Ratios Explained: How to Simplify, Scale and Split Them

Ratios turn up everywhere once you start looking: recipes, paint and concrete mixes, map scales, screen sizes, splitting a bill. Three skills cover almost every case — simplifying a ratio, scaling it to the amount you have, and splitting a total in a given ratio.

Simplifying a ratio

A ratio is in its simplest form when no whole number divides both sides. To get there, divide both parts by their greatest common divisor (GCD).

16 : 24 — the largest number that divides both is 8, so the ratio simplifies to 2 : 3.

Screen resolutions work the same way. 1920 × 1080 has a GCD of 120, which gives 16 : 9. A 1440 × 900 screen simplifies to 8 : 5, usually written 16 : 10.

Ratios as fractions and percentages

A ratio compares parts with each other. To see each part as a share of the whole, add the parts together first.

In 2 : 3 there are 5 parts in total, so the first part is 2/5 = 40% and the second is 3/5 = 60%. This is where people often slip: 2 : 3 does not mean the first part is two thirds of the second as a share of the total. It is two fifths of the total.

Scaling a ratio

Scaling keeps the relationship and changes the size. Multiply or divide both sides by the same number.

A bread recipe uses flour and water in the ratio 5 : 3. If you have 750 g of flour, the scale factor is 750 ÷ 5 = 150, so you need 3 × 150 = 450 g of water.

The same method works for anything mixed by parts. A general-purpose concrete mix of 1 : 2 : 3 (cement : sand : gravel) has 6 parts. For 0.6 cubic metres of dry mix, each part is 0.1 m³, so you need 0.1 m³ of cement, 0.2 m³ of sand and 0.3 m³ of gravel.

Splitting a total in a ratio

To divide 500 between two people in the ratio 2 : 3:

1. Add the parts: 2 + 3 = 5.
2. Find one part: 500 ÷ 5 = 100.
3. Multiply: the first person gets 200 and the second 300.

This is the fair way to split shared costs by income, by nights stayed or by how much each person used.

Map scales

A map scale of 1 : 25,000 means 1 unit on the map is 25,000 of the same unit on the ground. 4 cm on the map is 100,000 cm, which is 1 kilometre. Keep both sides in the same unit until the end, then convert.

Common mistakes

• Order matters. 2 : 3 and 3 : 2 are different mixes. Always state which comes first.
• Mixed units. A ratio of 1 cup to 200 ml is meaningless until both are in the same unit.
• Adding to both sides. Adding 1 to each side of 2 : 3 gives 3 : 4, which is a different ratio. Only multiplying or dividing keeps it the same.

Work it out instantly

The ratio calculator simplifies any ratio, shows it as a fraction, decimal and percentage, and scales it to the value you have. For straightforward percentage questions, use the percentage calculator.