Using Fractions to Solve Percentage Problems
There are three ways to solve percentage problems: 1) treat it like a ratio, 2) the 10% method and 3) substitute in a fraction. Today I’d like to talk about that third option.
This is a method that works with a limited number of percentage problems. The problems need to either use the percentages we know the fraction for or the part and whole needs to simplify to a fraction we know the percent for.
Before we even think about the percentages, we need to know a couple of identities. Those are:
1/2 = 0.5 = 50%
1/3 = 0.3333… = 33 1/3%
1/4 = 0.25 = 25%
1/5 = 0.2 = 20%
1/8 = 0.125 = 12.5%
we can also do multiples of these fractions. For example if 20% = 1/5 then 40% = 2/5
OK, now that’s done, we can put these to work. Let’s look at an example.
If a guy gets a 12.5% commission for a sale and earns $500, how much was the sale?
Setting up the percentage looks like this:
but we know that 12.5% = 1/8, so we can swap that in for the 12.5%/100 to get this:
