example
Translate and then simplify:
- The difference of [latex]13[/latex] and [latex]-21[/latex]
- Subtract [latex]24[/latex] from [latex]-19[/latex]
Solution
1. A
difference means subtraction. Subtract the numbers in the order they are given.
|
[latex]\text{the }\color{red}{difference}\text{ of }13\text{ and }--21[/latex] |
Translate. |
[latex]13--(--21)[/latex] |
Simplify. |
[latex]34[/latex] |
2. Subtract means to take [latex]24[/latex] away from [latex]-19[/latex].
|
[latex]\color{red}{subtract } 24\color{red}{ from }--19[/latex] |
Translate. |
[latex]--19--24[/latex] |
Simplify. |
[latex]--43[/latex] |
Watch teh following video to see more examples of how to translate an expression in words that represents subtraction into a mathematical expression.
https://youtu.be/yOeIxabFi0c
example
The temperature in Urbana, Illinois one morning was [latex]11[/latex] degrees Fahrenheit. By mid-afternoon, the temperature had dropped to [latex]-9[/latex] degrees Fahrenheit. What was the difference between the morning and afternoon temperatures?
Answer:
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 [latex]11[/latex] and [latex]-9[/latex] |
Step 3. Translate the phrase to an expression.
The word difference indicates subtraction. |
[latex]11-\left(-9\right)[/latex] |
Step 4. Simplify the expression. |
[latex]20[/latex] |
Step 5. Write a complete sentence that answers the question. |
The difference in temperature was [latex]20[/latex] degrees Fahrenheit. |
Geography provides another application of negative numbers with the elevations of places below sea level.
example
Dinesh hiked from Mt. Whitney, the highest point in California, to Death Valley, the lowest point. The elevation of Mt. Whitney is [latex]14,497[/latex] feet above sea level and the elevation of Death Valley is [latex]282[/latex] feet below sea level. What is the difference in elevation between Mt. Whitney and Death Valley?
Answer:
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. |
[latex]14,497-\left(-282\right)[/latex] |
Step 4. Simplify. |
[latex]14,779[/latex] |
Step 5. Write a complete sentence that answers the question. |
The difference in elevation is [latex]14,779[/latex] feet. |
Managing your money can involve both positive and negative numbers. You might have overdraft protection on your checking account. This means the bank lets you write checks for more money than you have in your account (as long as they know they can get it back from you!)
example
Leslie has [latex]$25[/latex] in her checking account and she writes a check for [latex]$8[/latex]
- What is the balance after she writes the check?
- She writes a second check for [latex]$20[/latex] What is the new balance after this check?
- Leslie’s friend told her that she had lost a check for [latex]$10[/latex] that Leslie had given her with her birthday card. What is the balance in Leslie’s checking account now?
Answer:
Solution
1. |
|
What are we asked to find? |
The balance of the account |
Write a phrase. |
[latex]$25[/latex] minus [latex]$8[/latex] |
Translate |
[latex]$25--$8[/latex] |
Simplify. |
[latex]$17[/latex] |
Write a sentence answer. |
The balance is [latex]$17[/latex] . |
2. |
|
What are we asked to find? |
The new balance |
Write a phrase. |
[latex]$17[/latex] minus [latex]$20[/latex] |
Translate |
[latex]$17--$20[/latex] |
Simplify. |
[latex]--$3[/latex] |
Write a sentence answer. |
She is overdrawn by [latex]$3[/latex] . |
3. |
|
What are we asked to find? |
The new balance |
Write a phrase. |
[latex]$10[/latex] more than [latex]-$3[/latex] |
Translate |
[latex]--$3+$10[/latex] |
Simplify. |
[latex]$7[/latex] |
Write a sentence answer. |
The balance is now [latex]$7[/latex] . |
Watch teh following video to see another example that uses integers to represent the balance of a checking account.