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Mathematics LibreTexts

1.4E: Exercises

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    30344
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    Practice Makes Perfect

    Use Negatives and Opposites of Integers

    In the following exercises, order each of the following pairs of numbers, using < or >.

    Exercise \(\PageIndex{1}\)

    1. 9___4
    2. −3___6
    3. −8___−2
    4. 1___−10
    Answer
    1. >
    2. <
    3. <
    4. >

    Exercise \(\PageIndex{2}\)

    1. −7___3
    2. −10___−5
    3. 2___−6
    4. 8___9

    In the following exercises, find the opposite of each number.

    Exercise \(\PageIndex{3}\)

    1. 2
    2. −6
    Answer
    1. −2
    2. 6

    Exercise \(\PageIndex{4}\)

    1. 9
    2. −4

    In the following exercises, simplify.

    Exercise \(\PageIndex{5}\)

    −(−4)

    Answer

    4

    Exercise \(\PageIndex{6}\)

    −(−8)

    Exercise \(\PageIndex{7}\)

    −(−15)

    Answer

    15

    Exercise \(\PageIndex{8}\)

    −(−11)

    In the following exercises, evaluate.

    Exercise \(\PageIndex{9}\)

    −c when

    1. c=12
    2. c=−12
    Answer
    1. −12
    2. 12
    1. Exercise \(\PageIndex{10}\)

    −d when

    1. d=21
    2. d=−21

    Simplify Expressions with Absolute Value

    In the following exercises, simplify.

    Exercise \(\PageIndex{11}\)

    1. |−32|
    2. |0|
    3. |16|
    Answer
    1. 32
    2. 0
    3. 16

    Exercise \(\PageIndex{12}\)

    1. |0|
    2. |−40|
    3. |22|

    In the following exercises, fill in <, >, or = for each of the following pairs of numbers.

    Exercise \(\PageIndex{13}\)

    1. −6___|−6|
    2. −|−3|___−3
    Answer
    1. <
    2. =

    Exercise \(\PageIndex{14}\)

    1. |−5|___−|−5|
    2. 9___−|−9|

    In the following exercises, simplify.

    Exercise \(\PageIndex{15}\)

    −(−5) and −|−5|

    Answer

    5,−5

    Exercise \(\PageIndex{16}\)

    −|−9| and −(−9)

    Exercise \(\PageIndex{17}\)

    8|−7|

    Answer

    56

    Exercise \(\PageIndex{18}\)

    5|−5|

    Exercise \(\PageIndex{19}\)

    |15−7|−|14−6|

    Answer

    0

    Exercise \(\PageIndex{20}\)

    |17−8|−|13−4|

    Exercise \(\PageIndex{21}\)

    18−|2(8−3)|

    Answer

    8

    Exercise \(\PageIndex{22}\)

    18−|3(8−5)|

    In the following exercises, evaluate.

    Exercise \(\PageIndex{23}\)

    1. −∣p∣ when p=19
    2. −∣q∣ when q=−33
    Answer
    1. −19
    2. −33

    Exercise \(\PageIndex{24}\)

    1. −|a| when a=60
    2. −|b| when b=−12

    Add Integers

    In the following exercises, simplify each expression.

    Exercise \(\PageIndex{25}\)

    −21+(−59)

    Answer

    -80

    Exercise \(\PageIndex{26}\)

    −35+(−47)

    Exercise \(\PageIndex{27}\)

    48+(−16)

    Answer

    32

    Exercise \(\PageIndex{28}\)

    34+(−19)

    Exercise \(\PageIndex{29}\)

    −14+(−12)+4

    Answer

    -22

    Exercise \(\PageIndex{30}\)

    −17+(−18)+6

    Exercise \(\PageIndex{31}\)

    135+(−110)+83

    Answer

    108

    Exercise \(\PageIndex{32}\)

    −38+27+(−8)+12

    Exercise \(\PageIndex{33}\)

    19+2(−3+8)

    Answer

    29

    Exercise \(\PageIndex{34}\)

    24+3(−5+9)

    Subtract Integers

    In the following exercises, simplify.

    Exercise \(\PageIndex{35}\)

    8−2

    Answer

    6

    Exercise \(\PageIndex{36}\)

    −6−(−4)

    Exercise \(\PageIndex{37}\)

    −5−4

    Answer

    -9

    Exercise \(\PageIndex{38}\)

    −7−2

    Exercise \(\PageIndex{39}\)

    8−(−4)

    Answer

    12

    Exercise \(\PageIndex{40}\)

    7−(−3)

    Exercise \(\PageIndex{41}\)

    1. 44−28
    2. 44+(−28)
    Answer
    1. 16
    2. 16

    Exercise \(\PageIndex{42}\)

    1. 35−16
    2. 35+(−16)

    Exercise \(\PageIndex{43}\)

    1. 27−(−18)
    2. 27+18
    Answer
    1. 45
    2. 45

    Exercise \(\PageIndex{44}\)

    1. 46−(−37)
    2. 46+37

    In the following exercises, simplify each expression.

    Exercise \(\PageIndex{45}\)

    15−(−12)

    Answer

    27

    Exercise \(\PageIndex{46}\)

    14−(−11)

    Exercise \(\PageIndex{47}\)

    48−87

    Answer

    -39

    Exercise \(\PageIndex{48}\)

    45−69

    Exercise \(\PageIndex{49}\)

    −17−42

    Answer

    -59

    Exercise \(\PageIndex{50}\)

    −19−46

    Exercise \(\PageIndex{51}\)

    −103−(−52)

    Answer

    -51

    Exercise \(\PageIndex{52}\)

    −105−(−68)

    Exercise \(\PageIndex{53}\)

    −45−(−54)

    Answer

    9

    Exercise \(\PageIndex{54}\)

    −58−(−67)

    Exercise \(\PageIndex{55}\)

    8−3−7

    Answer

    -2

    Exercise \(\PageIndex{56}\)

    9−6−5

    Exercise \(\PageIndex{57}\)

    −5−4+7

    Answer

    -2

    Exercise \(\PageIndex{58}\)

    −3−8+4

    Exercise \(\PageIndex{59}\)

    −14−(−27)+9

    Answer

    22

    Exercise \(\PageIndex{60}\)

    64+(−17)−9

    Exercise \(\PageIndex{61}\)

    (2−7)−(3−8)

    Answer

    0

    Exercise \(\PageIndex{62}\)

    (1−8)−(2−9)

    Exercise \(\PageIndex{63}\)

    −(6−8)−(2−4)

    Answer

    4

    Exercise \(\PageIndex{64}\)

    −(4−5)−(7−8)

    Exercise \(\PageIndex{65}\)

    25−[10−(3−12)]

    Answer

    6

    Exercise \(\PageIndex{66}\)

    32−[5−(15−20)]

    Exercise \(\PageIndex{67}\)

    6.3−4.3−7.2

    Answer

    -5.2

    Exercise \(\PageIndex{68}\)

    5.7−8.2−4.9

    Exercise \(\PageIndex{69}\)

    \(5^{2}−6^{2}\)

    Answer

    -11

    Exercise \(\PageIndex{70}\)

    \(6^{2}−7^{2}\)

    Everyday Math

    Exercise \(\PageIndex{71}\)

    Elevation The highest elevation in the United States is Mount McKinley, Alaska, at 20,320 feet above sea level. The lowest elevation is Death Valley, California, at 282 feet below sea level.

    Use integers to write the elevation of:

    1. Mount McKinley.
    2. Death Valley.
    Answer
    1. 20,329
    2. −282

    Exercise \(\PageIndex{72}\)

    Extreme temperatures The highest recorded temperature on Earth was 58° Celsius, recorded in the Sahara Desert in 1922. The lowest recorded temperature was 90° below 0° Celsius, recorded in Antarctica in 1983.

    Use integers to write the:

    1. highest recorded temperature.
    2. lowest recorded temperature.

    Exercise \(\PageIndex{73}\)

    State budgets In June, 2011, the state of Pennsylvania estimated it would have a budget surplus of $540 million. That same month, Texas estimated it would have a budget deficit of $27 billion.

    Use integers to write the budget of:

    1. Pennsylvania.
    2. Texas.
    Answer
    1. $540 million
    2. −$27 billion

    Exercise \(\PageIndex{74}\)

    College enrollments Across the United States, community college enrollment grew by 1,400,000 students from Fall 2007 to Fall 2010. In California, community college enrollment declined by 110,171 students from Fall 2009 to Fall 2010.

    Use integers to write the change in enrollment:

    1. in the U.S. from Fall 2007 to Fall 2010.
    2. in California from Fall 2009 to Fall 2010.

    Exercise \(\PageIndex{75}\)

    Stock Market The week of September 15, 2008 was one of the most volatile weeks ever for the US stock market. The closing numbers of the Dow Jones Industrial Average each day were:

    Monday −504
    Tuesday +142
    Wednesday −449
    Thursday +410
    Friday +369

    What was the overall change for the week? Was it positive or negative?

    Answer

    -32

    Exercise \(\PageIndex{76}\)

    Stock Market During the week of June 22, 2009, the closing numbers of the Dow Jones Industrial Average each day were:

    Monday −201
    Tuesday −16
    Wednesday −23
    Thursday +172
    Friday −34

    What was the overall change for the week? Was it positive or negative?

    Writing Exercises

    Exercise \(\PageIndex{77}\)

    Give an example of a negative number from your life experience.

    Answer

    Answers may vary

    Exercise \(\PageIndex{78}\)

    What are the three uses of the “−” sign in algebra? Explain how they differ.

    Exercise \(\PageIndex{79}\)

    Explain why the sum of −8 and 2 is negative, but the sum of 8 and −2 is positive.

    Answer

    Answers may vary

    Exercise \(\PageIndex{80}\)

    Give an example from your life experience of adding two negative numbers.

    Self Check

    ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

    A table is shown with four columns and five rows. The column titles, from left to right, are “I can …”, “Confidently”, “With some help” and “No – I don’t get it!” The first column includes the phrases “use negatives and opposites of integers.”, “Simplify: expressions with absolute value.”, “add integers.” and “subtract integers.”

    ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?