Unit 3: Working with Percent
Topic A: Finding a Percent of a Number
In problems in which you find a percent of a number, the missing term is the part. You will be given the % which is always 100.
Example A
What is [latex]25\%\text{ of }40[/latex]?
- Part (is) = N
- Whole (of) = 40
- % = 25
[latex]\dfrac{\textit{is}}{\textit{of}}=\dfrac{\%}{100}\longrightarrow\dfrac{\textit{N}}{40}=\dfrac{25}{100}[/latex]
Solve the proportion.
- Simplify if possible:
- [latex]\dfrac{\textit{N}}{40} = \dfrac{25}{100}[/latex]
[latex]\dfrac{\textit{N}}{40} = \dfrac{\cancel{25} 1}{\cancel{100} 4}[/latex] - [latex]\dfrac{\textit{N}}{40} =\dfrac{1}{4}[/latex]
- Cross multiply:
[latex]\begin{equation}\begin{split} \textit{N}\times4 &= 40\times1 \\ 4\textit{N} &= 40 \end{split}\end{equation}[/latex] - Divide:
[latex]\textit{N} = 40\div4=10[/latex]
[latex]25\%\text{ of }40 = 10[/latex]
Example B
What is [latex]20\%\text{ of }18[/latex]?
- Part (is) = N
- Whole (of) = 18
- % = 20
[latex]\dfrac{\textit{is}}{\textit{of}}=\dfrac{\%}{100}\longrightarrow\dfrac{\textit{N}}{18}=\dfrac{20}{100}[/latex]
Solve the proportion:
[latex]\begin{equation}\begin{split} \dfrac{\textit{N}}{18} &= \dfrac{20}{100} \\ \dfrac{\textit{N}}{18} &= \dfrac{\cancel{20} 1}{\cancel{100} 5} \\ \dfrac{\textit{N}}{18} &= \dfrac{1}{5} \\ 5\textit{N} &= 18 \\ \textit{N} &= 18\div5=3\tfrac{3}{5} \end{split}\end{equation}[/latex]
[latex]20\%\text{ of }18 = 3\tfrac{3}{5}[/latex]
The following examples all ask you to find a percent of a number. The missing term is the part (the “is” part). Look at the examples carefully so you’ll recognize the wording.
- What is [latex]14\%\text{ of }60[/latex]?[latex]\dfrac{\textit{is}}{\textit{of}}=\dfrac{\%}{100}\longrightarrow\dfrac{\textit{N}}{60}=\dfrac{14}{100}[/latex]
- Find [latex]10\%\text{ of }27[/latex].[latex]\dfrac{\textit{is}}{\textit{of}}=\dfrac{\%}{100}\longrightarrow\dfrac{\textit{P}}{27}=\dfrac{10}{100}[/latex]
- [latex]5\%\text{ of }15[/latex] is .[latex]\dfrac{\%}{100}=\dfrac{\textit{is}}{\textit{of}}\longrightarrow\dfrac{5}{100}=\dfrac{\textit{X}}{15}[/latex]
- [latex]75\%\text{ of }12 =[/latex] .[latex]\dfrac{\%}{100}=\dfrac{\textit{is}}{\textit{of}}\longrightarrow\dfrac{75}{100}=\dfrac{\textit{K}}{12}[/latex]
In percent problems, the number after the word of usually represents the whole.
Exercise 1
Solve each problem by setting up the proportion [latex]\dfrac{\text{is (part)}}{\text{of (whole)}}=\dfrac{\%}{100}[/latex].
- [latex]20\%\text{ of }18 =[/latex]
- [latex]19\%\text{ of }200 =[/latex]
- [latex]25\%\text{ of }44 =[/latex]
- [latex]6\%\text{ of }110 =[/latex]
- [latex]3\%\text{ of }33 =[/latex]
- [latex]30\%\text{ of }64 =[/latex]
- [latex]50\%\text{ of }60[/latex] is?
- [latex]30\%\text{ of }40[/latex] is?
- What is [latex]72\%\text{ of }$425[/latex]?
- What is [latex]20\%\text{ of }85[/latex]?
Answers to Exercise 1
- [latex]3\tfrac{3}{5}[/latex] or [latex]3.6[/latex]
- [latex]38[/latex]
- [latex]11[/latex]
- [latex]6\tfrac{3}{5}[/latex] or [latex]