Subtracting mixed numbers

The next question on the GCSE paper is about subtracting “mixed” numbers – numbers which have a “whole number” part and a fractional part. Specifically, we are asked to work out 3 3/4 - 1 2/5.

We can deal with the whole number parts separately from the fractional parts. Dealing first with the whole number parts we get 3 – 1 = 2.

For the fractional parts, we want to calculate 3/4 - 2/5. This would be easier to calculate if both denominators were the same. Right now the denominators are 4 and 5; if we could multiply the first one by 5, and the second one by 4, then they would both be 20.

With the 3/4, we want to multiply the denominator by 5. But we don’t want to change the actual value of the fraction, so we multiply the numerator by 5 as well. This gives us 15/20. Remember, if you multiply both the numerator and the denominator by the same number, the value of the fraction is unchanged.

With the 2/5 on the right hand side, we want to multiply the denominator by 4, so we multiply the numerator by 4 as well. This gives us 8/20.

Now we perform the subtraction of the fractions. 15/20 – 8/20 = 7/20, and we combine this 7/20 with the 2 that we got from the whole number parts, to give us the answer, 7 7/20.

Is this our final answer? To be sure, we need to check if the fraction can be simplified. The numerator, 7, is a prime and it isn’t one of the numbers that the denominator is divisible by. So there’s no number (apart from 1) which will divide into both the numerator and the denominator. We can’t simplify the answer we have, so 7 7/20 really is our final answer.

That sums it up.