How to calculate a ratio

What is a ratio? Ratios are used in math to make a comparison between two things or numbers. In other words the ratio of something to something else. This can be written in a fraction, using the word to, or with a colon.

For example the ratio of apples to oranges is 2:1, 2/1, 2 to 1.

Alright, you are probably following along so far as this is quite simple.

These ratios can also be shown in what are called equivalent ratios. Lets say you have a ratio of 4 to 8 or 4:8. This is the same as a ratio of 1:2. How did we arrive at this? You simple divide each number in the ratio by the greatest common denominator. The greatest common denominator is the largest number you can divide each number by and have the returned a whole number. For the ratio of 4 to 8 the greatest common denominator is 4.

Determining the greatest common denominator is easier the small the numbers and if the numbers are even. If the numbers are large and odd numbers, it can be quite difficult.

Ratios as percentage

Since ratios can be described as one number divided by another, you can actually describe a ratio of one number to another as a percent of one number to another. For example:

Let’s say you have 40 apples and 50 oranges. You want to compare the ratio of apples to oranges. So you say 40:50, apples to oranges. Which simplifies to 4:5 when you divide the two numbers by 10. 10 is the greatest common denominator.

Now you can also display 4:5 as 4/5 which is equal to .80.

Next, multiply that number by 100 to get the percentage

.80 * 100 = 80$

So, a ratio of 4:5 of apples to oranges is equal to 80% apples to oranges.

As you can see, ratios can be displayed in many ways to convey the same meaning. Which one you chose is up to you.

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