Dividing in a Given Ratio - How to share that cake

Cake. The fruit makes it ok.

Not everything in life is equal.

And not everything is shared equally - you don’t really want to split your chocolate cake and share it out… but sometimes you have to.

So how do you split things up when they aren’t equal.

For example, how do you split a cake in the ratio 1 : 3 (in your favour)?

Let’s look at how we would split something equally, i.e 1 : 1.

If you add both sides of the ratio, 1 + 1 = 2, so there are 2 parts in total.

So you take your cake and cut it into 2 equal parts (or shares).

Then the ratio shows you how many parts each person gets.

In this case, each person gets 1 part each or 1 share each.

Its the same process for when the ratio is different.

Let’s look at how to share a cake in the ratio: 1 : 3

1 + 3 = 4, so there are 4 shares.

Split the cake into 4 equal parts.

Then you multiply to work out how many parts everyone gets.

1 person gets 1 out of the 4 pieces and the other person gets 3 out of the 4 pieces.

Of course your maths questions aren’t always going to be that easy, let’s look at some other examples.

Let’s say you are given £120 for some work you did on the weekend.

You completed that work with the help of a good friend.

You’ve both agreed that you did 6 hours of work and your friend did 4, so you will split the money according to how many hours you both did.

So you need to split £120, in the ratio 6 : 4

6 + 4 = 10, so there are 10 parts.

£120 / 10 = £12. So the value of each part is £12 - this bit is super important.

Now we know that 1 part, which is 1 hour in this case, is worth £12.

If you worked 6 hours, you get 6 x 12, £72 out of the £120.

And then your friend will get 4 x 12 = £48.