5.8: Working With Percent
Each type of percent problem can be solved using the following proportion:
[latex]\dfrac{\text{is (part)}}{\text{of (whole)}}=\dfrac{\%}{100}[/latex]
Both ratios in this proportion use the same order of comparison because in the ratio [latex]\frac{\%}{100}[/latex], the % represents a part, and 100 is the whole. That is, the % is a part of the whole.
Percent problems involve knowing three pieces of information:
- the part (the “is” part)
- the whole (the “of” part)
- the percent
You will be given two pieces of information to find the third. That is, the problems will give two terms of the proportion, and you will solve for the missing term. Because these are problems of percent, the 100 is always known to you and will always be in the same position in the proportion.
Remember how to use cross multiplication to solve a proportion:
[latex]\dfrac{\text{N}}{4}=\dfrac{6}{8}\longrightarrow4\times6=8\times\text{N}\longrightarrow24=8\text{N}\longrightarrow \dfrac{24}{8} = \dfrac{8N}{8}\longrightarrow\dfrac{24}{8}=\dfrac{\cancel{8}\text{N}}{\cancel{8}}\longrightarrow3=\text{N}[/latex]
Attribution
This chapter has been adapted from Unit 3: Working with Percent in Adult Literacy Fundamental Mathematics: Book 6 – 2nd Edition (BCcampus) by Liz Girard and Wendy Tagami (2022), which is under a CC BY 4.0 license.
