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?
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?