How to simplify a ratio
Divide both parts by their greatest common factor. 12 : 18 → both divide by 6 → 2 : 3. If the ratio has decimals, multiply both parts by 10 (or 100) first to make them whole numbers.
Solving a proportion
A : B = C : x → x = B × C ÷ A
If 12 cups of flour need 18 cups of water, 30 cups of flour need 18 × 30 ÷ 12 = 45 cups of water. This is cross-multiplication.
Splitting an amount in a ratio
Add the parts, divide the total by that sum, then multiply each part. $500 split 2 : 3 → 5 parts of $100 → $200 and $300.
Ratio as 1 : n
Divide both parts by the first: 12 : 18 = 1 : 1.5. This form is handy for scales, mixes and comparisons.
Worked examples
- Simplify 12:18. Both numbers divide by 6, so the ratio is 2:3.
- Solve a proportion. 3/4 = x/20. Cross-multiply: 4x = 60, so x = 15.
- Split an amount. Share $500 in the ratio 2:3. There are 5 parts, each worth $100, so the shares are $200 and $300.
Ratios in everyday life
Recipes (2 cups flour to 1 cup sugar), screen sizes (16:9), maps (1:50,000) and mixing (1 part concentrate to 4 parts water) are all ratios. Scaling a recipe means multiplying every part by the same number.
Related calculators
- Fraction Calculator: Add, subtract, multiply and divide fractions.
- Percentage Calculator: X% of Y, X is what % of Y, and more.
- Decimal to Fraction Converter: Decimals to fractions and back.
Questions people ask
What is the difference between a ratio and a fraction?
A ratio compares two parts (2 boys to 3 girls); a fraction compares a part to the whole (2/5 of the class are boys).
Can a ratio have three parts?
Yes, like 2 : 3 : 5. To split an amount in a three-part ratio, add all three parts and share the total the same way.
Formula checked October 2026 · How we calculate