How to Divide Fractions — KS3 Maths

A bottle holds four fifths of a litre of juice. A glass holds one fifth of a litre. How many glasses can you fill?

That's $\frac{4}{5} \div \frac{1}{5}$ — and keep, change, flip answers it. Keep $\frac{4}{5}$. Change the $\div$ into $\times$. Flip $\frac{1}{5}$ upside down to $\frac{5}{1}$. From here it's just multiplying fractions:

$\frac{4}{5} \div \frac{1}{5} \;=\; \frac{4}{5} \times \frac{5}{1} \;=\; \frac{20}{5} \;=\; 4$

Four glasses — but why does flipping work? Look at what the question actually asks: how many one-fifths fit into four-fifths? So simply pour and count — one glass, two, three, four, and the bottle's empty. And the reason the trick works: a whole litre holds five fifths, so dividing by one fifth is exactly the same as multiplying by five.

Three quarters of a chocolate bar is left. A serving is three eighths of a bar. How many servings are left?

The bar had eight squares and two are gone, so six of the eight squares are left — and $\frac{6}{8}$ is $\frac{3}{4}$. A serving is three squares, and you can see two servings fit on the bar. Now the rule — keep $\frac{3}{4}$, change to multiply, flip $\frac{3}{8}$ to $\frac{8}{3}$:

$\frac{3}{4} \div \frac{3}{8} \;=\; \frac{3}{4} \times \frac{8}{3} \;=\; \frac{24}{12} \;=\; 2$

Two servings — the picture and the rule agree.

Three quarters of a pizza is left, shared equally between two friends. What fraction of the whole pizza does each friend get?

This one looks different — we're dividing by a whole number. But any whole number is already a fraction: $2$ is just $\frac{2}{1}$. So the same trick works. Keep $\frac{3}{4}$, change to multiply, flip $\frac{2}{1}$ to $\frac{1}{2}$ — which makes sense, because sharing between two people means each gets half of what's there:

$\frac{3}{4} \div 2 \;=\; \frac{3}{4} \times \frac{1}{2} \;=\; \frac{3}{8}$

Each friend gets three eighths of the whole pizza — already in its simplest form. Check it on the pizza: six slices dealt out is three each, and three of the eight slices is exactly $\frac{3}{8}$.