Ratio simplifier
Type a ratio such as 12:18 or 1.5:2:4 and see it reduced to its simplest form, with each step shown.
Simplify a ratio
How it works
What simplifying a ratio means
A ratio compares amounts. 12:18 and 2:3 describe the same comparison, in the way that 12/18 and 2/3 are the same fraction. To simplify, divide every part by the largest number that goes into all of them. For 12 and 18 that number is 6.
Ratios with decimals
A simplified ratio uses whole numbers, so decimals are cleared first by multiplying every part by the same amount. 1.5:2 becomes 3:4 when both parts are doubled. The comparison does not change, because both sides were scaled together.
The 1 : n form
For a two-part ratio, dividing both parts by the first gives the form 1 : n, which is how map scales and mixing instructions are usually written. 2:3 is 1 : 1.5, meaning one and a half of the second amount for each one of the first.
Sharing in a ratio
The parts of a simplified ratio add up to the number of equal shares. To split 40 in the ratio 2:3, there are 5 shares of 8, so the two amounts are 16 and 24. The calculator shows the total number of parts for this reason.
Worked examples
Simplify 45:60
45 : 60 simplifies to 3 : 4
- As 1 : n, that is 1 : ≈ 1.333333
- As n : 1, that is 0.75 : 1
- Find the largest number that divides every part. For 45, 60 that is 15.
- Divide each part by 15: 45 ÷ 15 = 3, 60 ÷ 15 = 4.
- The simplified ratio has 7 parts in total: 3 + 4 = 7.
Simplify 1.5:2:4
1.5 : 2 : 4 simplifies to 3 : 4 : 8
- Clear the decimals by multiplying every part by 2: 1.5 : 2 : 4 becomes 3 : 4 : 8.
- The parts 3, 4, 8 share no factor larger than 1, so 3 : 4 : 8 is already in its simplest form.
- The simplified ratio has 15 parts in total: 3 + 4 + 8 = 15.
Is 16:9 already in its simplest form?
16 : 9 simplifies to 16 : 9
- As 1 : n, that is 1 : 0.5625
- As n : 1, that is ≈ 1.777778 : 1
- The parts 16, 9 share no factor larger than 1, so 16 : 9 is already in its simplest form.
- The simplified ratio has 25 parts in total: 16 + 9 = 25.
Common questions
How do you simplify a ratio?
Find the greatest common factor of all the parts and divide each part by it. For 45:60 the greatest common factor is 15, giving 3:4.
Can a ratio have more than two parts?
Yes. A ratio such as 2:3:5 compares three amounts at once, and it is simplified in the same way, by dividing every part by a common factor.