Unit 3: Working with Percent
Topics
In this unit you will learn to solve three types of percent problems:
- Finding a given percent of a number (finding the part).
- Finding what percent one number is of another number (finding the %).
- Finding a number when a percent of it is given (finding the whole).
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 and you will 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]\frac{\text{N}}{4}=\frac{6}{8}\longrightarrow4\times6=8\times\text{N}\longrightarrow24=8\text{N}\longrightarrow \frac{24}{8} = \frac{8N}{8}\longrightarrow\frac{24}{8}=\frac{\cancel{8}\text{N}}{\cancel{8}}\longrightarrow3=\text{N}[/latex]
