Equivalent Fractions (No Calculator) — KS3 Maths

Mia and Ben each get an identical pizza. Mia's is cut into 2 equal slices and she eats 1 — that's $\frac{1}{2}$. Ben's is cut into 6 slices and he eats 3 — that's $\frac{3}{6}$.

Ben says he ate more, because three slices beats one. But look at the pizzas: the eaten amount is exactly the same — half of each pizza is gone.

The golden rule connects the two fractions: multiply the top and the bottom by the same number.

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

And you can see why on the pizzas: three of Ben's small slices, together, make exactly one of Mia's big slices.

A chocolate bar has 12 squares, and Sam eats two thirds of it. How many squares is that? That's the missing-number question $\frac{2}{3} = \frac{?}{12}$.

Look at the bottoms first: $3 \times 4 = 12$.

So do exactly the same to the top: $2 \times 4 = 8$.

$\frac{2}{3} = \frac{8}{12}$

Sam eats 8 squares — and on the bar, that's exactly 2 of its 3 rows. Two thirds, you can see it.

This time the top is given: $3 \times 4 = 12$, so multiply the bottom by four as well: $5 \times 4 = 20$.

$\frac{3}{5} = \frac{12}{20}$

Draw both as bars and the shaded amounts line up exactly — the second bar is the same bar, just cut into four times as many pieces.