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Evaluate each expression:

m 3 when

  1. m = 1
  2. m = −4

  1. −2
  2. −7

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Evaluate 20 z when

  1. z = 12
  2. z = 12

Solution

To evaluate 20 z when z = 12 , substitute 12 for z in the expression.

.
. .
Subtract. .

To evaluate 20 z when z = −12 , substitute −12 for z in the expression.

.
. .
Subtract. .

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Evaluate each expression:

17 k when

  1. k = 19
  2. k = −19

  1. −2
  2. 36

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Evaluate each expression:

−5 b when

  1. b = 14
  2. b = −14

  1. −19
  2. 9
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Translate word phrases to algebraic expressions

When we first introduced the operation symbols, we saw that the expression a b may be read in several ways as shown below.

This table has six rows. The first row has a - b. The second row states a minus b. The third row states the difference of a and b. The fourth row states subtract b from a. The fifth row states b subtracted from a. The sixth row states b less than a.

Be careful to get a and b in the right order!

Translate and then simplify:
the difference of 13 and −21

subtract 24 from −19

Solution

A difference means subtraction. Subtract the numbers in the order they are given.

.
Translate. .
Simplify. .

Subtract means to take 24 away from −19 .

.
Translate. .
Simplify. .

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Translate and simplify:

  1. the difference of 14 and −23
  2. subtract 21 from −17
  1. −14 − (−23) = 37
  2. −17 − 21 = −38
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Translate and simplify:

  1. the difference of 11 and −19
  2. subtract 18 from −11
  1. 11 − (−19) = 30
  2. −11 − 18 = −29
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Subtract integers in applications

It’s hard to find something if we don’t know what we’re looking for or what to call it. So when we solve an application problem, we first need to determine what we are asked to find. Then we can write a phrase that gives the information to find it. We’ll translate the phrase into an expression and then simplify the expression to get the answer. Finally, we summarize the answer in a sentence to make sure it makes sense.

Solve application problems.

  1. Identify what you are asked to find.
  2. Write a phrase that gives the information to find it.
  3. Translate the phrase to an expression.
  4. Simplify the expression.
  5. Answer the question with a complete sentence.

The temperature in Urbana, Illinois one morning was 11 degrees Fahrenheit. By mid-afternoon, the temperature had dropped to −9 degrees Fahrenheit. What was the difference between the morning and afternoon temperatures?

Solution

Step 1. Identify what we are asked to find. the difference between the morning and afternoon temperatures
Step 2. Write a phrase that gives the information to find it. the difference of 11 and −9
Step 3. Translate the phrase to an expression.
The word difference indicates subtraction.
11 ( −9 )
Step 4. Simplify the expression. 20
Step 5. Write a complete sentence that answers the question. The difference in temperature was 20 degrees Fahrenheit.
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The temperature in Anchorage, Alaska one morning was 15 degrees Fahrenheit. By mid-afternoon the temperature had dropped to 30 degrees below zero. What was the difference between the morning and afternoon temperatures?

45 degrees Fahrenheit

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The temperature in Denver was −6 degrees Fahrenheit at lunchtime. By sunset the temperature had dropped to −15 degree Fahrenheit. What was the difference between the lunchtime and sunset temperatures?

9 degrees Fahrenheit

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Geography provides another application of negative numbers with the elevations of places below sea level.

Dinesh hiked from Mt. Whitney, the highest point in California, to Death Valley, the lowest point. The elevation of Mt. Whitney is 14,497 feet above sea level and the elevation of Death Valley is 282 feet below sea level. What is the difference in elevation between Mt. Whitney and Death Valley?

Solution

Step 1. What are we asked to find? The difference in elevation between Mt. Whitney and Death Valley
Step 2. Write a phrase. elevation of Mt. Whitney−elevation of Death Valley
Step 3. Translate. 14,497 ( −282 )
Step 4. Simplify. 14,497
Step 5. Write a complete sentence that answers the question. The difference in elevation is 14,779 feet.
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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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