How to Multiply Fractions — KS3 Maths

After a party, three quarters of a brownie tray is left. Priya eats two thirds of what's left. What fraction of the whole tray does she eat?

The tray held 24 brownies in four rows of six. At the party the top row went — the rows are quarters, so with three of the four rows left, $\frac{3}{4}$ of the tray is left.

Now the key word: Priya eats two thirds OF what's left, and in maths of means multiply. So the question is really $\frac{2}{3} \times \frac{3}{4}$.

Watch it happen on the tray: three rows are left, so the rows are now thirds, and Priya takes two of the three — twelve brownies. And the rule gets the same answer straight across:

$\frac{2}{3} \times \frac{3}{4} \;=\; \frac{2 \times 3}{3 \times 4} \;=\; \frac{6}{12} \;=\; \frac{1}{2}$

The tray proves it: count Priya's brownies — twelve, and twelve of the twenty-four is exactly half the tray.

A recipe needs $\frac{4}{5}$ of a jug of water, but you're only making half the recipe. How much water do you need?

Half of the water — of means multiply: $\frac{1}{2} \times \frac{4}{5}$. Straight across:

$\frac{1}{2} \times \frac{4}{5} \;=\; \frac{1 \times 4}{2 \times 5} \;=\; \frac{4}{10} \;=\; \frac{2}{5}$

Four tenths simplifies (divide the top and the bottom by 2) to two fifths of a jug — and on the jug's scale, the water comes down to exactly the $\frac{2}{5}$ mark.

An apple pie was cut into eight slices. After lunch, five slices are left. Ben eats two fifths of what's left. What fraction of the whole pie does he eat?

Two fifths of five eighths — the same rule works: $\frac{2}{5} \times \frac{5}{8}$.

And look how friendly the picture is: five slices are left, so each slice is one fifth of what's left — two fifths is simply two slices. Now the rule:

$\frac{2}{5} \times \frac{5}{8} \;=\; \frac{2 \times 5}{5 \times 8} \;=\; \frac{10}{40} \;=\; \frac{1}{4}$

Ten and forty both divide by ten, so Ben eats one quarter of the whole pie. Check it on the pie: he ate two of the eight slices, and two eighths is exactly a quarter.