Simplifying a ratio
Divide both parts by their greatest common divisor (GCD). Decimals are scaled up to whole numbers first.
A:B simplified = (A ÷ GCD):(B ÷ GCD)
Proportion: A:B = C:D → D = C × B ÷ A
Example: 1920:1080 has a GCD of 120, so it simplifies to 16:9. To solve 3:4 = 15:?, cross-multiply: ? = 15 × 4 ÷ 3 = 20.
Where ratios come up
- Recipes: scale ingredients up or down while keeping the same proportions; the cooking converter also scales recipes.
- Screens and photos: aspect ratios like 16:9 and 4:3; try the aspect ratio calculator.
- Mixing: concrete, fuel, paint and cleaning solutions.
- Maps and models: a 1:24 scale model is 1/24 the real size.
Frequently asked questions
How do you simplify a ratio?
Find the largest number that divides both parts evenly and divide by it. 12:18 ÷ 6 = 2:3.
How do you solve a proportion?
Cross-multiply: in A:B = C:D, A × D = B × C, so D = B × C ÷ A.
How do I turn a ratio into a percentage?
Divide each part by the total. In 3:1, the first part is 3 ÷ 4 = 75%.
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