Quick start
- Enter a and b, the ratio you know. For 4 : 10, type 4 and 10.
- Enter c, the matching part of the new ratio.
- Read x, the simplified ratio and the steps.
How a proportion is solved
Two ratios are in proportion when a ÷ b = c ÷ x. Cross-multiplying gives a·x = b·c, so x = b·c ÷ a. With 4 : 10 = 6 : x, x = 10 × 6 ÷ 4 = 15.
Simplifying a ratio
Divide both parts by their greatest common factor. 4 : 10 shares a factor of 2, so it simplifies to 2 : 5. A ratio is fully simplified when the parts share no factor other than 1.
Everyday uses
- Recipes: a pancake recipe uses 3 eggs for 12 pancakes. For 20 pancakes, 3 : 12 = x : 20 gives x = 5 eggs.
- Maps: on a 1 : 50,000 map, 3 cm stands for 150,000 cm, which is 1.5 km.
- Mixing: paint mixed 2 : 3 needs 6 litres of the second colour for every 4 litres of the first.
Common questions
Is a ratio the same as a fraction?
They are closely linked. The ratio 2 : 5 compares two parts; as a fraction of the whole, the first part is 2/7.
Does the order matter?
Yes. 2 : 5 and 5 : 2 compare things the other way around, so keep the same order on both sides.
Can I use decimals?
Yes. 1.5 : 2 = 6 : x gives x = 8.