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A ratio is a way of comparing any two parts of a whole. You might use a ratio to compare the number of boys in a room to the number of girls in a room, or the number of students who had pizza for lunch versus the number of students who didn’t have pizza for lunch. Percentages are ratios too, but they’re a very specific type of ratio: Instead of comparing two parts of the whole against each other, percentages compare any one part against the whole.
Some Examples of Ratios
Before you start converting ratios into percentages, consider the information that’s encoded in a ratio and how it’s expressed. For example, imagine that you’re in a math class with 30 students. Of those students, 22 passed the last math test and 8 students did not. There are two ways of writing the ratio:
(22:8 text{ or } frac{22}{8})
In either case, you have to label what each number represents. Obviously there’s a big difference between a class where 22 students passed or a class where only 8 students passed, so getting the order of the terms correct matters – a lot! You read a ratio from left to right, in the first case, or top to bottom in the second case. So you’d describe either of the ratios just given as the ratio of students who did pass to the students who didn’t pass.
Note that the total number of students who took the test is in the ratio, too. Just add the number of students who did pass to the number of students who didn’t pass to get back to your total of 30 students.
Converting Ratios Into Percentages
When you want to turn a ratio into a percentage, you must choose just one part to compare against the whole. For example, using the example ratio just given, you could find out the percentage of students who passed the test.
1. Write a New Fraction
Because percentages compare one part against the whole, you can write the percentage of students who passed as a fraction with the number of students who passed in the numerator, and the number of students in the entire class as the denominator. In other words, you have:
(frac{22 text{ (students who passed) }}{30 text{ (students in the entire class)}})
Note that you could also write this as 22 : 30 – it’s really just another ratio in disguise. The key point that makes it a percentage, too, is that you’re comparing one part against the whole, instead of comparing one part against another part of the same whole.
2. Work the Division
Work the division represented by the fraction you just wrote. To continue the example:
(22 ÷ 30 = 0.7333)
This is a repeating decimal; your teacher will tell you which decimal point to round to.
3. Convert the Decimal to a Percentage
Multiply the result from Step 2 by 100 to convert it into a percentage. Continuing the example, you have:
(0.7333 × 100 = 73.33 text{ percent})
So of the entire class, 73.33 percent passed the last test.
