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.