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Translating Word Phrases into Expressions with Integers

Translating Word Phrases into Expressions with Integers

Now we can translate word phrases into expressions with integers. Look for words that indicate a negative sign. For example, the word negative in “negative twenty” indicates \(-20.\) So does the word opposite in “the opposite of \(20\text{.”}\)

Example

Translate each phrase into an expression with integers:

  1. the opposite of positive fourteen
  2. the opposite of \(-11\)
  3. negative sixteen
  4. two minus negative seven

Solution

  1. the opposite of fourteen
     

    \(-14\)

  2. the opposite of −11
     

    \(-\left(-11\right)\)

  3. negative sixteen
     

    \(-16\)

  4. two minus negative seven
     

    \(2-\left(-7\right)\)

As we saw at the start of this tutorial, negative numbers are needed to describe many real-world situations. We’ll look at some more applications of negative numbers in the next example.

Example

Translate into an expression with integers:

  1. The temperature is \(12\phantom{\rule{0.2em}{0ex}}\text{degrees Fahrenheit}\) below zero.
  2. The football team had a gain of \(3\phantom{\rule{0.2em}{0ex}}\text{yards.}\)
  3. The elevation of the Dead Sea is \(1,302\phantom{\rule{0.2em}{0ex}}\text{feet}\) below sea level.
  4. A checking account is overdrawn by \(\text{$40.}\)

Solution 

Look for key phrases in each sentence. Then look for words that indicate negative signs. Don’t forget to include units of measurement described in the sentence.

 The temperature is 12 degrees Fahrenheit below zero.
Below zero tells us that 12 is a negative number.\(-12ºF\)
 The football team had a gain of 3 yards.
A gain tells us that 3 is a positive number.\(3\) yards
 The elevation of the Dead Sea is 1,302 feet below sea level.
Below sea level tells us that 1,302 is a negative number.\(-1,302\) feet
 A checking account is overdrawn by $40.
Overdrawn tells us that 40 is a negative number.\(-$40\)

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