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3.1 Introduction to Integers

Negative numbers placed and ordered on the number line, opposites, absolute value as distance from zero, and phrases like below zero or a loss.

Prealgebra 2e, 3.1 Introduction to Integers

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62 exercises

3.1 Exercise 2

Fill in the appropriate symbol: (=, <, or >):2___4(=,\text{ }<,\text{ or }>): 2 ___ 4
If you missed this problem, review the reference.

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3.1 Exercise 7

Order each of the following pairs of numbers using << or >.>.

  1. ⓐ 15___715 ___ 7
  2. ⓑ −2___5−2 ___ 5
  3. ⓒ −3___−7−3 ___ −7
  4. ⓓ 5___−175 ___ −17

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3.1 Exercise 8

Order each of the following pairs of numbers using << or >.>.

  1. ⓐ 8___138 ___ 13
  2. ⓑ 3___−43 ___ −4
  3. ⓒ −5___−2−5 ___ −2
  4. ⓓ 9___−219 ___ −21

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3.1 Exercise 10

Find the opposite of each number:

  1. ⓐ 4 4
  2. ⓑ −3−3

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3.1 Exercise 11

Find the opposite of each number:

  1. ⓐ 88
  2. ⓑ −5−5

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3.1 Exercise 12

Simplify: −(−6).- \left(−6\right) .

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3.1 Exercise 13

Simplify:

−(−1)- \left(−1\right)

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3.1 Exercise 14

Simplify:

−(−5)- \left(−5\right)

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3.1 Exercise 16

Evaluate −n:- n :

  1. ⓐ whenn=4\text{when} n = 4
  2. ⓑ whenn=−4\text{when} n = −4

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3.1 Exercise 17

Evaluate: −m:- m :

  1. ⓐ whenm=11\text{when} m = 11
  2. ⓑ whenm=−11\text{when} m = −11

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3.1 Exercise 18

Simplify:

  1. ⓐ |3|\left|3\right|
  2. ⓑ |−44|\left|−44\right|
  3. ⓒ |0|\left|0\right|

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3.1 Exercise 19

Simplify:

  1. ⓐ |12|\left|12\right|
  2. ⓑ −|−28|- \left|−28\right|

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3.1 Exercise 20

Simplify:

  1. ⓐ |9|\left|9\right|
  2. ⓑ −|37|- \left|37\right|

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3.1 Exercise 22

Evaluate:

  1. ⓐ |x|whenx=−17\left|x\right| \text{when} x = −17
  2. ⓑ |−y|wheny=−39\left|−\textit{y}\right| \text{when} y = −39
  3. ⓒ −|m|whenm=22- \left|m\right| \text{when} m = 22
  4. ⓓ −|p|whenp=−11- \left|p\right| \text{when} p = −11

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3.1 Exercise 23

  1. ⓐ |y|wheny=−23\left|y\right| \text{when} y = −23
  2. ⓑ |−y|wheny=−21\left|- y\right| \text{when} y = −21
  3. ⓒ −|n|whenn=37- \left|n\right| \text{when} n = 37
  4. ⓓ −|q|whenq=−49- \left|q\right| \text{when} q = −49
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3.1 Exercise 24

Fill in <,>,or=< , > , \text{or} = for each of the following:

  1. ⓐ |−5|___−|−5|\left|−5\right| ___ - \left|−5\right|
  2. ⓑ 8___−|−8|8 ___ - \left|−8\right|
  3. ⓒ −9___−|−9|−9 ___ - \left|−9\right|
  4. ⓓ −|−7|___−7- \left|−7\right| ___ −7

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3.1 Exercise 25

Fill in <,>,or=for each of the following:< , > , \text{or} = \text{for each of the following}:

  1. ⓐ |−9|___−|−9|\left|−9\right| ___ - \left|−9\right|
  2. ⓑ 2___−|−2|2 ___ - \left|−2\right|
  3. ⓒ −8___|−8|−8 ___ \left|−8\right|
  4. ⓓ −|−5|___−5- \left|−5\right| ___ −5

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3.1 Exercise 26

Fill in <,>,or=< , > , \text{or} = for each of the following:

  1. ⓐ 7___−|−7|7 ___ - \left|−7\right|
  2. ⓑ −|−11|___−11- \left|−11\right| ___ −11
  3. ⓒ |−4|___−|−4|\left|−4\right| ___ - \left|−4\right|
  4. ⓓ −1___|−1|−1 ___ \left|−1\right|

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3.1 Exercise 27

Simplify:

  1. ⓐ |9−3|\left|9 −3\right|
  2. ⓑ 4|−2|4 \left|−2\right|

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3.1 Exercise 28

Simplify:

  1. ⓐ |12−9|\left|12 - 9\right|
  2. ⓑ 3|−6|3 \left|−6\right|

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3.1 Exercise 29

Simplify:

  1. ⓐ |27−16|\left|27 - 16\right|
  2. ⓑ 9|−7|9 \left|−7\right|

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3.1 Exercise 30

Simplify: |8+7|−|5+6|.\left|8 + 7\right| - \left|5 + 6\right| .

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3.1 Exercise 31

Simplify: |1+8|−|2+5|\left|1 + 8\right| - \left|2 + 5\right|

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3.1 Exercise 32

Simplify: |9−5|−|7−6|\left|9 −5\right| - \left|7 - 6\right|

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3.1 Exercise 33

Simplify: 24−|19−3(6−2)|.24 - \left|19 - 3 \left(6 - 2\right)\right| .

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3.1 Exercise 34

Simplify: 19−|11−4(3−1)|19 - \left|11 - 4 \left(3 - 1\right)\right|

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3.1 Exercise 35

Simplify: 9−|8−4(7−5)|9 - \left|8 - 4 \left(7 - 5\right)\right|

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3.1 Exercise 36

Translate each phrase into an expression with integers:

  1. ⓐ the opposite of positive fourteen
  2. ⓑ the opposite of −11−11
  3. ⓒ negative sixteen
  4. ⓓ two minus negative seven

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3.1 Exercise 37

Translate each phrase into an expression with integers:

  1. ⓐ the opposite of positive nine
  2. ⓑ the opposite of −15−15
  3. ⓒ negative twenty
  4. ⓓ eleven minus negative four

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3.1 Exercise 38

Translate each phrase into an expression with integers:

  1. ⓐ the opposite of negative nineteen
  2. ⓑ the opposite of twenty-two
  3. ⓒ negative nine
  4. ⓓ negative eight minus negative five

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3.1 Exercise 39

Translate into an expression with integers:

  1. ⓐ The temperature is 12degrees Fahrenheit12 \text{degrees Fahrenheit} below zero.
  2. ⓑ The football team had a gain of 3yards.3 \text{yards}.
  3. ⓒ The elevation of the Dead Sea is 1,302feet1,302 \text{feet} below sea level.
  4. ⓓ A checking account is overdrawn by $40.\$\text{40}.

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3.1 Exercise 40

Translate into an expression with integers:

The football team had a gain of 5yards.5 \text{yards}.

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3.1 Exercise 41

Translate into an expression with integers:

The scuba diver was 30feet30 \text{feet} below the surface of the water.

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3.1 Exercise 46

Order each of the following pairs of numbers, using << or >.>.

  1. ⓐ 9__49 __ 4
  2. ⓑ −3__6−3 __ 6
  3. ⓒ −8__−2−8 __ −2
  4. ⓓ 1__−101 __ −10

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3.1 Exercise 48

Order each of the following pairs of numbers, using << or >.>.

  1. ⓐ −5__1;−5 __ 1 ;
  2. ⓑ −4__−9;−4 __ −9 ;
  3. ⓒ 6__10;6 __ 10 ;
  4. ⓓ 3__−83 __ −8
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3.1 Exercise 50

Find the opposite of each number.

  1. ⓐ 22
  2. ⓑ −6−6
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3.1 Exercise 52

Find the opposite of each number.

  1. ⓐ −8−8
  2. ⓑ 11
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3.1 Exercise 54

Simplify.

−(−4)- \left(−4\right)

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3.1 Exercise 56

Simplify.

−(−15)- \left(−15\right)

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3.1 Exercise 58

Evaluate.

−mwhen- m \text{when}

  1. ⓐ m=3m = 3
  2. ⓑ m=−3m = −3

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3.1 Exercise 60

Evaluate.

−cwhen- c \text{when}

  1. ⓐ c=12c = 12
  2. ⓑ c=−12c = −12

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3.1 Exercise 62

Simplify each absolute value expression.

  1. ⓐ |7|\left|7\right|
  2. ⓑ |−25|\left|−25\right|
  3. ⓒ|0|\left|0\right|
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3.1 Exercise 64

Simplify each absolute value expression.

  1. ⓐ |−32|\left|−32\right|
  2. ⓑ |−18|\left|−18\right|
  3. ⓒ |16|\left|16\right|
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3.1 Exercise 66

Evaluate each absolute value expression.

  1. ⓐ |x|whenx=−28\left|x\right| \text{when} x = −28
  2. ⓑ |−u|whenu=−15\left|- u\right| \text{when} u = −15
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3.1 Exercise 68

Evaluate each absolute value expression.

  1. ⓐ −|p|whenp=19- \left|p\right| \text{when} p = 19
  2. ⓑ −|q|whenq=−33- \left|q\right| \text{when} q = −33
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3.1 Exercise 70

Fill in <,>,or=< , > , \text{or} = to compare each expression.

  1. ⓐ −6__|−6|−6 __ \left|−6\right|
  2. ⓑ −|−3|__−3- \left|−3\right| __ −3
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3.1 Exercise 72

Fill in <,>,or=< , > , \text{or} = to compare each expression.

  1. ⓐ |−3|__−|−3|\left|−3\right| __ - \left|−3\right|
  2. ⓑ 4__−|−4|4 __ - \left|−4\right|
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3.1 Exercise 74

Simplify each expression.

|8−4|\left|8 - 4\right|

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3.1 Exercise 76

Simplify each expression.

8|−7|8 \left|−7\right|

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3.1 Exercise 78

Simplify each expression.

|15−7|−|14−6|\left|15 - 7\right| - \left|14 - 6\right|

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3.1 Exercise 80

Simplify each expression.

18−|2(8−3)|18 - \left|2 \left(8 - 3\right)\right|

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3.1 Exercise 82

Simplify each expression.

8(14−2|−2|)8 \left(14 - 2 \left|−2\right|\right)

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3.1 Exercise 84

Translate each phrase into an expression with integers. Do not simplify.

  1. ⓐ the opposite of 88
  2. ⓑ the opposite of −6−6
  3. ⓒ negative three
  4. ⓓ 44 minus negative 33
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3.1 Exercise 86

Translate each phrase into an expression with integers. Do not simplify.

  1. ⓐ the opposite of 2020
  2. ⓑ the opposite of −5−5
  3. ⓒ negative twelve
  4. ⓓ 1818 minus negative 77
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3.1 Exercise 88

Translate each phrase into an expression with integers. Do not simplify.

a temperature of 6degrees6 \text{degrees} below zero

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3.1 Exercise 90

Translate each phrase into an expression with integers. Do not simplify.

an elevation of 40feet40 \text{feet} below sea level

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3.1 Exercise 92

Translate each phrase into an expression with integers. Do not simplify.

a football play loss of 12yards12 \text{yards}

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3.1 Exercise 94

Translate each phrase into an expression with integers. Do not simplify.

a stock gain of $3\$\text{3}

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3.1 Exercise 96

Translate each phrase into an expression with integers. Do not simplify.

a golf score one above par

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3.1 Exercise 98

Elevation The highest elevation in the United States is Mount McKinley, Alaska, at 20,320feet20,320 \text{feet} above sea level. The lowest elevation is Death Valley, California, at 282feet282 \text{feet} below sea level. Use integers to write the elevation of:

  1. ⓐ Mount McKinley
  2. ⓑ Death Valley

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3.1 Exercise 100

State budgets In June, 2011, the state of Pennsylvania estimated it would have a budget surplus of $540 million.\$\text{540 million}. That same month, Texas estimated it would have a budget deficit of $27 billion.\$\text{27 billion}. Use integers to write the budget:

  1. ⓐ surplus
  2. ⓑ deficit

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3.1 Exercise 102

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

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Adapted from Prealgebra 2e © 2020 Rice University. Licensed under CC BY 4.0. Source: Prealgebra 2e. Imported at revision 77a933c.