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Maths · Ratio

Scale quantities in a ratio

Find an equivalent pair of quantities by applying one scale factor.

Free to use and free to share. There is no sign-up, no score, and nothing a child does here is recorded or sent anywhere.

Practise it now

Mix blackcurrant squash and water in the ratio 1 : 3.

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A worked example

One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.

Scaling a recipe up

A recipe uses 4 peaches for every 3 plums. How many plums are needed for 16 peaches?

One batch is 4 peaches out of the 7 pieces of fruit it uses.

  • A bar cut into 7 equal parts, with 4 of them shaded.
  1. 7
  2. 16
  3. 12
  4. 15

Answer: 12

How you get there

16 divided by 4 is 4, so the recipe is repeated 4 times, which means the 3 plums are repeated 4 times too and give 12.

Why the other answers tempt

The two ingredients grow by the same number of times, not by the same amount.

If they are stuck, say this

Work out how many times the recipe is repeated by comparing 16 peaches with the 4 peaches in one batch.

Now do it live in Ratio Mixer

What this exercise is doing

Ratio Mixer

Mix blackcurrant squash and water in the ratio 1 : 3.

A ratio fixes the RECIPE, not the amount. 1:3 and 3:9 are the same drink because both are "one part squash for every three parts water" - the colour proves it. To scale a recipe, work out how many whole lots of the ratio you need (12÷4=3 lots) and multiply every part by that.

  1. Step 1. Mix the flavour. Mix blackcurrant squash and water in the ratio 1 : 3.
  2. Step 2. Party jug. Same flavour, bigger jug: fill 12 units and make it taste identical.

What to say if they get stuck

  1. Tap a tap to pour ONE unit. The recipe card shows how many of each you need.
  2. 1 : 3 means for every 1 part squash there are 3 parts water - 4 parts of liquid altogether.
  3. For the party jug, ask: how many lots of 4 fit into 12? Pour that many lots of the recipe.

Open Ratio Mixer on its own page to share it

Where scale quantities in a ratio sits in the 11+

The 11+ does not test these skills in isolation, and practising one in the wrong order wastes the practice. These are the skills the curriculum map connects this one to.

Sits alongside

Share a total in a ratio

Both use multiplicative comparison but solve different structures.

Questions parents ask about scale quantities in a ratio

Answered from what the skill map records about this skill, not from a template. Every answer here is on the page, and the same questions are the page's FAQ structured data.

Find an equivalent pair of quantities by applying one scale factor. It is one of 55 named maths skills in the 11+, in the ratio strand, and this page carries 1 interactive exercise that practises it.

Knowing which maths topic to practise is most of the work

A free diagnostic covers arithmetic, fractions, geometry, measure and data handling, and comes back with the topics to spend the next few weeks on.