Ratio definition
Ratio is a way of comparing two or more quantities. It tells us how much of one thing there is compared with another thing. For example, if a drink is made using 2 parts orange juice and 3 parts water, the ratio of orange juice to water is 2 to 3. This means that for every 2 equal parts of orange juice, there are 3 equal parts of water.
Ratios are often written using a colon, such as 2:3. The order matters. A ratio of boys to girls written as 4:5 means 4 parts boys and 5 parts girls. If the order is girls to boys, the ratio would be 5:4. Students should always read the words in the question carefully because changing the order changes the meaning of the ratio.
Ratio is used in number, fractions, percentages, proportion, recipes, scale drawings, maps, similarity, probability, algebra and real-life problem solving. At GCSE level, students simplify ratios, share amounts in a ratio, compare equivalent ratios, use ratio with fractions and solve direct proportion problems. Ratio also appears in science mixtures, exchange rates, speed, density and finance questions.
Ratios can be simplified in the same way as fractions. For example, the ratio 6:9 can be simplified by dividing both parts by 3. This gives 2:3. The simplified ratio has the same meaning because the comparison between the quantities has not changed. A ratio is in its simplest form when the parts have no common factor greater than 1.
Sharing in a ratio means splitting a total amount into parts. For example, if 30 pounds is shared in the ratio 2:3, there are 5 parts altogether because 2 plus 3 equals 5. Each part is worth 30 divided by 5, which is 6 pounds. The first share is 2 parts, so it is 12 pounds, and the second share is 3 parts, so it is 18 pounds.
Equivalent ratios show the same comparison using different numbers. The ratios 2:3, 4:6 and 10:15 are equivalent because each has the same relationship between the two parts. Equivalent ratios are created by multiplying or dividing every part by the same number. This idea is useful in recipes, scale models and questions where quantities increase or decrease together.
Ratio is closely linked to fractions. If a mixture contains red and blue counters in the ratio 3:2, there are 5 parts altogether. The fraction of the mixture that is red is 3 over 5, and the fraction that is blue is 2 over 5. This connection helps students move between ratio, fractions and percentages in multi-step questions.
Related ideas include proportion, fractions, percentages, scale factor, similar shapes, recipes, sharing, equivalent ratios and direct proportion. A clear definition of ratio helps students understand that ratio compares parts, not always parts out of 100. In exams, always identify the total number of parts, keep the order correct and simplify the ratio when required.