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Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

Chapter 3

Integers

Educators

GL

Problem 1

Locate and label the given points on a number line.
a. 2
b. ?2
c. ?5

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Problem 2

Locate and label the given points on a number line.
a. 5
b. ?5
c. ?2

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Problem 3

Locate and label the given points on a number line.
a. ?8
b. 8
c. ?6

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Problem 4

Locate and label the given points on a number line.
a. ?7
b. 7
c. ?1

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Problem 5

order each of the following pairs of numbers, using < or >.
a. 9__4
b. ?3__6
c. ?8__?2
d. 1__?10

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Problem 6

Order each of the following pairs of numbers, using < or >.
a. 6__2;
b. ?7__4;
c. ?9__?1;
d. 9__?3

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Problem 7

Order each of the following pairs of numbers, using < or >.
a. ?5__1;
b. ?4__?9;
c. 6__10;
d. 3__?8

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Problem 8

Order each of the following pairs of numbers, using < or >.
a. ?7__3;
b. ?10__?5;
c. 2__?6;
d. 8__9

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Problem 9

Find the opposite of each number.
a. 2
b. ?6

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Problem 10

Find the opposite of each number.
a. 9
b. ?4

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Problem 11

Find the opposite of each number.
a. ?8
b. 1

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Problem 12

Find the opposite of each number.
a. ?2
b. 6

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Problem 13

Simplify.
$-(-4)$

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Problem 14

Simplify.
$-(-8)$

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Problem 15

Simplify.
$-(-15)$

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Problem 16

Simplify.
$-(-11)$

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Problem 17

Evaluate.
$?m$ when
a. $m = 3$
b. $m = ?3$

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Problem 18

Evaluate.
$-p$ when
a. $p=6$
b. $p=-6$

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Problem 19

Evaluate.
$?c$ when
a. $c = 12$
b. $c = ?12$

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Problem 20

Evaluate.
$?d$ when
a. $d = 21$
b. $d = ?21$

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Problem 21

Simplify each absolute value expression.
(a) $|7|$
(b) $|-25|$
(c) $|0|$

GL
Gabriela L.
Numerade Educator

Problem 22

Simplify each absolute value expression.
(a) $|5|$
(b) $|20|$
(c) $|-19|$

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Problem 23

Simplify each absolute value expression.
(a) $|-31|$
(b) $|-18|$
(c) $|16|$

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Problem 24

Simplify each absolute value expression.
(a) $|-41|$
(b) $|-40|$
(c) $|22|$

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Problem 25

Evaluate each absolute value expression.
(a) $|x|$ when $x=-28$
( b) $|-u|$ when $u=-15$

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Problem 26

Evaluate each absolute value expression.
(a) $|y|$ when $y=-37$
(b) $|-z|$ when $z=-24$

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Problem 27

Evaluate each absolute value expression.
(a) $-|p|$ when $p=19$
(b) $-|q|$ when $q=-33$

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Problem 28

Evaluate each absolute value expression.
(a) $-|a|$ when $a=60$
(b) $-|b|$ when $b=-12$

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Problem 29

Fill in $<,>,$ or $=$ to compare each expression.
a. ?6__|?6|
b. ? |?3|__?3

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Problem 30

Fill in $<,>,$ or $=$ to compare each expression.
a. ?8__|?8|
b. ? |?2|__?2

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Problem 31

Fill in $<,>,$ or $=$ to compare each expression.
a. |?5|__ ? |?5|
b. 9__ ? |?9|

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Problem 31

Fill in $<,>,$ or $=$ to compare each expression.
a. |?3|__ ? |?3|
b. 4__ ? |?4|

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Problem 33

Simplify each expression.
$|8-4|$

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Problem 34

Simplify each expression.
$|9-6|$

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Problem 35

Simplify each expression.
8$|-7|$

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Problem 36

Simplify each expression.
5$|-5|$

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Problem 37

Simplify each expression.
$|15-7|-|14-6|$

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Problem 38

Simplify each expression.
$|17-8|-|13-4|$

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Problem 39

Simplify each expression.
$18-|2(8-3)|$

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Problem 40

Simplify each expression.
$15-|3(8-5)|$

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Problem 41

Simplify each expression.
8$(14-2|-2|)$

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Problem 42

Simplify each expression.
6$(13-4|-2|)$

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Problem 43

Translate each phrase into an expression with integers. Do not simplify.
a the opposite of 8
b the opposite of ?6
c negative three
d 4 minus negative 3

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Problem 44

Translate each phrase into an expression with integers. Do not simplify.
a the opposite of 11
b the opposite of ?4
c negative nine
d 8 minus negative 2

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Problem 45

Translate each phrase into an expression with integers. Do not simplify.
a the opposite of 20
b the opposite of ?5
c negative twelve
d 18 minus negative 7

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Problem 46

Translate each phrase into an expression with integers. Do not simplify.
a the opposite of 15
b the opposite of ?9
c negative sixty
d 12 minus 5

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Problem 47

Translate each phrase into an expression with integers. Do not simplify.
a temperature of 6 degrees below zero

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Problem 48

Translate each phrase into an expression with integers. Do not simplify.
a temperature of 14 degrees below zero

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Problem 49

Translate each phrase into an expression with integers. Do not simplify.
an elevation of 40 feet below sea level

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Problem 50

Translate each phrase into an expression with integers. Do not simplify.
an elevation of 65 feet below sea level

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Problem 51

Translate each phrase into an expression with integers. Do not simplify.
a football play loss of 12 yards

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Problem 52

Translate each phrase into an expression with integers. Do not simplify.
a football play gain of 4 yards

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Problem 53

Translate each phrase into an expression with integers. Do not simplify.
a stock gain of $3

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Problem 54

Translate each phrase into an expression with integers. Do not simplify.
a stock loss of $5

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Problem 55

Translate each phrase into an expression with integers. Do not simplify.
a golf score one above par

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Problem 56

Translate each phrase into an expression with integers. Do not simplify.
a golf score of 3 below par

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Problem 57

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:
a. Mount McKinley
b. Death Valley

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Problem 58

Extreme temperatures The highest recorded a temperature on Earth is $58^{\circ}$ Celsius, recorded in the Sahara Desert in 1922 . The lowest recorded e temperature is $90^{\circ}$ below $0^{\circ}$ Celsius, recorded in Antarctica in $1983 .$ Use integers to write the:
a. highest recorded temperature
b. lowest recorded temperature

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Problem 59

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
a. surplus
b. deficit

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Problem 60

College enrollments Across the United States, community college enrollment grew by 1,400,000 students from 2007 to 2010. In California, community college enrollment declined by 110,171 students from 2009 to 2010. Use integers to write the change in enrollment:
a. growth
b. decline

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Problem 61

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

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Problem 62

What are the three uses of the $"_{-}^{m}$ sign in algebra? Explain how they differ.

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