What does a child have to do to scale quantities in a ratio in the 11+?

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.

What is the trap in an 11+ scale quantities in a ratio question?

The two ingredients grow by the same number of times, not by the same amount. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.

What can I say if my child is stuck on scale quantities in a ratio?

Point at the next move rather than explaining the whole rule. Work out how many times the recipe is repeated by comparing 16 peaches with the 4 peaches in one batch.

What is not part of scale quantities in a ratio in the 11+?

The skill map draws the line here: Excludes sharing a total. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.

Which other 11+ skills should we practise alongside scale quantities in a ratio?

The skill map connects it to share a total in a ratio. Both use multiplicative comparison but solve different structures. That skill has its own page here.

How can my child practise scale quantities in a ratio for free?

Use Ratio Mixer, embedded on this page. It is the exercise the skill map attaches to scale quantities in a ratio, it runs in the browser with no account to make, these exercises are not scored and do not save learner records. The separate quiz sends answers for marking and shows a score, without saving an assessment record. It also has its own link, so you can send it to a child without sending them anywhere else first.

Maths · Ratio

Scale quantities in a ratio

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

Watch the worked example

Open the video page

Scale Both, Keep the Ratio

This video shows how to apply the same scale factor to both quantities to find an equivalent pair. Watch an 11+ maths question solved step by step.

0:00 / 2:36

Turn on captions with the CC button. Jump to any part with the chapter buttons.

Read the transcript

Keep practising with Trace Learn. Find topics to practise next

Quick quiz: Scale quantities in a ratio

10 questions, with feedback after each one. No sign-up needed.

Read the questions in this quiz

Question 1
A recipe uses 5 pears for every 9 cherries. How many cherries are needed for 45 pears?
5/14
- A.90
- B.45
- C.81
- D.1
Question 2
A recipe uses 4 apples for every 7 peaches. How many peaches are needed for 52 apples?
4/11
- A.52
- B.98
- C.91
- D.84
Question 3
A recipe uses 4 plums for every 7 pears. How many pears are needed for 72 plums?
4/11
- A.126
- B.119
- C.72
- D.133
Question 4
A recipe uses 5 lemons for every 9 plums. How many plums are needed for 90 lemons?
5/14
- A.171
- B.90
- C.162
- D.99
Question 5
A recipe uses 8 apricots for every 5 oranges. How many oranges are needed for 136 apricots?
8/13
- A.85
- B.80
- C.136
- D.133
Question 6
A recipe uses 8 pears for every 5 peaches. How many peaches are needed for 56 pears?
8/13
- A.56
- B.61
- C.12
- D.35
Question 7
A recipe uses 8 peaches for every 5 oranges. How many oranges are needed for 144 peaches?
8/13
- A.141
- B.40
- C.144
- D.90
Question 8
A recipe uses 8 peaches for every 5 oranges. How many oranges are needed for 48 peaches?
8/13
- A.30
- B.53
- C.48
- D.25
Question 9
A recipe uses 9 apricots for every 5 peaches. How many peaches are needed for 153 apricots?
9/14
- A.22
- B.158
- C.85
- D.153
Question 10
A recipe uses 5 plums for every 8 peaches. How many peaches are needed for 30 plums?
5/13
- A.56
- B.48
- C.40
- D.30

Practise it now

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

Loading the interactive exercise. Nothing you do here is saved or scored.

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.

4/7

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

Kitchen-table script for parents

Try this together

A friendly mini script for the breakfast table, school run or a quiet two minutes. Read it aloud as written, or make it your own.

Ready? Let's have a go at Scale quantities in a ratio together. Take a look at the picture. Here is what matters: One batch is 4 peaches out of the 7 pieces of fruit it uses. Here comes the question: A recipe uses 4 peaches for every 3 plums. How many plums are needed for 16 peaches? Before we race ahead, let us choose one good first step. Here is a helpful clue: Work out how many times the recipe is repeated by comparing 16 peaches with the 4 peaches in one batch. Nice work. Now let us follow the thinking: 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. So our answer is: 12. There is one sneaky trap to watch for: The two ingredients grow by the same number of times, not by the same amount. Can you show me that first move again in your own words? Brilliant. No rush; we are practising a method you can reuse, not trying to win a speed contest.

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 $(12 \div 4 = 3$ lots) and multiply every part by that.

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

What to say if they get stuck

Tap a tap to pour ONE unit. The recipe card shows how many of each you need.
1 : 3 means for every 1 part squash there are 3 parts water - 4 parts of liquid altogether.
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

What this skill involves, common mistakes and ways to practise it at home.

: 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.
: The two ingredients grow by the same number of times, not by the same amount. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.
: Point at the next move rather than explaining the whole rule. Work out how many times the recipe is repeated by comparing 16 peaches with the 4 peaches in one batch.
: The skill map draws the line here: Excludes sharing a total. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.
: The skill map connects it to share a total in a ratio. Both use multiplicative comparison but solve different structures. That skill has its own page here.
: Use Ratio Mixer, embedded on this page. It is the exercise the skill map attaches to scale quantities in a ratio, it runs in the browser with no account to make, these exercises are not scored and do not save learner records. The separate quiz sends answers for marking and shows a score, without saving an assessment record. It also has its own link, so you can send it to a child without sending them anywhere else first.

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.