same number of tornadoes for 10 years in a row, what would be the 10-year total?

11. There were 1,071 tornadoes in the U.S. in 2000. What is the number of tornadoes multiplied by 20?

12. If 4 ! 312 " 4 ! 300 $ n, which is the value of n?A 4 B 12 C 48 D 300

13. Explain It Margaret said that she used the Distributive Property to solve 4 ! 444. Is her answer shown below correct? Explain.

4 ! 444 " 4 ! (400 $ 40 $ 4) "(4 ! 400) $ (4 ! 40) $ (4 ! 4) "1,600 $ 160 $ 16 " 1,776

Practice

6-4Pr

actic

e 6-4

2,640

3,035 1,6322,940 1,325

4,18012,600 10,912

1030 1,470

11,330

21,420

Margaret correctly used the Distributive Property to solve 4 ! 444.

30428_T06_042_051_44 44 3/18/08 2:13:31 PM

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Topic 6 45

Find the Products1. Circle the letter of the problem that has the greatest

product.

a. 85 b. 224 c. 471 ! 41 ! 13 ! 5

2. Write an estimate for each product in Exercise 1.

a. b. c.

3. Find the exact product for each problem in Exercise 1.

a. b. c.

4. Circle the letter of the problem that has a product that is about four times greater than the product of one of the other problems.

a. 201 b. 509 c. 198 ! 79 ! 11 ! 20


a. b. c.


a. b. c.

7. What are some real-life situations in which you would not want an estimate that is too low or too high? Write one example of each.

Enrichment

6-4Enrichm

ent 6-4

Reasoning

30428_T06__45 45 1/16/08 5:13:38 PM

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Topic 6 45

Find the Products1. Circle the letter of the problem that has the greatest

product.

a. 85 b. 224 c. 471 ! 41 ! 13 ! 5


a. b. c.


a. b. c.

4. Circle the letter of the problem that has a product that is about four times greater than the product of one of the other problems.

a. 201 b. 509 c. 198 ! 79 ! 11 ! 20


a. b. c.


a. b. c.

7. What are some real-life situations in which you would not want an estimate that is too low or too high? Write one example of each.

Enrichment

6-4

Enrichment 6

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Reasoning

3,600 3,000 2,500

3,485 2,912 2,355

16,000 5,500 4,000

15,879 5,599 3,960

Check that students have written oneexample of an underestimate and oneexample of an overestimate.

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46 Topic 6

1. Giancarlo and his friends are getting ready for a costume party. They buy 6 packages of fake noses and 8 packages of masks. Each package contains 2 sets. Use the Distributive Property to ! nd the answer that shows how many sets of costume party items Giancarlo and his friends have bought altogether.A 28B 22C 20D 16

2. Which answer shows how you can use the Distributive Property to ! nd the product of 16 ! 34?A (10 ! 30) " (6 ! 4)B (10 ! 34) " (16 ! 4)C (16 ! 3) " (16 ! 4)D (16 ! 30) " (16 ! 4)

3. Evaluate the following expressions, using the parentheses to choose which operations to solve ! rst.

(44 # 12) " 3 ! (8 $ 2)

(7 ! 11) # (16 " 28)

4. Rewrite the problem using the Distributive Property, and then ! nd the product.

607 ! 20

5. Use the Distributive Property to ! ll in the blanks.

411 ! 8 % (400 ! ) " ( ! 8)

% " 88

%

Daily Spiral Review

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46 Topic 6

1. Giancarlo and his friends are getting ready for a costume party. They buy 6 packages of fake noses and 8 packages of masks. Each package contains 2 sets. Use the Distributive Property to ! nd the answer that shows how many sets of costume party items Giancarlo and his friends have bought altogether.A 28B 22C 20D 16

2. Which answer shows how you can use the Distributive Property to ! nd the product of 16 ! 34?A (10 ! 30) " (6 ! 4)B (10 ! 34) " (16 ! 4)C (16 ! 3) " (16 ! 4)D (16 ! 30) " (16 ! 4)

3. Evaluate the following expressions, using the parentheses to choose which operations to solve ! rst.

(44 # 12) " 3 ! (8 $ 2)

(7 ! 11) # (16 " 28)

4. Rewrite the problem using the Distributive Property, and then ! nd the product.

607 ! 20

5. Use the Distributive Property to ! ll in the blanks.

411 ! 8 % (400 ! ) " ( ! 8)

% " 88

%

Daily Spiral Review

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4433

(600 ! 20) " (7 ! 20) # 12,000 " 140 # 12,140

8 113,2003,288

30428_T06_042_051_46 46 3/18/08 2:13:37 PM


Topic 6 4

7

There were 126 applicants for a sales job. For every 4 who would relocate, there were 2 who would not relocate. How many applicants would relocate?



Problem of the Day

6-5

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48 Topic 6

1. What is the value of the expression? Use the correct order of operations.

4 ! 5 " 9 # 2 ! (6 " 1)

A 15B 69C 119D 378

2. What is the ! rst operation that you will perform when you evaluate this expression?

12 " (18 # a) ! 3 $ 24

A additionB subtractionC multiplicationD division

3. How would you insert parentheses to make the equation true?

2 ! 4 " 6 # 2 " 8 $ 4 % 18

A 2 ! 4 " (6 # 2) " 8 $ 4 % 18B (2 ! 4 " 6) # 2 " 8 $ 4 % 18C 2 ! 4 " 6 # (2 " 8 $ 4) % 18D 2 ! (4 " 6 # 2) " 8 $ 4 % 18

4. How can this expression be simpli! ed? Use the correct order of operations.

3 " 2 ! a " b ! 4 $ 2 # 4

A 2a " 2b # 1B 2a " 2b # 2C 2a # 2b " 3D 5a " 2b # 4

5. Writing to Explain Evaluate the expression below step by step, identifying the operations that you perform and the order in which you perform them.

18 " 5 " (5 # 3) ! 6 $ 3 # 2

Quick Check

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48 Topic 6

1. What is the value of the expression? Use the correct order of operations.

4 ! 5 " 9 # 2 ! (6 " 1)

A 15B 69C 119D 378

2. What is the ! rst operation that you will perform when you evaluate this expression?

12 " (18 # a) ! 3 $ 24


3. How would you insert parentheses to make the equation true?

2 ! 4 " 6 # 2 " 8 $ 4 % 18

A 2 ! 4 " (6 # 2) " 8 $ 4 % 18B (2 ! 4 " 6) # 2 " 8 $ 4 % 18C 2 ! 4 " 6 # (2 " 8 $ 4) % 18D 2 ! (4 " 6 # 2) " 8 $ 4 % 18

4. How can this expression be simpli! ed? Use the correct order of operations.

3 " 2 ! a " b ! 4 $ 2 # 4

A 2a " 2b # 1B 2a " 2b # 2C 2a # 2b " 3D 5a " 2b # 4

5. Writing to Explain Evaluate the expression below step by step, identifying the operations that you perform and the order in which you perform them.

18 " 5 " (5 # 3) ! 6 $ 3 # 2

Quick Check

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Topic 6 49

Order of OperationsIf you do not use the proper order of operations, you will not get the correct answer.

Evaluate 8 ! 2 " 3 # 6 $ (1 # 5).

Step 1. Do the operations inside theparentheses.

(1 # 5) % 5 8 ! 2 " 3 # 6 $ 5

Step 3. Add and subtract in order from left to right.

4 " 18 % 22 22 $ 5 % 17 So, 8 ! 2 " 3 # 6 $ (1 # 5) % 17

Step 2. Multiply and divide in order from left to right.

8 ! 2 % 4 and 3 # 6 % 18 4 " 18 $ 5

Write which operation should be done first.

1. 6 " 3 # 2 2. 13 $ 1 " 4 ! 2

3. 5 # (7 $ 2) " 1 4. (19 " 23) $ (4 # 5)

For questions 5 through 8, evaluate the expression for x % 6 and y % 17.

5. 4x " 5y 6. 2x " (20 $ y )

7. x ! 3 " y 8. 4y ! 2 " (8x " 10)

9. There are 22 students in Natalie’s class. New reading books cost $7 each. Natalie’s class raised $50 washing cars. If there are 2 teachers in Natalie’s class, write and evaluate an expression to show how much more each teacher will have to pay to buy the new reading books.

10. Number Sense Carlos solved 20 $ (2 # 6) " 8 ! 4 % 29. Is this the correct answer?

Reteaching

6-5Reteaching 6

-5

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Topic 6 49

Order of OperationsIf you do not use the proper order of operations, you will not get the correct answer.

Evaluate 8 ! 2 " 3 # 6 $ (1 # 5).

Step 1. Do the operations inside theparentheses.

(1 # 5) % 5 8 ! 2 " 3 # 6 $ 5

Step 3. Add and subtract in order from left to right.

4 " 18 % 22 22 $ 5 % 17 So, 8 ! 2 " 3 # 6 $ (1 # 5) % 17

Step 2. Multiply and divide in order from left to right.

8 ! 2 % 4 and 3 # 6 % 18 4 " 18 $ 5

Write which operation should be done first.

1. 6 " 3 # 2 2. 13 $ 1 " 4 ! 2

3. 5 # (7 $ 2) " 1 4. (19 " 23) $ (4 # 5)

For questions 5 through 8, evaluate the expression for x % 6 and y % 17.

5. 4x " 5y 6. 2x " (20 $ y )

7. x ! 3 " y 8. 4y ! 2 " (8x " 10)

9. There are 22 students in Natalie’s class. New reading books cost $7 each. Natalie’s class raised $50 washing cars. If there are 2 teachers in Natalie’s class, write and evaluate an expression to show how much more each teacher will have to pay to buy the new reading books.

10. Number Sense Carlos solved 20 $ (2 # 6) " 8 ! 4 % 29. Is this the correct answer?

Reteaching

6-5Reteaching 6

-5

multiplication divisionsubtraction addition

and multiplication

109 1519 92

No. Carlos solved the equation from left to right instead of following the order of operations.

(22 ! 7 " 50) # 2 $52

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50 Topic 6

Order of OperationsUse the order of operations to evaluate each expression.

1. 4 ! 4 " 3 # 2. 3 " 6 ! 2 $ 3 #

3. 24 % (8 $ 2) " 6 # 4. (15 % 11) ! (25 $ 5) #

5. 26 % 4 ! 5 " 2 # 6. 15 ! (7 % 7) " (5 ! 2) #

7. (8 $ 4) ! (7 ! 0) # 8. 5 ! (6 %3) " 10 $ (8 % 3) #

9. Explain It Which is a true statement, 5 ! 4 " 1 # 25 or 3 " 7 ! 2 # 17? Explain your answer.

Insert parentheses to make each statement true.

10. 25 $ 5 % 4 # 25

11. 7 ! 4 % 4 $ 2 # 26

12. 3 " 5 ! 2 % 10 # 6

13. Strategy Practice Insert parentheses in the expression 6 " 10 ! 2 so that:

a. the expression equals 32.

b. the expression equals (12 " 1) ! 2.

14. Solve (25 % 7) ! 2 $ 4 " 2.

A 18 B 11 C 6 D 5

15. Write two order-of-operation problems. Then trade with a classmate and solve the problems.

Practice

6-5Pr

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50 Topic 6

Order of OperationsUse the order of operations to evaluate each expression.

1. 4 ! 4 " 3 # 2. 3 " 6 ! 2 $ 3 #

3. 24 % (8 $ 2) " 6 # 4. (15 % 11) ! (25 $ 5) #

5. 26 % 4 ! 5 " 2 # 6. 15 ! (7 % 7) " (5 ! 2) #

7. (8 $ 4) ! (7 ! 0) # 8. 5 ! (6 %3) " 10 $ (8 % 3) #

9. Explain It Which is a true statement, 5 ! 4 " 1 # 25 or 3 " 7 ! 2 # 17? Explain your answer.

Insert parentheses to make each statement true.

10. 25 $ 5 % 4 # 25

11. 7 ! 4 % 4 $ 2 # 26

12. 3 " 5 ! 2 % 10 # 6

13. Strategy Practice Insert parentheses in the expression 6 " 10 ! 2 so that:

a. the expression equals 32.

b. the expression equals (12 " 1) ! 2.

14. Solve (25 % 7) ! 2 $ 4 " 2.

A 18 B 11 C 6 D 5

15. Write two order-of-operation problems. Then trade with a classmate and solve the problems.

Practice

6-5Pr

actic

e 6-5

192680

3 ! 7 " 2 # 3 ! (7 " 2) # 17; 5 " 4 ! 1 # (5 " 4) ! 1 # 21

25 $ (5 – 4) # 257 " 4 – (4 $ 2) # 26(3 ! 5) " 2 % 10 # 6

(6 ! 10) " 2

Sample answers: 2 " 6 ! 3 % (8 $ 8); 14; (9 ! 20) % (24 $ 2) % 6; 11

6 ! (10 " 2)

7201017

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Topic 6 51

Decision Making

Parentheses PleaseYou have a total of six sets of parentheses to use. Insert the parentheses where needed to make the number sentences below true. Three of the number sentences do not need additional parentheses.

( ) ( ) ( ) ( ) ( ) ( )1. 5 ! (3 " 2) # 2 " 5 ! 3 $ 4

2. 2 ! 2 ! 2 " 3 % 3 ! 5 $ 13

3. 4 " 3 ! 4 # 3 $ 25

4. (3 ! 6) # 2 " 2 ! 5 $ 26

5. 10 % 2 # 3 " 1 $ 3

6. 1.3 " 2.6 ! 2 # 5 $ 2.8

7. 56 % 8 " 3 " 2 ! 2 $ 17

8. (7 ! 4) " 3 ! 6 " 5 # 1 $ 50

Enrichment

6-5Enrichm

ent 6-5

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Topic 6 51

Decision Making

Parentheses PleaseYou have a total of six sets of parentheses to use. Insert the parentheses where needed to make the number sentences below true. Three of the number sentences do not need additional parentheses.

( ) ( ) ( ) ( ) ( ) ( )1. 5 ! (3 " 2) # 2 " 5 ! 3 $ 4

2. 2 ! 2 ! 2 " 3 % 3 ! 5 $ 13

3. 4 " 3 ! 4 # 3 $ 25

4. (3 ! 6) # 2 " 2 ! 5 $ 26

5. 10 % 2 # 3 " 1 $ 3

6. 1.3 " 2.6 ! 2 # 5 $ 2.8

7. 56 % 8 " 3 " 2 ! 2 $ 17

8. (7 ! 4) " 3 ! 6 " 5 # 1 $ 50

Enrichment

6-5

Enrichment 6

-5

( )

( )

( )

( )

( )

( )

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52 Topic 6

Daily Spiral Review

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1. Which answer shows the operation that should be done ! rst in the following expression?

15 ! (16 " 4) # (5 $ 2)


2. Using the order of operations, which answer shows the correct value of the following expression?

22 # (8 ! 5) $ (12 " 3)

A 10 B 34 C 40D 100

3. Which answer is correct? (45 ! 16) ! 12

A 41B 27C 19D 17

4. Pam’s suitcase can weigh up to 50 pounds. She is planning to pack 5 school books, each of which weighs 2 pounds. She will also pack 3 notebooks weighing 1 pound each, and 6 boxes of golf balls weighing 2 pounds each. Her clothing weighs a total of 16 pounds. Write and evaluate an expression to show how many pounds Pam has to pack.

Will Pam’s suitcase be under the 50-pound weight limit?

5. Insert parentheses to make each statement true.

47 ! 36 " 12 % 44

18 ! 2 # 16 % 0

50 " 2 # 5 % 30

14 " 7 $ 2 % 1

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52 Topic 6

Daily Spiral Review

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1. Which answer shows the operation that should be done ! rst in the following expression?

15 ! (16 " 4) # (5 $ 2)


2. Using the order of operations, which answer shows the correct value of the following expression?

22 # (8 ! 5) $ (12 " 3)

A 10 B 34 C 40D 100

3. Which answer is correct? (45 ! 16) ! 12

A 41B 27C 19D 17

4. Pam’s suitcase can weigh up to 50 pounds. She is planning to pack 5 school books, each of which weighs 2 pounds. She will also pack 3 notebooks weighing 1 pound each, and 6 boxes of golf balls weighing 2 pounds each. Her clothing weighs a total of 16 pounds. Write and evaluate an expression to show how many pounds Pam has to pack.

Will Pam’s suitcase be under the 50-pound weight limit?

5. Insert parentheses to make each statement true.

47 ! 36 " 12 % 44

18 ! 2 # 16 % 0

50 " 2 # 5 % 30

14 " 7 $ 2 % 1

(5 ! 2) " (3 ! 1) "(6 ! 2) " 16 # 41pounds

Yes, 41 & 50pounds.

( )(

((

))

)

30428_T06_052_052_52 52 3/18/08 2:14:01 PM


Topic 6 5

3



Problem of the Day

6-6

Raymond has as many brothers as sisters, but each of his sisters has only half as many sisters as brothers. How many brothers and sisters are in Raymond’s family?

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1. Mike has 15 coins in his pocket. One third of the coins are dimes and the rest are nickels. How much money does he have? You can use objects to act out the problem.

A $0.50

B $0.75

C $1.00

D $1.50

2. Linda has 50 pages in her scrapbook. She used 8 pages for things about her family. Two-thirds of the remaining pages are about her friends, and the rest are blank. How many blank pages remain? You can use objects to act out the problem.

A 12

B 14

C 21

D 48

3. A car dealership has 64 vehicles on its lot. Of the total, 1 _ 4 are pickup trucks and there are twice as many cars as there are SUVs. How many of each type of vehicle are on the lot. You can use objects to act out the problem.

A 16 pickup trucks, 32 cars, 16 SUVs

B 24 pickup trucks, 32 cars, 16 SUVs

C 16 pickup trucks, 16 cars, 32 SUVs

D 22 pickup trucks, 28 cars, 14 SUVs

4. Writing to Explain There are 42 houses on Main Street. Three less than half of the houses are made of brick. Of the rest of the houses, 3 _ 4 are painted white and the rest painted other colors. Explain how you could use objects to act out this problem. Then use cubes or coins to act out the problem and fill in the table.

House NumberTotal 42BrickWhite

Other colors

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Quick Check

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1. Mike has 15 coins in his pocket. One third of the coins are dimes and the rest are nickels. How much money does he have? You can use objects to act out the problem.

A $0.50

B $0.75

C $1.00

D $1.50

2. Linda has 50 pages in her scrapbook. She used 8 pages for things about her family. Two-thirds of the remaining pages are about her friends, and the rest are blank. How many blank pages remain? You can use objects to act out the problem.

A 12

B 14

C 21

D 48

3. A car dealership has 64 vehicles on its lot. Of the total, 1 _ 4 are pickup trucks and there are twice as many cars as there are SUVs. How many of each type of vehicle are on the lot. You can use objects to act out the problem.

A 16 pickup trucks, 32 cars, 16 SUVs

B 24 pickup trucks, 32 cars, 16 SUVs

C 16 pickup trucks, 16 cars, 32 SUVs

D 22 pickup trucks, 28 cars, 14 SUVs

4. Writing to Explain There are 42 houses on Main Street. Three less than half of the houses are made of brick. Of the rest of the houses, 3 _ 4 are painted white and the rest painted other colors. Explain how you could use objects to act out this problem. Then use cubes or coins to act out the problem and fill in the table.

House NumberTotal 42BrickWhite

Other colors


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Topic 6 55

Reteaching

6-6Reteaching 6

-6

Problem Solving: Act It Out and Use Reasoning In Mackenzie’s class there are 23 students. 14 students have brown hair. 2 times as many students have blonde hair as have red hair. How many students have each color hair?

Draw a diagram to show what you know.

There are 9 students left. You know that two times asmany have blonde hair as have red hair. Make a table totry different numbers and see which pair fits the problem.

red blonde Do numbers add up to 9?1 1 ! 2 " 2 does not equal 92 2 ! 2 " 4 does not equal 93 3 ! 2 " 6 equals 9

Since 6 are two times 3 and 6 # 3 " 9, this is the correct answer.

So, in Mackenzie’s class, there are 14 students with brown hair, 6 with blonde hair, and 3 with red hair.

In 1 and 2, solve. Draw a picture and/or table to help find the answer.

1. Jacobson Animal Shelter has half as many cats as dogs. The shelter has 30 dogs. How many total animals does the shelter have?

2. Summer’s mother gave Summer $20 to share with her 3 brothers equally. How much did each person get?

23 students total

14 students with brown hair

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Topic 6 55

Reteaching

6-6Reteaching 6

-6

Problem Solving: Act It Out and Use Reasoning In Mackenzie’s class there are 23 students. 14 students have brown hair. 2 times as many students have blonde hair as have red hair. How many students have each color hair?

Draw a diagram to show what you know.

There are 9 students left. You know that two times asmany have blonde hair as have red hair. Make a table totry different numbers and see which pair fits the problem.

red blonde Do numbers add up to 9?1 1 ! 2 " 2 does not equal 92 2 ! 2 " 4 does not equal 93 3 ! 2 " 6 equals 9

Since 6 are two times 3 and 6 # 3 " 9, this is the correct answer.

So, in Mackenzie’s class, there are 14 students with brown hair, 6 with blonde hair, and 3 with red hair.

In 1 and 2, solve. Draw a picture and/or table to help find the answer.

1. Jacobson Animal Shelter has half as many cats as dogs. The shelter has 30 dogs. How many total animals does the shelter have?

2. Summer’s mother gave Summer $20 to share with her 3 brothers equally. How much did each person get?

23 students total

14 students with brown hair

45 animals

$5

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56 Topic 6

Practice

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Problem Solving: Act It Out and Use Reasoning

1. Christina collects stamps. She has 47 stamps in all. She has 20 stamps from Europe. The number of African stamps is 2 times the number of Asian stamps. How many stamps from each of these three continents does she have?

2. Write a Problem Write a problem that can be solved by acting it out and using reasoning.

3. A public pool opened for the summer. A total of 246 people came swimming over the first 3 days it was open. On the first day, 79 came to swim. On the second day, 104 people swam. How many people swam on the third day?

4. Marissa earned $480 in the summer. If she earned $40 a week, how many weeks did she work?

A 48 B 12 C 10 D 9

5. Explain It How could you use cubes to act out a problem?

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56 Topic 6

Practice

6-6Pr

actic

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Problem Solving: Act It Out and Use Reasoning

1. Christina collects stamps. She has 47 stamps in all. She has 20 stamps from Europe. The number of African stamps is 2 times the number of Asian stamps. How many stamps from each of these three continents does she have?

2. Write a Problem Write a problem that can be solved by acting it out and using reasoning.

3. A public pool opened for the summer. A total of 246 people came swimming over the first 3 days it was open. On the first day, 79 came to swim. On the second day, 104 people swam. How many people swam on the third day?

4. Marissa earned $480 in the summer. If she earned $40 a week, how many weeks did she work?

A 48 B 12 C 10 D 9

5. Explain It How could you use cubes to act out a problem?

Answers will vary.

Sample answer: You can count out thetotal number of cubes in the word problem and then divide them upaccording to the problem to help youfigure out the numbers.

63

20 European, 18 African, 9 Asian

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Topic 6 57

Enrichment

6-6

Visual Thinking

Enrichment 6

-6

Acting OutSolve using cubes to act out each problem.

1. Brian has a model collection of cars, trains, and fire engines. He has 28 cars. The number of fire engines is 2 times the number of trains. He has 67 models in all. How many of each type of model does he have?

2. Sharon has a carton of quilting notions. She has a total of 52 notions. She has 16 patterns. She has three times as many thimbles as templates. How many of each notion does she have?

3. The Busy Bee Quilters made 42 quilts to donate to a nursing home. There are 13 purple quilts. There are 5 more blue quilts than red quilts. How many of each color quilts are they donating?

4. Nancy runs a dog obedience school. There are a total of 58 dogs enrolled in the school. There are 22 dogs in obedience class. There are 1 _ 2 as many dogs in competition as there are in agility class. How many dogs are in each class?

5. The dog obedience school had agility trials. A total of 171 dogs competed in 3 days. On the first day, 87 dogs competed. Twice as many dogs competed on the second than the third day. How many dogs competed on the second and third days?

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Topic 6 57

Enrichment

6-6

Visual Thinking

Enrichment 6

-6

Acting OutSolve using cubes to act out each problem.

1. Brian has a model collection of cars, trains, and fire engines. He has 28 cars. The number of fire engines is 2 times the number of trains. He has 67 models in all. How many of each type of model does he have?

2. Sharon has a carton of quilting notions. She has a total of 52 notions. She has 16 patterns. She has three times as many thimbles as templates. How many of each notion does she have?

3. The Busy Bee Quilters made 42 quilts to donate to a nursing home. There are 13 purple quilts. There are 5 more blue quilts than red quilts. How many of each color quilts are they donating?

4. Nancy runs a dog obedience school. There are a total of 58 dogs enrolled in the school. There are 22 dogs in obedience class. There are 1 _ 2 as many dogs in competition as there are in agility class. How many dogs are in each class?

5. The dog obedience school had agility trials. A total of 171 dogs competed in 3 days. On the first day, 87 dogs competed. Twice as many dogs competed on the second than the third day. How many dogs competed on the second and third days?

28 cars, 13 trains, 26 fire engines

16 patterns, 27 thimbles, 9 templates

13 purple quilts, 17 blue quilts, 12 redquilts

22 in obedience, 12 in competition, 24 in agility

56 dogs on the second day and 28 dogson the third day

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1. Translate the algebraic expression into words: n ! 12. (6-1)

A 12 more than a number

B 12 less than a number

C A number divided by 12

D A number multiplied by 12

2. If Ryan orders 7 boxes of pencils and each box has 198 pencils, he will have 7 " 198 pencils. Which of the following is equal to 7 " 198? (6-4)

A (7 " 200) ! (7 " 2)

B (7 ! 200) " (7 # 2)

C (7 " 200) # (7 " 2)

D (7 ! 200) # (7 " 2)

3. Sandy ate 3 more carrots than Laura, who ate 8. Evaluate the expression n ! 3 for n $ 8. (6-2)

A 5

B 11

C 13

D 14

4. Amy finds a pair of shoes that is twice the amount of money she has. If m stands for the amount of money she has, which expression tells the price of the shoes? (6-1)

A m ! 2

B m # 2

C m " 2

D m % 2

5. The expression f – 6 represents the amount of flour left after baking cookies when the original flour sack had f cups. How many cups of flour are left when f $ 10? (6-2)

A 2

B 4

C 5

D 6

6. What is the first step in evaluating the expression below? (6-5)

2 ! (3 " 5) # 4 # 1

A Add 2 and 3.

B Multiply 3 and 5.

C Subtract 4 from 5.

D Subtract 1 from 4

Topic 6Multiple-Choice Test

Topi

c 6

M

ultip

le-C

hoic

e Te

st

58 Topic 6

Mark the best answer.

30428_T06__58 58 1/16/08 5:14:32 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

1. Translate the algebraic expression into words: n ! 12. (6-1)

A 12 more than a number

B 12 less than a number

C A number divided by 12

D A number multiplied by 12

2. If Ryan orders 7 boxes of pencils and each box has 198 pencils, he will have 7 " 198 pencils. Which of the following is equal to 7 " 198? (6-4)

A (7 " 200) ! (7 " 2)

B (7 ! 200) " (7 # 2)

C (7 " 200) # (7 " 2)

D (7 ! 200) # (7 " 2)

3. Sandy ate 3 more carrots than Laura, who ate 8. Evaluate the expression n ! 3 for n $ 8. (6-2)

A 5

B 11

C 13

D 14

4. Amy finds a pair of shoes that is twice the amount of money she has. If m stands for the amount of money she has, which expression tells the price of the shoes? (6-1)

A m ! 2

B m # 2

C m " 2

D m % 2

5. The expression f – 6 represents the amount of flour left after baking cookies when the original flour sack had f cups. How many cups of flour are left when f $ 10? (6-2)

A 2

B 4

C 5

D 6

6. What is the first step in evaluating the expression below? (6-5)

2 ! (3 " 5) # 4 # 1

A Add 2 and 3.

B Multiply 3 and 5.

C Subtract 4 from 5.

D Subtract 1 from 4

Topic 6Multiple-Choice Test

Topi

c 6

M

ultip

le-C

hoic

e Te

st

58 Topic 6

Mark the best answer.

30428_T06_058-060_58 58 3/18/08 2:15:07 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Translate each algebraic expression into words.

1. n ! 6

2. r " 4

3. 6x

4. y # 7

Write each word phrase as an algebraic expression.

5. 8 less than a number

6. 4 times a number

7. 5 more than another number

8. 6 divided by a number

Evaluate for x $ 3 and x $ 5.

9. 3x

10. 4 ! x

11. 7 # x

12. 15 ___ x


13.

14.

15.

Topic 6 61

Topic 6Free-Response Test


x 2x8 16

9

10 20

15 30

x x ! 24 6

7 9

12 14

15

x x ! 51 6

4 9

6

9 14

30428_T06__61 61 1/16/08 5:14:46 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Translate each algebraic expression into words.

1. n ! 6

2. r " 4

3. 6x

4. y # 7

Write each word phrase as an algebraic expression.

5. 8 less than a number

6. 4 times a number

7. 5 more than another number

8. 6 divided by a number

Evaluate for x $ 3 and x $ 5.

9. 3x

10. 4 ! x

11. 7 # x

12. 15 ___ x


13.

14.

15.

Topic 6 61



x 2x8 16

9

10 20

15 30

x x ! 24 6

7 9

12 14

15

x x ! 51 6

4 9

6

9 14

6 more than another number

A number divided by 4

6 times a number

x " 8

4n

m ! 5

6 __ y

7 less thananother number

9, 157, 94, 25, 3

17

11

18

30428_T06_61-62_61 61 3/18/08 2:15:35 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

1. Use the table to the right.

If one serving has C calories, write an expression to show the number of calories in 3 servings. Explain how to use your expression to find the number of calories in 3 servings of lettuce.

2. Plan a dinner party. Choose one food from each food group to serve. Complete the food item column with your choices. Then complete the columns for fat and calories for each person.

3. To complete the table, which computations did you do with mental math? Why?

4. Explain how you could reduce the total amount of fat and calories for each person by changing one item.

Food item Number of Servings for Each Person

Grams of Fat for Each Person

Calories for Each Person

Meat 2Dairy 2Vegetable 3Fruit 1.5Bread or pasta 2.5Total

Food Item Fat Grams CaloriesMeat groupTurkey, 1 ounce 2 51Ham, 3.5 ounces 5 159Hamburger, 3 ounces 20 286Dairy groupMilk, 1 cup whole 8 150American cheese 1 oz. 9 110Yogurt, 1 cup plain 4 144Vegetable groupGreen beans, 1 cup 0.2 36Lettuce, 1 cup 0.2 10Peas, 1 cup 0.4 134Fruit groupBanana, 1 0.6 105Apple, 1 0.5 81Bread and pasta groupWheat bread, 1 slice 1 70Macaroni, 1 cup 0 159

Topic 6

Performance Assessm

ent Topic 6 63

Topic 6Performance Assessment

30428_T06__63 63 1/16/08 5:14:41 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

1. Use the table to the right.

If one serving has C calories, write an expression to show the number of calories in 3 servings. Explain how to use your expression to find the number of calories in 3 servings of lettuce.

2. Plan a dinner party. Choose one food from each food group to serve. Complete the food item column with your choices. Then complete the columns for fat and calories for each person.

3. To complete the table, which computations did you do with mental math? Why?

4. Explain how you could reduce the total amount of fat and calories for each person by changing one item.

Food item Number of Servings for Each Person

Grams of Fat for Each Person

Calories for Each Person

Meat 2Dairy 2Vegetable 3Fruit 1.5Bread or pasta 2.5Total

Food Item Fat Grams CaloriesMeat groupTurkey, 1 ounce 2 51Ham, 3.5 ounces 5 159Hamburger, 3 ounces 20 286Dairy groupMilk, 1 cup whole 8 150American cheese 1 oz. 9 110Yogurt, 1 cup plain 4 144Vegetable groupGreen beans, 1 cup 0.2 36Lettuce, 1 cup 0.2 10Peas, 1 cup 0.4 134Fruit groupBanana, 1 0.6 105Apple, 1 0.5 81Bread and pasta groupWheat bread, 1 slice 1 70Macaroni, 1 cup 0 159

Topic 6

Performance Assessm

ent Topic 6 63

Topic 6Performance Assessment

3c; substitute 10 for c and multiply. 3 ! 10 " 30, so 3 servings of lettuce have 30 calories.

It was easy to use mental math to find the total grams of fat.

4 18 0.6 0.9 0 23.5

102220108157.5397.5985

An apple has fewer grams of fat and fewer calories than a banana. So, I could reduce the total fat and calories by serving apples instead of bananas.

30428_T06_063_63 63 3/18/08 2:15:22 PM

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