Articles

13.5.4E: Exercises - Mathematics


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.

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


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