Unit 4: More Working with Percent
Topic A: Finding What Percent One Number is of Another
In problems where you must find what percent one number is of another, the missing term is the percent. You will be told the part (is) and the whole (of), you know the 100, and you solve for the missing percent.
Example A
4 is what percent of 5?
- 4 is the part (is)
- 5 is the whole (of)
- % is unknown (call it P)
- Write the proportion:
[latex]\dfrac{4}{5} = \dfrac{\textit{P}}{100}[/latex] - Cross-multiply to solve:
[latex]\begin{equation}\begin{split} 4\times100 &= 5\times\textit{P} \\ 400 &= 5\textit{P} \\ 400\div5 &= \textit{P} \\ 80\% &= \textit{P} \end{split}\end{equation}[/latex]
Be sure to write the percent sign – %.
In percent problems, the number after “of” usually is the whole.The number close to “is” usually is the part. You may find it helpful to think “is over of”.
Like this: [latex]\dfrac{\text{is}}{\text{of}}[/latex].
An equal to sign (=) can substitute for “is”.
12 is what percent of 15?
[latex]\dfrac{\text{is}}{\text{of}}[/latex] will help to find [latex]\dfrac{\text{part}}{\text{whole}}[/latex].
[latex]\dfrac{12\text{ (is)}}{15\text{ (of)}}=\dfrac{\textit{N}}{100}[/latex]
Example B
What percent of 85 is 60?
- 60 = the part (close to “is”)
- 85 = the whole (after “of”)
- % = the unknown
- Set up the proportion: [latex]\dfrac{\text{is}}{\text{of}}[/latex]
[latex]\dfrac{60}{85} = \dfrac{\textit{P}}{100}[/latex]
- Simplify:
[latex]\dfrac{\cancel{60}12}{\cancel{85}17} = \dfrac{\textit{P}}{100}[/latex] - [latex]\dfrac{12}{17} = \dfrac{\textit{P}}{100}[/latex]
- Cross-multiply to solve:
[latex]12\times100 = 1,200[/latex], and [latex]17\times\textit{P}=17\textit{P}[/latex][latex]\begin{equation}\begin{split} 1,200 &= 17\textit{P} \\ 1,200\div17 &= \textit{P} \\ 70.588\% &= \textit{P} \end{split}\end{equation}[/latex]Round to 70.6%.
Exercise 1
The following examples ask you to find what percent one number is of another. The missing term is the percent. Look carefully at the wording and decide which number is the part (close to “is”) and which number is the whole thing (after “of”).Write the proportion but do not solve the problem.
- 3 is what % of 6?
- 12 is % of 5?
- What % of 27 is 9?
- What % of ½ is ¼?
- % of 50 is 25?
- % of 64 = 48
Answers to Exercise 1
- [latex]\dfrac{3}{6}=\dfrac{\textit{N}}{100}[/latex]
- [latex]\dfrac{\textit{F}}{100}=\dfrac{12}{5}[/latex]
- [latex]\dfrac{9}{27}=\dfrac{\textit{X}}{100}[/latex]
- [latex]\dfrac{\tfrac{1}{4}}{\tfrac{1}{2}}=\dfrac{\textit{P}}{100}[/latex]
- [latex]\dfrac{\textit{X}}{100}=\dfrac{25}{50}[/latex]
- [latex]\dfrac{48}{64}=\dfrac{\textit{N}}{100}[/latex]
Exercise 2
Solve each question by first setting up the proportion [latex]\dfrac{\text{is (part)}}{\text{of (whole)}}=\dfrac{\%}{100}[/latex]. Review p. 70 as necessary.
- 3 is what percent of 60?
- 3 is what percent of 4?
- 1 is what percent of 3?
- What % of 50 is 35?
- What percent of 350 is 42?
- 15 is % of 12.
- 14 is % of 700.
- What percent of