How to Work with Ratios
A ratio compares two quantities of the same kind — 2:3 means for every 2 of the first thing there are 3 of the second. To simplify a ratio, divide both sides by their greatest common factor. Two ratios are equivalent when one is a scaled copy of the other, which you can test (or solve) with cross-multiplication.
A recipe uses flour and sugar in the ratio 3:2. If you have 9 cups of flour, how much sugar? Set 3:2 = 9:x, cross-multiply: 3x = 18, so x = 6 cups of sugar.
Where Ratios Show Up
- Cooking and mixing: recipes, paint, concrete and fuel mixes all scale by ratio.
- Maps and models: a 1:50,000 map means 1 cm on paper is 50,000 cm (500 m) of ground.
- Screens and images: 16:9 and 4:3 aspect ratios describe width relative to height.
- Finance: price-to-earnings and debt-to-income are ratios used to compare at different scales.
Frequently Asked Questions
How do you simplify a ratio?
Divide both sides of the ratio by their greatest common factor. The ratio 12:18 has a GCF of 6, so it simplifies to 2:3.
How do you solve a ratio like 3:4 = x:20?
Use cross-multiplication: 3 × 20 = 4 × x, so x = 60 ÷ 4 = 15. This calculator does the cross-multiplication for you and shows the steps.
What is the difference between a ratio and a fraction?
A fraction compares a part to the whole (3/4 of the class), while a ratio usually compares one part to another part (3:1 boys to girls). Mathematically they behave the same way, which is why ratio problems are solved with fraction arithmetic.
Can ratios include decimals?
Yes. A ratio like 2.5:4 is valid, and can be scaled to whole numbers by multiplying both sides by the same amount — 2.5:4 is the same ratio as 5:8.
Cite This Calculator
Using this calculator in an assignment, article or lesson? Copy a ready-made citation — or the link snippet if you're referencing it from a web page.
The CalculatorsGuide Editorial Team. (2026). Ratio Calculator. CalculatorsGuide. Retrieved from https://www.calculatorsguide.com/math/ratio-calculator/