Countdown to the 11+ exam: Ratio

The Bond Countdown to the 11+ exam series offers step-by-step guides to answering key 11+ exam questions.

Previous articles in the series: Comprehension | Vocabulary | Identifying patterns

Maths seems to be a subject that many children can get anxious about.

There are many reasons for this, but lack of confidence around new concepts is often the root cause. Ratio is a topic that may be quite new to children who are preparing for the 11+ exam.

In maths, ratio is used to compare two or more numbers or quantities. When you share out an amount using a given ratio, then each share is a proportion of the total amount. A ratio is expressed as two or more numbers with a colon in between. The colon stands for ‘to’, so in the ratio 2:3, there are 2 parts to every 3 – you could say ‘2 to every 3’.

Ratio is all about sharing. It encompasses division, fractions and multiplication, so brushing up on times tables will help with this 11+ question type.

Using the ratio 2:3 means that there are five items in total, of which two are one type and three are another. So this could be five people, of which two are male and three are female, or a necklace with five beads, two of which are red and three of which are blue.

Let’s try an example by sharing £15 in the ratio 2:3:

  • First, add both numbers (2 + 3 = 5) and divide £15 by 5 to find one part; in this instance, one part equals £3
  • Multiply one part (£3) by each number included in the ratio: £3 x 2 = £6, and £3 x 3 =£9
  • Be sure to double-check your total by adding together the two amounts: £6 + £9 = £15

Where do fractions come into this?

If we look at the ratio total as our whole amount, this works in the same way as the denominator (or bottom number) representing the whole amount in a fraction. Using the same 2:3 ratio, our whole amount is 5, out of which one share will be 2/5 and the other will be 3/5. This is just another way of looking at the same type of question. A great way of getting to grips with tricky ratios and fractions is to draw a circle, and, using our 2:3 ratio, divide it into five equal parts and ask your child to shade two parts with one colour and the remaining three parts with another colour. A visual representation can be a big help!

What if there’s more than one number in the ratio?

If your child comes across a ratio like 1:3:4:2, it simply means the whole amount is being shared more than two ways – in this case it’s being shared four ways. Add each of these numbers together and you’ll get 10, meaning each part represents 1/10. Therefore, your four shares will be 1/10, 3/10, 4/10 and 2/10. Remember that your child should keep their answers in the same sequence as the question, to make sure they it's clear what each part represents.

Let’s work through an 11+ practice question from Bond Online:

Alan and Ahmed win £750 between them. They agree to divide the money in the ratio 2:3. How much money does Alan receive?

  • Add up the ratio numbers 2 and 3 to make 5.
    Each part of the share will be 1/5 of £750
  • Divide £750 by 5 to get one part – £150.
    Because they decided to split the money 2:3, Alan will get two parts of £150 – a total of £300.
    Ahmed will get three parts at the same amount, meaning he will receive £450.
  • Don’t forget the final step: add £300 and £450 together to make sure the answers match up!

Helping at home:

  • Try cooking or baking together: recipes are a fun way to get your child thinking about quantities and ratio.
  • Why not help with times tables by creating a poster together to try and memorise them or making flashcards to test quick recall?
  • Bond Online’s Free Resources page is packed with sample papers, answers and useful documents for every 11+ exam subject.

Michellejoy Hughes

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