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Simplify Expressions with Integers

In the following exercises, simplify each expression.

  1. 15 6
  2. 15 + ( −6 )

  1. 9
  2. 9

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  1. 12 9
  2. 12 + ( −9 )

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  1. 44 28
  2. 44 + ( −28 )

  1. 16
  2. 16

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  1. 35 16
  2. 35 + ( −16 )

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  1. 8 ( −9 )
  2. 8 + 9

  1. 17
  2. 17

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  1. 4 ( −4 )
  2. 4 + 4
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  1. 27 ( −18 )
  2. 27 + 18
  1. 45
  2. 45
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  1. 46 ( −37 )
  2. 46 + 37
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In the following exercises, simplify each expression.

−103 ( −52 )

−51

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−14 ( −27 ) + 9

22

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−16 ( −4 + 1 ) 7

−20

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−15 ( −6 + 4 ) 3

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( 2 7 ) ( 3 8 )

0

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( 1 8 ) ( 2 9 )

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( 6 8 ) ( 2 4 )

4

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( 4 5 ) ( 7 8 )

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25 [ 10 ( 3 12 ) ]

6

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32 [ 5 ( 15 20 ) ]

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6 · 3 4 · 3 7 · 2

−8

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5 · 7 8 · 2 4 · 9

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Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression for the given values.

x 6 when

  1. x = 3
  2. x = −3

  1. −3
  2. −9
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x 4 when

  1. x = 5
  2. x = −5

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5 y when

  1. y = 2
  2. y = −2

  1. 3
  2. 7
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8 y when

  1. y = 3
  2. y = −3

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4 x 2 15 x + 1 when x = 3

−8

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5 x 2 14 x + 7 when x = 2

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−12 5 x 2 when x = 6

−192

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−19 4 x 2 when x = 5

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Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

  1. The difference of 3 and −10
  2. Subtract −20 from 45
  1. −3 − (−10) = 13
  2. 45 − (−20) = 65
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  1. The difference of 8 and −12
  2. Subtract −13 from 50
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  1. The difference of −6 and 9
  2. Subtract −12 from −16
  1. −6 − 9 = −15
  2. −16 − (−12) = −4
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  1. The difference of −8 and 9
  2. Subtract 15 from 19
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  1. 8 less than −17
  2. 24 minus 37
  1. −17 − 8 = −25
  2. −24 − 37 = −61
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  1. 5 less than −14
  2. −13 minus 42
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  1. 21 less than 6
  2. 31 subtracted from −19
  1. 6 − 21 = −15
  2. −19 − 31 = −50
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  1. 34 less than 7
  2. 29 subtracted from −50
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Subtract Integers in Applications

In the following exercises, solve the following applications.

Temperature One morning, the temperature in Urbana, Illinois, was 28° Fahrenheit. By evening, the temperature had dropped 38° Fahrenheit. What was the temperature that evening?

−10°

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Temperature On Thursday, the temperature in Spincich Lake, Michigan, was 22° Fahrenheit. By Friday, the temperature had dropped 35° Fahrenheit. What was the temperature on Friday?

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Temperature On January 15, the high temperature in Anaheim, California, was 84° Fahrenheit. That same day, the high temperature in Embarrass, Minnesota was −12° Fahrenheit. What was the difference between the temperature in Anaheim and the temperature in Embarrass?

96°

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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?

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Football At the first down, the Warriors football team had the ball on their 30-yard line. On the next three downs, they gained 2 yards, lost 7 yards, and lost 4 yards. What was the yard line at the end of the third down?

21-yard line

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Football At the first down, the Barons football team had the ball on their 20-yard line. On the next three downs, they lost 8 yards, gained 5 yards, and lost 6 yards. What was the yard line at the end of the third down?

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Checking Account John has $148 in his checking account. He writes a check for $83. What is the new balance in his checking account?

$65

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Checking Account Ellie has $426 in her checking account. She writes a check for $152. What is the new balance in her checking account?

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Checking Account Gina has $210 in her checking account. She writes a check for $250. What is the new balance in her checking account?

−$40

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Checking Account Frank has $94 in his checking account. He writes a check for $110. What is the new balance in his checking account?

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Checking Account Bill has a balance of −$14 in his checking account. He deposits $40 to the account. What is the new balance?

$26

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Checking Account Patty has a balance of −$23 in her checking account. She deposits $80 to the account. What is the new balance?

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Everyday math

Camping Rene is on an Alpine hike. The temperature is 7 ° . Rene’s sleeping bag is rated “comfortable to 20 °”. How much can the temperature change before it is too cold for Rene’s sleeping bag?

13°

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Scuba Diving Shelly’s scuba watch is guaranteed to be watertight to −100 feet . She is diving at −45 feet on the face of an underwater canyon. By how many feet can she change her depth before her watch is no longer guaranteed?

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Writing exercises

Explain why the difference of 9 and −6 is 15 .

Sample answer: On a number line, 9 is 15 units away from −6.

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Why is the result of subtracting 3 ( −4 ) the same as the result of adding 3 + 4 ?

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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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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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