Three tools in one: fill in any three values of a proportion to find the fourth, reduce a ratio to its simplest whole-number form, or divide an amount between two or three parts in a given ratio.
A proportion says two ratios are equal: A : B = C : D, which is the same as A/B = C/D. Cross-multiplying gives A × D = B × C, so any one missing value can be found from the other three. For 3 : 4 = 9 : D, D = 4 × 9 ÷ 3 = 12.
To simplify a ratio, every part is divided by the greatest common divisor (GCD). 24 : 36 has a GCD of 12, so it simplifies to 2 : 3. Decimal ratios are first multiplied by a power of ten so every part is a whole number: 1.5 : 2.5 becomes 15 : 25, then 3 : 5.
To split a total, add the ratio parts to find how many shares there are, then give each part its number of shares. Sharing 500 in the ratio 2 : 3 means 5 shares of 100 each, so the parts are 200 and 300.
Cross-multiply. If A : B = C : D, then A × D = B × C. Put the three known numbers in and divide: for example, D = B × C ÷ A.
Divide every part by the greatest common divisor. 18 : 12 : 6 has a GCD of 6, so it simplifies to 3 : 2 : 1. If the ratio contains decimals, multiply every part by 10, 100 and so on until they are whole numbers first.
A ratio compares parts to each other (2 red : 3 blue); a fraction compares a part to the whole (2/5 of the marbles are red). A 2 : 3 split means the first part gets 2/5 of the total and the second gets 3/5.
Add the parts to find the total number of shares, divide the amount by that, then multiply by each part. £900 in the ratio 1 : 2 is 3 shares of £300: £300 and £600.
Aspect Ratio is built for screens, images and video (width × height, 16:9, resizing pixels). This page is the general maths version for any quantities: recipes, maps, mixtures, sharing costs or homework.
