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1.5E: Exercises

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Practice Makes Perfect

Multiply Integers

In the following exercises, multiply.

Exercise $$\PageIndex{55}$$

$$−4\cdot 8$$

-32

Exercise $$\PageIndex{56}$$

$$-3\cdot 9$$

Exercise $$\PageIndex{57}$$

$$9(-7)$$

-63

Exercise $$\PageIndex{58}$$

$$13(-5)$$

Exercise $$\PageIndex{59}$$

$$-1\cdot 6$$

-6

Exercise $$\PageIndex{60}$$

$$-1\cdot 3$$

Exercise $$\PageIndex{61}$$

$$-1(-14)$$

14

Exercise $$\PageIndex{62}$$

$$-1(-19)$$

Divide Integers

In the following exercises, divide.

Exercise $$\PageIndex{63}$$

$$-24\div 6$$

-4

Exercise $$\PageIndex{64}$$

$$35\div (-7)$$

Exercise $$\PageIndex{65}$$

$$-52 \div (-4)$$

13

Exercise $$\PageIndex{66}$$

$$-84 \div (-6)$$

Exercise $$\PageIndex{67}$$

$$-180 \div 15$$

-12

Exercise $$\PageIndex{68}$$

$$-192\div 12$$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

Exercise $$\PageIndex{69}$$

5(−6)+7(−2)−3

-47

Exercise $$\PageIndex{70}$$

8(−4)+5(−4)−6

Exercise $$\PageIndex{71}$$

$$(-2)^{6}$$

64

Exercise $$\PageIndex{72}$$

$$(-3)^{5}$$

Exercise $$\PageIndex{73}$$

$$(-4)^{2}$$

-16

Exercise $$\PageIndex{74}$$

$$(-6)^{2}$$​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​

Exercise $$\PageIndex{75}$$

−3(−5)(6)

90

Exercise $$\PageIndex{76}$$

−4(−6)(3)

Exercise $$\PageIndex{77}$$

(8−11)(9−12)

9

Exercise $$\PageIndex{78}$$

(6−11)(8−13)

Exercise $$\PageIndex{79}$$

26−3(2−7)

41

Exercise $$\PageIndex{80}$$

23−2(4−6)

Exercise $$\PageIndex{81}$$

$$65\div (−5)+(−28)\div (−7)$$

-9

Exercise $$\PageIndex{82}$$

$$52\div(−4)+(−32)\div(−8)$$

Exercise $$\PageIndex{83}$$

9−2[3−8(−2)]

-29

Exercise $$\PageIndex{84}$$

11−3[7−4(−20)]

Exercise $$\PageIndex{85}$$

$$(−3)^{2}−24\div (8−2)$$

5

Exercise $$\PageIndex{86}$$

$$(−4)^{2}−32\div (12−4)$$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

Exercise $$\PageIndex{87}$$

y+(−14) when

1. y=−33
2. y=30
1. −47
2. 16

Exercise $$\PageIndex{88}$$

x+(−21) when

1. x=−27
2. x=44

Exercise $$\PageIndex{89}$$

1. a+3 when a=−7
2. −a+3 when a=−7
1. −4
2. 10

Exercise $$\PageIndex{90}$$

1. d+(−9) when d=−8
2. −d+(−9) when d=−8

Exercise $$\PageIndex{91}$$

m+n when
m=−15,n=7

-8

Exercise $$\PageIndex{92}$$

p+q when
p=−9,q=17

Exercise $$\PageIndex{93}$$

r+s when r=−9,s=−7

-16

Exercise $$\PageIndex{94}$$

t+u when t=−6,u=−5

Exercise $$\PageIndex{95}$$

$$(x+y)^{2}$$ when
x=−3,y=14

121

Exercise $$\PageIndex{96}$$

$$(y+z)^{2}$$ when
y=−3, z=15

Exercise $$\PageIndex{97}$$

−2x+17 when

1. x=8
2. x=−8
1. 1
2. 33

Exercise $$\PageIndex{98}$$

−5y+14 when

1. y=9
2. y=−9

Exercise $$\PageIndex{99}$$

10−3m when

1. m=5
2. m=−5
1. −5
2. 25

Exercise $$\PageIndex{100}$$

18−4n when

1. n=3
2. n=−3

Exercise $$\PageIndex{101}$$

$$2w^{2}−3w+7$$ when
w=−2

21

Exercise $$\PageIndex{102}$$

$$3u^{2}−4u+5$$

Exercise $$\PageIndex{103}$$

9a−2b−8 when
a=−6 and b=−3

-56

Exercise $$\PageIndex{104}$$

7m−4n−2 when
m=−4 and n=−9

​​​​​Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

Exercise $$\PageIndex{105}$$

the sum of 3 and −15, increased by 7

(3+(−15))+7;−5

Exercise $$\PageIndex{106}$$

the sum of −8 and −9, increased by 23

Exercise $$\PageIndex{107}$$

the difference of 10 and −18

10−(−18);28

Exercise $$\PageIndex{108}$$

subtract 11 from −25

Exercise $$\PageIndex{109}$$

the difference of −5 and −30

−5−(−30);25

Exercise $$\PageIndex{110}$$

subtract −6 from −13

Exercise $$\PageIndex{111}$$

the product of −3 and 15

$$−3\cdot 15$$;−45

Exercise $$\PageIndex{112}$$

the product of −4 and 16

Exercise $$\PageIndex{113}$$

the quotient of −60 and −20

$$−60\div(−20)$$;3

Exercise $$\PageIndex{114}$$

the quotient of −40 and −20

Exercise $$\PageIndex{115}$$

the quotient of −6 and the sum of a and b

$$\frac{-6}{a + b}$$

Exercise $$\PageIndex{116}$$

the quotient of −6 and the sum of a and b

Exercise $$\PageIndex{117}$$

the product of −10 and the difference of p and q

−10(p−q)

Exercise $$\PageIndex{118}$$

the product of −13 and the difference of c and d

​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​Use Integers in Applications

In the following exercises, solve.

Exercise $$\PageIndex{119}$$

Temperature On January 15, the high temperature in Anaheim, California, was 84°. That same day, the high temperature in Embarrass, Minnesota was −12°. What was the difference between the temperature in Anaheim and the temperature in Embarrass?

96°

Exercise $$\PageIndex{120}$$

Temperature On January 21, the high temperature in Palm Springs, California, was 89°, and the high temperature in Whitefield, New Hampshire was −31°. What was the difference between the temperature in Palm Springs and the temperature in Whitefield?

Exercise $$\PageIndex{121}$$

Football At the first down, the Chargers had the ball on their 25 yard line. On the next three downs, they lost 6 yards, gained 10 yards, and lost 8 yards. What was the yard line at the end of the fourth down?

21

Exercise $$\PageIndex{122}$$

Football At the first down, the Steelers had the ball on their 30 yard line. On the next three downs, they gained 9 yards, lost 14 yards, and lost 2 yards. What was the yard line at the end of the fourth down?

Exercise $$\PageIndex{123}$$

Checking Account Mayra has $124 in her checking account. She writes a check for$152. What is the new balance in her checking account?

−$28 Exercise $$\PageIndex{124}$$ Checking Account Selina has$165 in her checking account. She writes a check for $207. What is the new balance in her checking account? Exercise $$\PageIndex{125}$$ Checking Account Diontre has a balance of −$38 in his checking account. He deposits $225 to the account. What is the new balance? Answer$187

Exercise $$\PageIndex{126}$$

Checking Account Reymonte has a balance of −$49 in his checking account. He deposits$281 to the account. What is the new balance?

Everyday Math

​​​​​​​

Exercise $$\PageIndex{127}$$

Stock market Javier owns 300 shares of stock in one company. On Tuesday, the stock price dropped \$12 per share. What was the total effect on Javier’s portfolio?

Weight loss In the first week of a diet program, eight women lost an average of 3 pounds each. What was the total weight change for the eight women?

Exercise $$\PageIndex{128}$$

Weight loss In the first week of a diet program, eight women lost an average of 3 pounds each. What was the total weight change for the eight women?

Writing Exercises

Exercise $$\PageIndex{129}$$

In your own words, state the rules for multiplying integers.

Exercise $$\PageIndex{130}$$

In your own words, state the rules for dividing integers.

Exercise $$\PageIndex{131}$$

Why is $$−2^{4}\neq (−2)^{4}$$?

Exercise $$\PageIndex{132}$$

Why is $$−4^{3}\neq (−4)^{3}$$?​​​​​​

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. ⓑ On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

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