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1.10E: Exercises

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Practice Makes Perfect

Use the Commutative and Associative Properties

In the following exercises, use the associative property to simplify.

Exercise 1

3(4x)

Answer

12x

Exercise 2

4(7m)

Exercise 3

(y+12)+28

Answer

y+40

Exercise 4

(n+17)+33

In the following exercises, simplify.

Exercise 5

12+78+(12)

Answer

78

Exercise 6

25+512+(25)

Exercise 7

3204911203

Answer

4911

Exercise 8

13182571813

Exercise 9

24738

Answer

63

Exercise 10

361149

Exercise 11

(56+815)+715

Answer

156

Exercise 12

(1112+49)+59

Exercise 13

17(0.25)(4)

Answer

17

Exercise 14

36(0.2)(5)

Exercise 15

[2.48(12)](0.5)

Answer

14.88

Exercise 16

[9.731(4)](0.75)

Exercise 17

7(4a)

Answer

28a

Exercise 18

9(8w)

Exercise 19

15(5m)

Answer

75m

Exercise 20

23(2n)

Exercise 21

12(56p)

Answer

10p

Exercise 22

20(35q)

Exercise 23

43m+(12n)+(16m)+(9n)

Answer

27m+(21n)

Exercise 24

22p+17q+(35p)+(27q)

Exercise 25

38g+112h+78g+512h

Answer

54g+12h

Exercise 26

56a+310b+16a+910b

Exercise 27

6.8p+9.14q+(4.37p)+(0.88q)

Answer

2.43p+8.26q

Exercise 28

9.6m+7.22n+(2.19m)+(0.65n)

Use the Identity and Inverse Properties of Addition and Multiplication

In the following exercises, find the additive inverse of each number

Exercise 29
  1. 25
  2. 4.3
  3. 8
  4. 103
Answer
  1. 25
  2. 4.3
  3. 8
  4. 103
Exercise 30
  1. 59
  2. 2.1
  3. 3
  4. 95
Exercise 31
  1. 76
  2. 0.075
  3. 23
  4. 14
Answer
  1. 76
  2. 0.075
  3. 23
  4. 14
Exercise 32
  1. 83
  2. 0.019
  3. 52
  4. 56

In the following exercises, find the multiplicative inverse of each number.

Exercise 33
  1. 6
  2. 34
  3. 0.7
Answer
  1. 16
  2. 43
  3. 107
Exercise 34
  1. 12
  2. 92
  3. 0.13
Exercise 35
  1. 1112
  2. 1.1
  3. 4
Answer
  1. 1211
  2. 1011
  3. 14
Exercise 36
  1. 1720
  2. 1.5
  3. 3

Use the Properties of Zero

In the following exercises, simplify.

Exercise 37

06

Answer

0

Exercise 38

30

Exercise 39

0÷1112

Answer

0

Exercise 40

03

Exercise 41

60

Answer

undefined

Exercise 42

0815

Exercise 43

(3.14)(0)

Answer

0

Exercise 44

1100

Mixed Practice

In the following exercises, simplify.

Exercise 45

19a+4419a

Answer

44

Exercise 46

27c+1627c

Exercise 47

10(0.1d)

Answer

1d

Exercise 48

100(0.01p)

Exercise 49

0u4.99, where u4.99

Answer

0

Exercise 50

0v65.1, where v65.1

Exercise 51

0÷(x12), where x12

Answer

0

Exercise 52

0÷(y16), where y16

Exercise 53

325a0, where 325a0

Answer

undefined

Exercise 54

289b0, where 289b0

Exercise 55

(34+910m)÷0 where 34+910m0

Answer

undefined

Exercise 56

(516n37)÷0 where 516n370

Exercise 57

1535(4d+10)

Answer

36d+90

Exercise 58

1856(15h+24)

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the distributive property.

Exercise 59

8(4y+9)

Answer

32y+72

Exercise 60

9(3w+7)

Exercise 61

6(c13)

Answer

6c78

Exercise 62

7(y13)

Exercise 63

14(3q+12)

Answer

34q+3

Exercise 64

15(4m+20)

Exercise 65

9(59y13)

Answer

5y3

Exercise 66

10(310x25)

Exercise 67

12(14+23r)

Answer

3+8r

Exercise 68

12(16+34s)

Exercise 69

r(s18)

Answer

rs18r

Exercise 70

u(v10)

Exercise 71

(y+4)p

Answer

yp+4p

Exercise 72

(a+7)x

Exercise 73

7(4p+1)

Answer

28p7

Exercise 74

9(9a+4)

Exercise 75

3(x6)

Answer

3x+18

Exercise 76

4(q7)

Exercise 77

(3x7)

Answer

3x+7

Exercise 78

(5p4)

Exercise 79

163(y+8)

Answer

3y8

Exercise 80

184(x+2)

Exercise 81

411(3c2)

Answer

33c+26

Exercise 82

96(7n5)

Exercise 83

22(a+3)

Answer

a+19

Exercise 84

8(r7)

Exercise 85

(5m3)(m+7)

Answer

4m10

Exercise 86

(4y1)(y2)

Exercise 87

5(2n+9)+12(n3)

Answer

22n+9

Exercise 88

9(5u+8)+2(u6)

Exercise 89

9(8x3)(2)

Answer

72x25

Exercise 90

4(6x1)(8)

Exercise 91

14(c1)8(c6)

Answer

6c+34

Exercise 92

11(n7)5(n1)

Exercise 93

6(7y+8)(30y15)

Answer

12y+63

Exercise 94

7(3n+9)(4n13)

Everyday Math

Exercise 95

Insurance copayment Carrie had to have 5 fillings done. Each filling cost $80. Her dental insurance required her to pay 20% of the cost as a copay. Calculate Carrie’s copay:

  1. First, by multiplying 0.20 by 80 to find her copay for each filling and then multiplying your answer by 5 to find her total copay for 5 fillings.
  2. Next, by multiplying [5(0.20)](80)
  3. Which of the properties of real numbers says that your answers to parts (a), where you multiplied 5[(0.20)(80)] and (b), where you multiplied [5(0.20)](80), should be equal?
Answer
  1. $80
  2. $80
  3. answers will vary
Exercise 96

Cooking time Helen bought a 24-pound turkey for her family’s Thanksgiving dinner and wants to know what time to put the turkey in to the oven. She wants to allow 20 minutes per pound cooking time. Calculate the length of time needed to roast the turkey:

  1. First, by multiplying 24·20 to find the total number of minutes and then multiplying the answer by 160 to convert minutes into hours.
  2. Next, by multiplying 24(20160).
  3. Which of the properties of real numbers says that your answers to parts (a), where you multiplied (2420)160, and (b), where you multiplied 24(20160), should be equal?
Exercise 97

Buying by the case Trader Joe’s grocery stores sold a bottle of wine they called “Two Buck Chuck” for $1.99. They sold a case of 12 bottles for $23.88. To find the cost of 12 bottles at $1.99, notice that 1.99 is 2−0.01.

  1. Multiply 12(1.99) by using the distributive property to multiply 12(2−0.01).
  2. Was it a bargain to buy “Two Buck Chuck” by the case?
Answer
  1. $23.88
  2. no, the price is the same
Exercise 98

Multi-pack purchase Adele’s shampoo sells for $3.99 per bottle at the grocery store. At the warehouse store, the same shampoo is sold as a 3 pack for $10.49. To find the cost of 3 bottles at $3.99, notice that 3.99 is 4−0.01.

  1. Multiply 3(3.99) by using the distributive property to multiply 3(4−0.01).
  2. How much would Adele save by buying 3 bottles at the warehouse store instead of at the grocery store?

Writing Exercises

Exercise 99

In your own words, state the commutative property of addition.

Answer

Answersmayvary

Exercise 100

What is the difference between the additive inverse and the multiplicative inverse of a number?

Exercise 101

Simplify 8(x14) using the distributive property and explain each step.

Answer

Answersmayvary

Exercise 102

Explain how you can multiply 4($5.97) without paper or calculator by thinking of $5.97 as 6−0.03 and then using the distributive property.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This is a table that has five rows and four columns. In the first row, which is a header row, the cells read from left to right “I can…,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can…” reads “use the commutative and associative properties,” “use the identity and inverse properties of addition and multiplication,” “use the properties of zero,” and “simplify expressions using the distributive property.” The rest of the cells are blank.

ⓑ After reviewing this checklist, what will you do to become confident for all objectives?


This page titled 1.10E: Exercises is shared under a not declared license and was authored, remixed, and/or curated by OpenStax.

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