Ratio separates the field because it is not really one topic. It sits on top of times tables, fractions and division, and it exposes any of those that are shaky.
Which means that when a child struggles here, the fix is usually underneath rather than in ratio itself.
What has to be solid first
| Needs to be secure | Where it shows up in ratio |
|---|---|
| Times tables, to instant recall | Multiplying the unit value by each part |
| Division | Finding the unit value from the total |
| Fractions | Seeing 2:3 as two fifths and three fifths |
| Simplifying | Reducing 10:15 to 2:3 before starting |
If a child hesitates on seven eights, ratio will feel impossible, and no amount of ratio practice will fix it. Go back a step.
The three step method
Nearly every ratio question in this test yields to the same three steps. Teach them as a fixed routine.
- Add the parts together.
- Divide the total by that number. This gives the value of one part.
- Multiply that unit value by each part to find what each one represents.
Two worked examples
Share £60 between two people in the ratio 2:3.
- Add the parts: 2 plus 3 is 5.
- Divide the total: 60 divided by 5 is 12. That is one part.
- Multiply: 2 times 12 is 24, and 3 times 12 is 36.
Check it: 24 plus 36 is 60. Always add your answers back and confirm they make the total.
Share 120 sweets in the ratio 3:5.
- 3 plus 5 is 8.
- 120 divided by 8 is 15.
- 3 times 15 is 45, and 5 times 15 is 75.
Check: 45 plus 75 is 120. Correct.
The harder versions
Two variants come up often, and both are the same three steps entered at a different point.
- You are given one share, not the total. If the smaller share in a 2:3 split is £24, then one part is 24 divided by 2, which is 12. From there everything follows.
- You are given the difference. If one person gets £12 more in a 2:3 split, that difference is one part, so one part is 12.
The habit that makes both easy: always find the value of one part first, whatever the question gives you. Every ratio question is a hunt for that single number.
And they will be worded
You will rarely see "share 60 in the ratio 2:3". You will see a recipe, a sum of money between two cousins, or paint mixed in a particular shade. The work is extracting the ratio and the total from the sentences before any arithmetic starts.
See our guide to 11+ maths topics and our guide to fractions, decimals and percentages.
See where your child stands today
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Ratio is where the gaps underneath show up
Ratio and proportion is a unique subject, only because there has to be an element of knowledge in other aspects of mathematics first. Times tables have to be strong. Fractions have to be understood. Division as well.
So ratio is the subject where you have to incorporate all the other things learned earlier on. That is how I would have a child understand it: not as a new topic, but as the place where everything they have already done gets used at once. It is also why a shaky times table shows up here rather than anywhere else.
The method itself is normally a three step process. You add the ratios together, you divide the total by that combined number, and that gives you a unique number. Then you multiply that number by each of the ratios to give what each one represents. Teach it as a fixed routine and children stop being frightened of it.
Mushtaque Ahmed, Founder of GrammarPath and Bright Mentors
Frequently asked questions
How do you solve 11+ ratio questions?
In three steps. Add the parts of the ratio together, divide the total by that number to find the value of one part, then multiply that unit value by each part. Always add your answers back to check they make the original total.
How do you share an amount in a given ratio?
To share £60 in the ratio 2:3, add the parts to get 5, divide 60 by 5 to get 12 as the value of one part, then multiply: 2 times 12 is 24 and 3 times 12 is 36. Checking, 24 plus 36 makes 60.
Why does my child find ratio so hard?
Because ratio sits on top of several other topics. It needs times tables to instant recall, confident division, an understanding of fractions and the ability to simplify. A child who hesitates on their tables will find ratio impossible, and more ratio practice will not fix it.
What if the question gives one share instead of the total?
Find the value of one part from what you are given. If the smaller share in a 2:3 split is £24 then one part is 24 divided by 2, which is 12, and everything follows from there. Every ratio question is a hunt for the value of a single part.
What if the question gives the difference between two shares?
In a 2:3 split the difference between the shares is exactly one part, so if one person receives £12 more then one part is £12. The same three steps then apply.