Ratio and Proportion: Sharing in the Right Amounts

Imagine you are making a fruit punch for 4 friends. The recipe says: use 2 cups of juice for every 1 cup of water. You decide to make a bigger batch, but you pour in 6 cups of juice and 4 cups of water. Something tastes off — and it is not the fruit! The ratios have changed. In this lesson you will discover exactly what went wrong, and how to make sure mixtures, shares, and recipes always stay perfectly balanced.

A ratio compares two or more quantities of the same kind. We write it with a colon (:). For example, if there are 3 red counters and 5 blue counters, the ratio of red to blue is written 3:5. The order matters — always match the order of the words. Simplifying a ratio works just like simplifying a fraction. Divide every part of the ratio by the highest common factor (HCF) — the largest number that divides into all parts exactly. For example, 6:9 simplifies to 2:3 because the HCF of 6 and 9 is 3. Sharing in a ratio: If you share 20 sweets in the ratio 3:2 between Alex and Billie, first add the parts: 3 + 2 = 5 parts in total. Each part is worth 20 ÷ 5 = 4 sweets. Alex gets 3 × 4 = 12 sweets; Billie gets 2 × 4 = 8 sweets. Check: 12 + 8 = 20. ✓ Proportion tells you that two ratios are equivalent — they represent the same relationship scaled up or down. For example, 2:3 and 4:6 are in proportion because 4:6 simplifies to 2:3. You can also check by cross-multiplying: if a:b = c:d, then a × d = b × c.