example

Translate and then simplify:

1. The difference of [latex]13[/latex] and [latex]-21[/latex]
2. 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]

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.

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.

example

Leslie has [latex]$25[/latex] in her checking account and she writes a check for [latex]$8[/latex]

1. What is the balance after she writes the check?
2. She writes a second check for [latex]$20[/latex] What is the new balance after this check?
3. 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] .