Splitting the total when a ratio is given is a fairly basic bit of number maths. I first encounter this at middle school level, typically for an 11+ or 13+ maths ISEB entrance exam, or at GCSE maths.

I made a video three years ago on how I explain how a total is split into a given ratio.

Once you have watched the video you will notice how I use whitespace to decode the question and make the problem clearer first.

The problem is a simple one, there are 140 students at a school and the ratio of girls to boys is 3:4. How many girls and how many boys are there at the school?

I first put down the information in a very compact and clean form. Writing the ratio down, and the letter G and B above the relevant part of the ratio. I also write out the total number of students below.

The key to ratio questions is finding 1 part and then amplifying the 1 part to 3 or 4 parts later. Once you have 1 part, it is easy to find as many other parts as you want. So I work out that:

3 parts + 4 parts = 7 parts.

7 parts = 140 students

1 part = 140/7 = 20 students

3 parts = 20 students x 3 = 60 students

4 parts = 20 students x 4 = 80 students

And that’s the question done! Please let me know if you have any comments on the video or this method below.

Lewis BrownThanks for clearing the concept. Thanks for sharing. Keep posting