How to Simplify Ratios: Whole Numbers, Decimals, Fractions and Three Terms

A ratio is in simplest form when its terms are whole numbers with no common factor other than 1. Simplifying doesn't change the relationship the ratio describes; it just makes it easier to read and compare. 24:36, 6:9 and 2:3 all say the same thing, but 2:3 says it most clearly.

Whole-number ratios

Find the greatest common factor (GCF) of all the terms.
Divide every term by it.

For 24:36 the GCF is 12, so the ratio becomes 2:3. If you don't spot the GCF at once, you can divide repeatedly by any common factor: 24:36 → 12:18 (÷2) → 4:6 (÷3) → 2:3 (÷2). The answer is the same; it just takes more steps. The GCF calculator finds the factor for large numbers.

Ratios with decimals

Multiply every term by the same power of ten to clear the decimals, then simplify as usual.

Example: 0.75 : 2.5. The most decimal places is two, so multiply by 100 to get 75 : 250. The GCF is 25, giving 3 : 10.

Ratios with fractions

Multiply every term by the least common multiple of the denominators.

Example: ½ : ⅔. The denominators are 2 and 3, with an LCM of 6. Multiplying gives 3 : 4. Another route is to divide: ½ ÷ ⅔ = ¾, so the ratio is 3 : 4.

Ratios with mixed units

Convert to the same unit first. "45 minutes to 2 hours" becomes 45 : 120, which simplifies to 3 : 8. Comparing 45 to 2 directly would give a meaningless result.

Ratios with three or more terms

The GCF has to divide every term. For 12 : 18 : 30 the GCF is 6, giving 2 : 3 : 5. If one term is 0, ignore it when finding the GCF; the zero stays zero.

The "1 to n" form

Sometimes it's clearer to make one term equal to 1, even if the other becomes a decimal. Divide both terms by the first term: 4 : 7 becomes 1 : 1.75. Fuel mixes, map scales and gear ratios are often written this way. Screen sizes are usually left in whole numbers instead, such as 16 : 9.

Checking your answer

Every term should be a whole number.
No number other than 1 should divide all the terms.
Dividing the original first term by the simplified first term should give the same factor as doing it with any other term. For 24 : 36 → 2 : 3, both 24 ÷ 2 and 36 ÷ 3 equal 12.

Worked examples

Original	Step	Simplest form
45 : 60	÷ 15	3 : 4
1.2 : 3.6	× 10, then ÷ 12	1 : 3
¾ : 1½	× 4, then ÷ 3	1 : 2
2 m : 50 cm	200 : 50, ÷ 50	4 : 1
16 : 24 : 40	÷ 8	2 : 3 : 5

Use the calculator to check

Type the terms separated by colons into the ratio calculator and choose "Simplify." It clears decimals automatically, divides by the GCF and shows each term's share of the total, which is handy for mixes and budgets. To keep a ratio but change its size, read how to divide an amount in a ratio.