• How to simplify a ratio.
  • How to scale up a quantity in a ratio.
  • How to share an amount in a given ratio.
  • How to solve problems that involve ratios made up of three or more numbers.


The year 7 intake of a school is split between siblings of current pupils, new pupils from within the catchment area and new pupils from outside the catchment area in the ratio 1:4:3.

The intake includes 99 new pupils from outside the catchment area.

The school splits that new intake evenly into twelve tutor groups. How many children are in each tutor group?

Show Answer


The ‘Guide to the QTS Numeracy Skills Test’ book contains a full chapter on ratio, including step-by-step explanations and demonstrations of all the skills that you need to know, and a practice exercise on the topic with 20 questions.

If you would like to be sent fully worked solutions to that exercise, just pop your details in the boxes and we will send them over to you.

If you are still struggling with this topic, we have created a selection of resources to provide all the help you need.


  • QTS Numeracy Revision Book – The Guide to the QTS Skills Tests book devotes a whole chapter to the topic of ratio, with detailed methods, worked examples and plenty of practice questions for you to have a go at.
  • Practice QTS Numeracy Tests – Want to put your skills to the test and see how ready you are? Take a look at our selection of practice papers for the QTS numeracy test.
  • QTS Numeracy Revision Cheat Sheets – Our cheat sheets boil down everything you need to know to just the key points on the topic. They are a perfect resource for your last minute revision!
  • QTS Numeracy Coaching – Coaching is the ultimate in personalised support. Book your one-on-one Skype video calls where you can work through the issues that you struggle with at a pace that suits you.