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Mathematics LibreTexts

1.5E: Exercises

  • Page ID
    30459
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    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

    ​​​​​​​

    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.

    A table is shown that is composed of four columns and seven rows. The titles of the columns are “I can …”, “Confidently”, “With some help” and “No – I don’t get it!”. The first column reads “multiple integers.”, “divide integers.”, “simplify expressions with integers.”, “evaluate variable expressions with integers.”, “translate English phrases to algebraic expressions.” and “use integers in applications.”

    ⓑ 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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