Simplifying and cross-multiplying
A ratio simplifies by dividing both terms by their greatest common divisor: 16:48 becomes 1:3. Decimal ratios are scaled to whole numbers first, so 2.5:5 also reduces to 1:2.
Proportions are solved by cross-multiplication. In A:B = C:D, the products A×D and B×C are always equal, so any one missing term follows from the other three.
Ratios with more than two terms
A three-part ratio like 2:3:5 works the same way — divide all terms by their greatest common divisor to simplify, and the parts sum to the whole. Here the total is ten parts, so the shares are 20%, 30% and 50%.
This is how profit-sharing, inheritance splits and concrete mixes are specified. To apply a ratio to a quantity, divide the quantity by the total number of parts, then multiply by each term.
Scaling recipes and mixtures
Ratios are what make recipes scalable. A 1:2 rice-to-water ratio holds whether you cook one cup or five, which is why professional kitchens work in ratios rather than fixed quantities.
The same logic applies to fuel mixes, fertiliser blends and mortar. Keep the ratio and change the total, and the properties of the mixture stay the same.
Frequently asked questions
What is the difference between a ratio and a fraction? +
A ratio compares two parts to each other (1:3 means one part to three parts, four parts total). A fraction compares a part to the whole (1/4 of the total). The same situation gives 1:3 as a ratio and 1/4 as a fraction.
How do I scale a ratio to a specific total? +
Add the parts to get the total number of shares, divide your quantity by that, then multiply by each part. For 2:3 across 100 units: 100 ÷ 5 = 20, giving 40 and 60.
Can a ratio have decimals? +
Yes, though it is conventionally converted to whole numbers. 1.5:2 is usually written 3:4 after multiplying both sides by two.