Selected Answers - Big Ideas Learning

Selected Answers

Evaluating Algebraic Expressions

Section 1.1

1.

(pages 6 and 7)

Algebraic

Expression

Numbers

Variables

Operations

x?8

8

x

Subtraction

3w + 9

3, 9

w

Multiplication

and addition

y

Multiplication

and subtraction

6y ? 12

6, 12

17. 9

19. 24

21. $15; $105

25. 23

27. 6

29. 22

31. 46

33. 24

3. smaller; When you subtract

larger and larger values from 20,

you will have less and less left.

5. $120

7. $8

9. 10

11. 9

13. 17

15. 2

23.

x

3

6

9

?

24

48

72

x 8

35. What shape could have an area of 128 square feet? What shape could have an

area of s 2 square feet?

37.

8

7

6

5

4

3

2

1

39.

y

(3, 2)

1 2 3 4 5 6 7 8x

Section 1.2

8

7

6

5

4

3

2

1

41. C

y

(5, 1)

1 2 3 4 5 6 7 8x

Writing Expressions

(pages 12 and 13)

1. x take away 12; x ? 12; x + 12

7. 18 ? 3

13. 7 + w or w + 7

3. 8 ? 5

9. x ? 13

5. 28 ¡Â 7

11. 18 ¡Â a

?

15. y + 4 or 4 + y

?

17. 2 z or z 2

8

y

19. The expression is not written in the correct order; ¡ª

21. a. x ¡Â 5

b. Sample answer: If the total cost is $30, then the cost per person is x ¡Â 5 = 30 ¡Â 5 = $6.

The result is reasonable.

23?25. Sample answers are given.

23. The sum of n and 6; 6 more than a number n

y

4

27. ¡ª ? 3; 2

A60

25. A number b less than 15; 15 take away a number b

29. 8x + 6; 46

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Game

1

2

3

4

5

Cost

$5

$8

$11

$14

$17

b.

Cost (dollars)

31. a.

33. It might help to see the pattern

if you make a table of the data

in the bar graph.

x

4

35. ¡ª

y

18

16

14

12

10

8

6

4

2

0

c. 2 + 3y

(5, 17)

d. $26

(4, 14)

(3, 11)

(2, 8)

(1, 5)

0 1 2 3 4 5 6 7 x

Game

37. 59

39. 140

Properties of Addition and Multiplication

Section 1.3

(pages 18 and 19)

3 3

5 5

4 4

¡ª=¡ª

5 5

1

5

5. Comm. Prop. of Mult.

3. Sample answer:

7. Assoc. Prop. of Mult.

? ?

? ?

(5 x) 1 = 5 (x 1)

Selected Answers

1

5

1. Sample answer: ¡ª + ¡ª = ¡ª + ¡ª

= 5x

9. Add. Prop. of Zero

11. The grouping of the numbers did not change. The statement illustrates the Commutative

Property of Addition because the order of the addends changed.

13. (14 + y ) + 3 = ( y + 14) + 3

= y + (14 + 3)

Assoc. Prop. of Add.

= y + 17

Add 14 and 3.

?

15. 7(9w) = (7 9)w

Add. Prop. of Zero

Multiply 7 and 9.

? ?

19. (18.6 d ) 1 = 18.6 (d 1)

= 18.6d

Assoc. Prop. of Mult.

Mult. Prop. of One

21. (2.4 + 4n) + 9 = (4n + 2.4) + 9

? ?

17. (0 + a) + 8 = a + 8

Assoc. Prop. of Mult.

= 63w

? ?

Comm. Prop. of Add.

Comm. Prop. of Add.

= 4n + (2.4 + 9)

Assoc. Prop. of Add.

= 4n + 11.4

Add 2.4 and 9.

? ?

= 0 ? 12

23. z 0 12 = (z 0) 12

=0

Assoc. Prop. of Mult.

Mult. Prop. of Zero

Mult. Prop. of Zero

25. a. x represents the cost of a box of cookies.

27. 7 + (x + 5) = x + 12

? ?

b. 120x

29. (7 2) y

31. (17 + 6) = 2x

33. w 16

35. 98

37. 90

39. 37 is already prime.

41. 3 ¡Á 72

43. B

?

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A61

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The Distributive Property

Section 1.4

(pages 26 and 27)

1. Sample answer: You must distribute or give the number outside the parentheses to the

numbers inside the parentheses.

?

3. 4 + (x 4) does not belong because it doesn¡¯t represent the Distributive Property.

5. 684

7. 440

9. 216

15. 56 + 7y

17. 9n + 9

25. 29 + 8x

27. 5x + 52

19. 18w + 90

11. 196

13. 10b ? 60

21. 70 + 7x

23. 78 + 6z

29. a. 30(8 + x) = 240 + 30x

b. Sample answer: $2; It is less than the regular price to the exhibit.

c. Sample answer: $300; yes

31. 10(103 ? x) = 1030 ? 10x

33. 13(7 ? x) = 91 ? 13x

35. x = 8

37. x = 3

39. 2(3 + x)

41. 7(1 + 2x + 3)

43. The expression for the profit will contain an expression for the large candles and an

expression for the small candles.

45. 14

47. 120

2

49. no; ¡ª

3

51. no; ¡ª

19

31

53. C

Using Formulas to Solve Problems

Section 1.5

(pages 32 and 33)

1. Sample answer: You substitute value(s) for the variable(s) to find the value of the formula.

3. 48 in.2

9. a. 234 ft2

5. 108 in.2

b.

7. 30 ft2

9 ft

26 ft

c. 26 ft; The base of the parking space is related to the length of the car.

11. a. 192 in.3

b. almost 13 bowls

13. 4x ? 9

15. 32x ? 40 ? x 2

17. 24 carats; If you let c = 24, then P = 100.

19. Area of black = 252 in.2

Area of yellow = 244 in.2

Area of each blue stripe = 328 in.2

1

2

21. ¡ª

A62

23. 1

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Fractions and Estimation

Section 2.1

(pages 48 and 49)

1. rounding; The product will be easier to compute.

3. rounding; The product will be easier to compute.

5.

How to Round

Estimate

Round 77 to the nearest hundred.

100 ¡Â 4 = 25

Round 77 to the nearest ten.

80 ¡Â 4 = 20

Round 77 to the nearest compatible number.

76 ¡Â 4 = 19

5

12

1

2

5

12

9

10

1

2

7. 0

9. 0

1

2

1

15. ¡ª

2

1

3

1

17. ¡ª

2

11. ¡ª

13. ¡ª

19. 27

21. 6

1

2

23. ¡ª is closer to ¡ª than to 0. ¡ª ¡Á ¡ª ¡Ö ¡ª ¡Á 1 = ¡ª

25. 8

27. 203

29. 7

31. 20

33. Which operation should you use?

35. 27 in.2; underestimate

Selected Answers

37. 18

39. 5

41. Sample answer: low estimate: 198 in.2; high estimate: 336 in.2

To find a low estimate, round the dimensions down.

To find a high estimate, round the dimensions up.

Section 2.2

Multiplying Fractions and Whole Numbers

(pages 54 and 55)

1

1 1

3. ¡ª ¡Á 24; because ¡ª > ¡ª

1. Multiply the numerator of the fraction

by the whole number. Then write the

product over the denominator.

5

8

3

7

9

5. ¡ª

7. 1¡ª

1

10

13. 2 ¡ª

1

2

45. 4 ¡ª

43. 36

3

4

1

2

11. 17 ¡ª

9. 15

15. 26

1

2

19. 13 ¡ª

17. 9

3

7

9¡Á3

7

27

7

6

7

21. 9 should be multiplied by 3, not 7. 9 ¡Á ¡ª = ¡ª = ¡ª, or 3 ¡ª

2

3

23. 2 ¡ª cups

25. 6

27. 20

2

5

29. Multiply 25 ¡Á ¡ª first by the Comm. Prop. of Mult.; 60

3

7

31. Multiply ¡ª ¡Á 14 first by the Comm. Prop. of Mult.; 78

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A63

2/7/09 11:42:04 AM

Multiplying Fractions and Whole Numbers

(cont.) (pages 54 and 55)

Section 2.2

1

2

2

3

33. 1¡ª

1

2

35. 2 ¡ª

1

6

37. 22 ¡ª

39. 4 ¡ª

1

1

41. yes; If you have more money than your friend, then ¡ª of your money could be greater than ¡ª

3

2

of your friend¡¯s money.

32

175

7

8

45. ¡ª

43. 1 ¡ª

47. D

Multiplying Fractions

Section 2.3

(pages 60 and 61)

1. Multiply numerators and multiply denominators, then simplify the fraction.

2

21

5. ¡ª

3. 4

2

5

1

6

15. ¡ª

13. 4 ¡ª

7. ¡ª

1

10

9. ¡ª

8

15

9

49

19. ¡ª

13

21

17. ¡ª

2

5

1

2¡Á3

5 ¡Á 10

3

10

1

24

11. ¡ª

2¡Á3

5 ¡Á 10

3

25

21. You did not multiply the denominators. ¡ª ¡Á ¡ª = ¡ª = ¡ª = ¡ª

1

23. ¡ª

4

2

25. ¡ª

21

9

80

7

45

33. ¡ª

41.

(

5

8

3

27. ¡ª

10

22

15

)

5

8

7

10

29. ¡ª

27

125

35. ¡ª

5

21

40

31. ¡ª

25

196

37. ¡ª

39. ¡ª

22

15

5

8

¡ª ¡Á ¡ª > ¡ª; Because ¡ª > 1, the product will be greater than ¡ª.

1

3

3

50

43. Sample answer: ¡ª

45. a. ¡ª

35

8

b. 45 people

23

6

47. ¡ª

49. ¡ª

Multiplying Mixed Numbers

Section 2.4

(pages 66 and 67)

1. a fraction with a numerator that is greater than or equal to the denominator

1

2

1

7

3

7. ¡ª

4

3. Sample answer: 3 ¡ª ¡Á 3 ¡ª = 11

5. 2

1

2

3

14

15. 1¡ª

A64

17. 1¡ª

9. 2

11. 2

2

3

19. 36 ¡ª

13. 2

4

9

21. 6 ¡ª

3

8

23. 11¡ª

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