How to Add & Subtract Fractions — KS3 Maths

Friday night's pizza box has half a pizza left. Saturday's box has a third of a pizza left. How much pizza is that altogether?

Can we just count the slices? One big slice and one smaller slice — two slices? Two what? The pieces are different sizes, so counting tells us nothing. So here's the move: cut both pizzas into sixths — sixths work because 2 and 3 both go into 6.

The half becomes $\frac{1}{2} = \frac{3}{6}$, and the third becomes $\frac{1}{3} = \frac{2}{6}$. Now every piece is the same size, so just count them:

$\frac{3}{6} + \frac{2}{6} \;=\; \frac{5}{6}$

Slide all five slices into one box and they fill five sixths of a pizza — one slice short of a whole. That's the whole secret: same-size pieces (a common denominator), then count the tops.

Gran's vegetable patch has 12 equal plots. She plants two thirds of the patch with carrots and a quarter of it with peas. How much of the patch is planted?

Thirds and quarters — neither bottom divides the other, so list the multiples:

• multiples of 3: 3, 6, 9, 12
• multiples of 4: 4, 8, 12

12 is in both lists — that's the common denominator. Rewrite both fractions (whatever you do to the bottom, do to the top):

$\frac{2}{3} = \frac{8}{12} \qquad \frac{1}{4} = \frac{3}{12}$

The bottoms match, so add the tops: $\frac{8}{12} + \frac{3}{12} = \frac{11}{12}$.

On the patch that's 8 plots of carrots plus 3 of peas — 11 of the 12 plots planted, and just one plot of bare soil left.

A bottle of juice is $\frac{5}{6}$ full. Amir drinks $\frac{1}{3}$ of the bottle. How much juice is left?

Here 3 goes into 6, so only one fraction needs rewriting: $\frac{1}{3} = \frac{2}{6}$. Now subtract the tops:

$\frac{5}{6} - \frac{2}{6} \;=\; \frac{3}{6}$

Not finished! 3 and 6 share a factor of 3, so simplify: $\frac{3}{6} = \frac{1}{2}$. Exactly half the bottle is left — and on the bottle's scale, the juice sits exactly on the halfway mark.