To calculate a ratio, find the greatest common factor, or GCF, between two opposing sets of numbers and divide both numbers by the GCF. Calculate ratios up or down to find the answer to a specific ration question.
- Find the GCF
Ratios can be viewed as simple fractions, but with the numerator and denominator being two different parts of the comparison. For example, 20:4 can be written as 20/4. If you're looking at this as a fraction, you can see that 20 is divisible by 4, allowing 4 to be the GCF. In cases where the larger number is not divisible by the lower number, you would still look for the greatest common factor. For example, 20:15. 15 can not directly go into 20, but 5 can go into both, making 5 the GCF.
- Divide both numbers by the GCF
Once you find your greatest common factor, you want to divide both numbers by that common number. 20:4 leaves you with a GCF of 4. 20 divided by 4 equals 5, while 4 only goes into itself 1 time. Your calculated ratio would be 4:1 or 4 to 1. 20:15 leaves you with a GCF of 5. 20 divided by 5 equals 4, while 15 divided by 5 equals 3, resulting in a calculated ratio of 4:3 or 4 to 3.
- Calculate ratios up or down
Once the basics of bringing down a set of compared numbers to their lowest form is understood, you can also manipulate ratios in the opposite direction. If you're told that two out of three students are selected to visit the aquarium today, you already have a baseline ratio of 2:3. Now, you want to figure out exactly how many that is if you have a class of 30 students. You want the denominator to be the total population, so you multiply 3 times 10, and whatever you do to one side of the ratio, you must always do to the other, so you multiply 2 times 10. Your end result would be 20:30 or 20 out of 30 students.