Example
Translate each phrase into an expression with integers:
- The opposite of positive fourteen
- The opposite of [latex]-11[/latex]
- Negative sixteen
- Two minus negative seven
Solution:
- The opposite of fourteen is [latex]-14[/latex]
- The opposite of −11 is [latex]-\left(-11\right)[/latex]
- Negative sixteen is [latex]-16[/latex]
- Two minus negative seven is [latex]2-\left(-7\right)[/latex]
As we saw at the start of this section, 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:
- The temperature is [latex]12\text{degrees Fahrenheit}[/latex] below zero.
- The football team had a gain of [latex]3\text{yards.}[/latex]
- The elevation of the Dead Sea is [latex]1,302\text{feet}[/latex] below sea level.
- A checking account is overdrawn by [latex]$40[/latex]
Answer:
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.
| 1. |
The temperature is [latex]12 degrees[/latex] Fahrenheit below zero. |
| Below zero tells us that [latex]12[/latex] is a negative number. |
[latex]-12[/latex] F |
| 2. |
The football team had a gain of [latex]3[/latex] yards. |
| A gain tells us that [latex]3[/latex] is a positive number. |
[latex]3[/latex] yards |
| 3. |
The elevation of the Dead Sea is [latex]1,302[/latex] feet below sea level. |
| Below sea level tells us that [latex]1,302[/latex] is a negative number. |
[latex]-1,302[/latex] feet |
| 4. |
A checking account is overdrawn by [latex]$40[/latex]. |
| Overdrawn tells us that [latex]40[/latex] is a negative number. |
[latex]-$40[/latex] |
