Ratios, Fractions, & Percentages

As we discussed in ratios for kids, ratios can be written as fractions. We can do this to help reduce ratios to their simplest form.

Here’s an example of using fractions to help reduce the ratio:

Reduce the ratio 6:72 to its simplest form

6:72 can be written as the fraction 6/72
6/72 can be reduced to 3/36 by dividing both the numerator and denominator by 2
3/36 can be further reduced to 1/12 by dividing both the numerator and denominator by 3
1:12 is the simplest form of the ratio

Proportions

We haven’t used this term yet, but a proportion is when ratios are equal to each other. Similar to when we have reduced ratios to their simplest form using fractions, we have created ratios that are proportional.

The above example shows a proportion where:

6/72 = 1/12

In this case 6 is to 72 as 1 is to 12. These ratios are proportional and say the same thing.

Percentages

Proportions are often written as percentages.

Here is a simple example:

The following ratios are all proportional:

5:50 6:60 10:100

They all can be reduced to another proportion 1:10. This can be written as a percentage of 10 %. All of the above ratios can be written as 10 %.

Note: in order for a percentage to make sense, the second number or term in the ratio needs to be a total number or the total set number. This is a bit confusing, so we’ll describe this concept more in the next section.