How to Simplify Fractions — KS3 Maths

A box has room for 12 eggs, and 8 of them are full — the box is $\frac{8}{12}$ full.

The biggest number that divides into both 8 and 12 is 4 — that's the highest common factor. Divide the top and the bottom by it:

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

2 and 3 share no common factor, so $\frac{2}{3}$ is fully simplified. And you can see it on the box: ring the eggs in blocks of 4 and there are three blocks — exactly two of the three blocks are full. Two thirds.

A jar holds 16 sweets and 10 of them are strawberry. What fraction is strawberry, in simplest form?

The highest common factor of 10 and 16 is just 2:

$\frac{10}{16} \;=\; \frac{10 \div 2}{16 \div 2} \;=\; \frac{5}{8}$

5 and 8 share no common factor — done. $\frac{5}{8}$ of the jar is strawberry.

45 minutes is what fraction of an hour? An hour is 60 minutes, so the fraction is $\frac{45}{60}$.

The highest common factor of 45 and 60 is 15:

$\frac{45}{60} \;=\; \frac{45 \div 15}{60 \div 15} \;=\; \frac{3}{4}$

Didn't spot 15? No problem. Divide by anything that works and keep going: $\frac{45}{60} \xrightarrow{\div 5} \frac{9}{12} \xrightarrow{\div 3} \frac{3}{4}$. Every route lands in the same place.