How to simplify a ratio, step by step
The greatest common divisor method, with examples for decimals, three-part ratios and mixed units.
3 min read →The short answer
A ratio compares parts with each other. A fraction compares one part with the whole. That single difference explains almost every mix-up.
An example you can picture
A bag has 3 red sweets and 2 blue sweets.
| Statement | Form | Reads as |
|---|---|---|
| Red to blue | Ratio 3 : 2 | For every 3 red there are 2 blue |
| Red out of all | Fraction 3/5 | Three fifths of the sweets are red |
| Blue out of all | Fraction 2/5 | Two fifths of the sweets are blue |
The ratio 3 : 2 has two numbers because it compares two parts. The fractions 3/5 and 2/5 have the same denominator, 5, because that is the whole bag: 3 + 2.
Ratio to fraction
To turn a ratio into fractions of the whole, add the parts to find the total. Each part divided by the total is its fraction.
A drink is mixed 1 : 4 (syrup to water). The whole is 1 + 4 = 5 parts.
Syrup = 15 Water = 45
A common error is to write 1/4 for the syrup share. That compares syrup with water, not syrup with the whole drink.
Fraction to ratio
Going back is easy. If 3/5 of a class are girls, then 2/5 are boys, so the ratio of girls to boys is 3 : 2. The matching denominators cancel and the numerators become the ratio.
More than two parts
A ratio can compare three or more things, for example 2 : 3 : 5. A single fraction cannot do that on its own, because it only compares one part with the whole. You would need a set of fractions: 2/10, 3/10 and 5/10, which simplify to 1/5, 3/10 and 1/2.
When a fraction and a ratio are the same thing
There is one case where they overlap. The ratio "A to B" can be written as the fraction A/B when you want to know how many times bigger A is than B. The ratio 3 : 2 gives 3/2 = 1.5, so the first part is 1.5 times the second. That is a quotient of two parts, and it is a different question from "what fraction of the whole".
Quick test
- Does the question mention the whole, the total or out of? Use a fraction (or percentage).
- Does it compare two groups, or say "for every"? Use a ratio.
See the fractions as percentages
Open the ratio to % calculatorEnter a ratio and see every part as a share of the whole, with the working in maths form.
Frequently asked questions
Is a ratio the same as a fraction?
Not exactly. A ratio compares parts with each other (3 : 2). A fraction compares a part with the whole (3/5). They are closely related and easy to convert.
How do I turn the ratio 3 : 2 into a fraction?
Add the parts: 3 + 2 = 5. The first part is 3/5 of the whole and the second is 2/5.
Can a ratio have more than two numbers?
Yes. Ratios such as 2 : 3 : 5 compare three parts. Fractions need a separate value for each part.