Ratios are a useful way of expressing the proportion of quantities in a mix, without having to specify the entire quantity. So if I’m making ham and cheese sandwiches (with one slice of ham and one of cheese per sandwich) I will require two slices of bread for every one slice of ham and one slice of cheese. I need slices of ham, cheese and bread in the ratio 1:1:2 – and that ratio never changes regardless of the total number of sandwiches required. Typically in questions, you will be given an original amount that must be split into a given ratio.

The colon in a ratio is read “to”. So ‘2:1’ is read as “two to one”, or “two parts to one part”. This is a crucial concept - that the ratio describes how many equal parts each share gets. Consider the following question;

Another crucial point to note in ratios is the order of the words. The order that the words appear in is matched to the order that the numbers appear in.

The first step to solving this type of question is to add the various parts of the ratio together (2+1) this case...

Now that you have calculated the number of equal parts or shares, 3, you can divide the original quantity (£900) by the total number to find out what each equal part is worth...

Now that we know how much one part is worth, we can work out what two parts is worth by multiplying this by two...

Simple as that. When the ratio quantities are larger and when the original amount is less of a whole number these questions become more of a challenge in division, so once again the basic skill of times-tables and division becomes important. Consider a second version of this question...

[hint: In the second example John gets £248 - ((434÷7) x 4)]

Good luck,