# 1.5E: Exercises

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- Page ID
- 30459

- Contributed by Lynn Marecek
- Professor (Mathematics) at Santa Ana College
- Publisher: OpenStax CNX

## 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

- y=−33
- y=30

**Answer**-
- −47
- 16

Exercise \(\PageIndex{88}\)

x+(−21) when

- x=−27
- x=44

Exercise \(\PageIndex{89}\)

- a+3 when a=−7
- −a+3 when a=−7

**Answer**-
- −4
- 10

Exercise \(\PageIndex{90}\)

- d+(−9) when d=−8
- −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

- x=8
- x=−8

**Answer**-
- 1
- 33

Exercise \(\PageIndex{98}\)

−5y+14 when

- y=9
- y=−9

Exercise \(\PageIndex{99}\)

10−3m when

- m=5
- m=−5

**Answer**-
- −5
- 25

Exercise \(\PageIndex{100}\)

18−4n when

- n=3
- 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

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?