Adding and subtracting fractions is easy if the bottom number is the same in each fraction, as with^{1}/_{6}+^{2}/_{6}=^{3}/_{6}where the bottom number is 6 every time. If you look carefully at that sum, however, you may notice that it's actually the same sum as^{1}/_{6}+^{1}/_{3}=^{1}/_{2}(because^{2}/_{6}=^{1}/_{3}and^{3}/_{6}=^{1}/_{2}). This may give you a clue as to what you need to do when the bottom number of the fractions you're adding together are different: you have to change one or both of the fractions until the bottom numbers are the same in each. Let's see the process in action:-

__ _ 1 3 + __ _ 1 4 =

__ _ 4 12 + __ _ 3 12 =

__ _ 7 12 = __ _Click the button and read the comments here for each step towards solving the sum.

Let's now do another one, this time taking away instead of adding (though it only makes a real difference when we get to the very last step):-

__ _ 3 7 - __ _ 2 5 =

__ _ 15 35 - __ _ 14 35 =

__ _ 1 35 = __ _Click the button and read the comments here for each step towards solving the sum.

Let's now do another one, but this time there's an extra little task to carry out at the end as the answer can be turned into a simpler fraction:-

__ _ 2 5 + __ _ 2 8 =

__ _ 16 40 + __ _ 10 40 =

__ _ 26 40 = __ _ 13 20Click the button and read the comments here for each step towards solving the sum.

There are alternative ways of solving some fraction sums of this kind, but the method you've just learned will always work. The alternative methods can be used if you notice an easier way of making the bottom numbers the same size, and sometimes you can make them match simply by doubling the top and bottom number in one of the fractions, as with 1/2 + 1/4 where you can change the 1/2 into 2/4 rather than turning the whole sum into 4/8 + 2/8.

You now need some practice at solving more of these, so ... (practice program yet to be written - come back later).