example
Translate and simplify: the sum of [latex]-9[/latex] and [latex]5[/latex].
Solution:
| The sum of [latex]−9[/latex] and [latex]5[/latex] indicates addition. |
the sum of [latex]-9[/latex] and [latex]5[/latex] |
| Translate. |
[latex]-9+5[/latex] |
| Simplify. |
[latex]-4[/latex] |
Now you can try a similar problem.
In the next example we add another term to the expression that is being translated. The result is an expression that contains three terms that are added or subtracted.
example
Translate and simplify: the sum of [latex]8[/latex] and [latex]-12[/latex], increased by [latex]3[/latex].
Answer:
Solution:
The phrase increased by indicates addition.
|
The sum of [latex]8[/latex] and [latex]-12[/latex] , increased by [latex]3[/latex] |
| Translate. |
[latex]\left[8+\left(-12\right)\right]+3[/latex] |
| Simplify. |
[latex]-4+3[/latex] |
| Add. |
[latex]-1[/latex] |
Now you can try a similar problem.
example
The temperature in Buffalo, NY, one morning started at [latex]7\text{ degrees}[/latex] below zero Fahrenheit. By noon, it had warmed up [latex]12\text{ degrees}[/latex]. What was the temperature at noon?
Answer:
Solution:
We are asked to find the temperature at noon.
| Write a phrase for the temperature. |
The temperature warmed up 12 degrees from 7 degrees below zero. |
| Translate to math notation. |
[latex]−7 + 12[/latex] |
| Simplify. |
[latex]5[/latex] |
| Write a sentence to answer the question. |
The temperature at noon was [latex]5[/latex] degrees Fahrenheit. |
Now you can try a similar problem.
In the following video we show a similar example.
https://youtu.be/Ozqs2JdnOI8
In the next example, a football team gaining and losing yardage can be represented with positive and negative numbers.
example
A football team took possession of the football on their [latex]\text{42-yard line.}[/latex] In the next three plays, they lost [latex]\text{6 yards,}[/latex] gained [latex]\text{4 yards,}[/latex] and then lost [latex]\text{8 yards.}[/latex] On what yard line was the ball at the end of those three plays?
Answer:
Solution:
We are asked to find the yard line the ball was on at the end of three plays.
| Write a word phrase for the position of the ball. |
Start at [latex]42[/latex], then lose [latex]6[/latex], gain [latex]4[/latex], lose [latex]8[/latex]. |
| Translate to math notation. |
[latex]42-6+4−8[/latex] |
| Simplify. |
[latex]32[/latex] |
| Write a sentence to answer the question. |
At the end of the three plays, the ball is on the 32-yard line. |
Now you can try a similar problem.
The following video shows more examples of translating expressions that involve integers, and simplifying the result.
https://youtu.be/Cv3cIoiSUtk
