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Ratio and Proportion: Comparing and Scaling Amounts

In one line: A ratio compares two or more amounts, such as 2 cups of flour to 1 cup of sugar, and proportion means keeping that comparison the same when the amounts get bigger or smaller.

Why it works

Ratios are everywhere in everyday life: following a recipe, mixing paint, reading a map scale or working out which pack of cereal is better value. Understanding proportion helps you scale things up or down correctly by multiplying, not guessing. It is also the foundation for percentages, fractions of amounts, speed, scale drawings and later algebra.

Think of it like: Think of making orange squash. If the bottle says 1 part squash to 4 parts water (written 1:4), one glass might use 1 cap of squash and 4 caps of water. For a whole jug you might use 5 caps of squash and 20 caps of water. The amounts are bigger, but the taste is the same because you multiplied both parts by the same number. That is proportion: same ratio, different size. (Where this breaks: The squash example works for things that mix evenly, but not everything scales this way. Doubling a cake recipe does not mean you bake it for twice as long, and a ratio on its own never tells you the actual amounts, only how they compare.)

Worked example

Mia and Sam share £40 in the ratio 3:5. How much does each person get?

  1. The ratio 3:5 means Mia gets 3 parts for every 5 parts Sam gets.
  2. Add the parts to find the total number of parts: 3 + 5 = 8 parts.
  3. Find the value of one part: £40 ÷ 8 = £5.
  4. Mia gets 3 parts: 3 × £5 = £15. Sam gets 5 parts: 5 × £5 = £25.
  5. Check: £15 + £25 = £40, and 15:25 simplifies to 3:5, so the answer is correct.

Answer: Mia gets £15 and Sam gets £25.

Common mistakes

  • Dividing the total by just one number in the ratio (such as £40 ÷ 3) instead of by the total number of parts; always add the parts first.
  • Writing the ratio in the wrong order, such as 5:3 instead of 3:5; the order must match the order of the words in the question.
  • Adding the same number to both parts to scale a ratio (turning 2:3 into 4:5) instead of multiplying both parts by the same number (turning 2:3 into 4:6).
  • Comparing amounts in different units, such as 50 cm to 2 m; change them to the same unit (50 cm to 200 cm) before simplifying.

Try it · 1 of 3

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Write the ratio 12:18 in its simplest form.

Questions parents ask

What year do kids learn ratio and proportion?

In the UK, ratio and proportion is introduced in Year 6 and developed through Years 7 to 9. In Australia, ratios are mainly taught in Years 7 and 8, and in the US they are a key topic in Grades 6 and 7.

How can I help my child with ratio and proportion at home?

Cooking is ideal: ask your child to double or halve a recipe, or scale it for a different number of people. Mixing squash, sharing sweets fairly in a given ratio and reading map scales are also quick, practical ways to practise.

What is the difference between a ratio and a fraction?

A ratio compares one part with another part, while a fraction compares a part with the whole. For example, if a bag has 2 red and 3 blue counters, the ratio of red to blue is 2:3, but the fraction of counters that are red is 2/5.

Why does my child keep getting ratio sharing questions wrong?

The most common reason is dividing by one number in the ratio instead of by the total number of parts. Encourage your child to draw a bar split into equal parts, add up the parts first, and then work out the value of one part.