1.5E: Exercises

Practice Makes Perfect

Multiply Integers

In the following exercises, multiply.

Exercise $\PageIndex{55}$

$−4\cdot 8$

Answer

-32

Exercise $\PageIndex{56}$

$-3\cdot 9$

Exercise $\PageIndex{57}$

$9(-7)$

Answer

-63

Exercise $\PageIndex{58}$

$13(-5)$

Exercise $\PageIndex{59}$

$-1\cdot 6$

Answer

-6

Exercise $\PageIndex{60}$

$-1\cdot 3$

Exercise $\PageIndex{61}$

$-1(-14)$

Answer

14

Exercise $\PageIndex{62}$

$-1(-19)$

Divide Integers

In the following exercises, divide.

Exercise $\PageIndex{63}$

$-24\div 6$

Answer

-4

Exercise $\PageIndex{64}$

$35\div (-7)$

Exercise $\PageIndex{65}$

$-52 \div (-4)$

Answer

13

Exercise $\PageIndex{66}$

$-84 \div (-6)$

Exercise $\PageIndex{67}$

$-180 \div 15$

Answer

-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

Answer

-47

Exercise $\PageIndex{70}$

8(−4)+5(−4)−6

Exercise $\PageIndex{71}$

$(-2)^{6}$

Answer

64

Exercise $\PageIndex{72}$

$(-3)^{5}$

Exercise $\PageIndex{73}$

$(-4)^{2}$

Answer

-16

Exercise $\PageIndex{74}$

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

Exercise $\PageIndex{75}$

−3(−5)(6)

Answer

90

Exercise $\PageIndex{76}$

−4(−6)(3)

Exercise $\PageIndex{77}$

(8−11)(9−12)

Answer

9

Exercise $\PageIndex{78}$

(6−11)(8−13)

Exercise $\PageIndex{79}$

26−3(2−7)

Answer

41

Exercise $\PageIndex{80}$

23−2(4−6)

Exercise $\PageIndex{81}$

$65\div (−5)+(−28)\div (−7)$

Answer

-9

Exercise $\PageIndex{82}$

$52\div(−4)+(−32)\div(−8)$

Exercise $\PageIndex{83}$

9−2[3−8(−2)]

Answer

-29

Exercise $\PageIndex{84}$

11−3[7−4(−20)]

Exercise $\PageIndex{85}$

$(−3)^{2}−24\div (8−2)$

Answer

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

Answer

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

Answer

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

Answer

-8

Exercise $\PageIndex{92}$

p+q when
p=−9,q=17

Exercise $\PageIndex{93}$

r+s when r=−9,s=−7

Answer

-16

Exercise $\PageIndex{94}$

t+u when t=−6,u=−5

Exercise $\PageIndex{95}$

$(x+y)^{2}$ when
x=−3,y=14

Answer

121

Exercise $\PageIndex{96}$

$(y+z)^{2}$ when
y=−3, z=15

Exercise $\PageIndex{97}$

−2x+17 when

1. x=8
2. x=−8

Answer

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

Answer

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

Answer

21

Exercise $\PageIndex{102}$

$3u^{2}−4u+5$

Exercise $\PageIndex{103}$

9a−2b−8 when
a=−6 and b=−3

Answer

-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

Answer

(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

Answer

10−(−18);28

Exercise $\PageIndex{108}$

subtract 11 from −25

Exercise $\PageIndex{109}$

the difference of −5 and −30

Answer

−5−(−30);25

Exercise $\PageIndex{110}$

subtract −6 from −13

Exercise $\PageIndex{111}$

the product of −3 and 15

Answer

$−3\cdot 15$;−45

Exercise $\PageIndex{112}$

the product of −4 and 16

Exercise $\PageIndex{113}$

the quotient of −60 and −20

Answer

$−60\div(−20)$;3

Exercise $\PageIndex{114}$

the quotient of −40 and −20

Exercise $\PageIndex{115}$

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

Answer

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

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

Answer

−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?

Answer

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?

Answer

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?

Answer​​​​​​​

−$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

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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?

Answer

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.

Answer

Answers may vary

Exercise $\PageIndex{130}$

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

Exercise $\PageIndex{131}$

Why is $−2^{4}\neq (−2)^{4}$?

Answer

Answers may vary

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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