About this calculator
Three jobs in one: simplify a ratio to its lowest terms, solve a proportion to find a missing value, or share an amount in a given ratio.
Decimals are fine; the calculator scales them up to whole numbers to simplify.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
Simplify 12 : 18
- Simplest ratio
- 2 : 3
- As a decimal (a ÷ b)
- 0.666667
- a as a fraction of the total
- 40%
- b as a fraction of the total
- 60%
12 : 18 simplifies to 2 : 3.
Show the working
- The greatest common factor of 12 and 18 is 6.
- Divide both sides by 6: 2 : 3.
2 : 3 = 10 : x
- Missing value (x)
- 15
If 2 : 3 = 10 : x, then x = 15.
Show the working
- Set up the proportion: 2 ÷ 3 = 10 ÷ x.
- Cross-multiply: x = 3 × 10 ÷ 2 = 15.
Share 100 in the ratio 2:3:5
- Part 1 (2)
- 20
- Part 2 (3)
- 30
- Part 3 (5)
- 50
- Total
- 100
Sharing 100 in the ratio 2:3:5 gives 20, 30, 50.
Show the working
- Add the parts: 2 + 3 + 5 = 10.
- One part is worth 100 ÷ 10 = 10.
- Multiply each part by that: 2 × 10 = 20; 3 × 10 = 30; 5 × 10 = 50.
Simplifying a ratio
Divide both sides by their greatest common factor. 12 : 18 has a common factor of 6, so it simplifies to 2 : 3. A ratio in simplest form has no common factor left.
Solving a proportion
If a : b = c : x, the two fractions a/b and c/x are equal, so x = b × c ÷ a. For example, if a recipe uses 2 cups of flour to 3 cups of milk, then 10 cups of flour needs x cups of milk where 2 : 3 = 10 : x, so x = 3 × 10 ÷ 2 = 15 cups.
Sharing in a ratio
Add the parts to get the total number of shares, divide the amount by that to find one share, then multiply by each part. Sharing 100 in the ratio 2 : 3 : 5 has 10 shares of 10, giving 20, 30 and 50.
Frequently asked questions
How do I simplify a ratio?
Divide every part by the greatest number that goes into all of them.
How do I find a missing value in a proportion?
Cross-multiply: for a : b = c : x, x = b × c ÷ a.
How do I split money in a ratio?
Add the parts, divide the total by that sum to get one part, then multiply by each part.
Can a ratio have decimals?
Yes. Decimals are scaled to whole numbers before simplifying.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.