Simplifying Fractions

In a Nutshell

Keep dividing the top and bottom by the same factor until they share no common factor except 1.

Simplifying a fraction means finding an equivalent fraction with the smallest possible numerator and denominator. We also call this writing the fraction "in its lowest terms" or "in its simplest form".

Divide the numerator and denominator by their highest common factor (HCF). If you cannot spot the HCF straight away, divide by any common factor you can see and repeat until no common factor remains.

ab=a÷HCFb÷HCF\frac{a}{b} = \frac{a \div \text{HCF}}{b \div \text{HCF}}

On the fraction wall, a simplified fraction sits in a row with fewer (bigger) pieces, but it covers exactly the same length.

Fraction wall Horizontal bars stacked vertically. The top bar is one whole. Below it, bars are divided into halves, thirds, quarters, fifths, sixths, eighths, tenths, and twelfths, so you can see which fractions are equivalent.

Click a segment in a row with many pieces. The guide line shows which segments in rows with fewer pieces cover the same amount. The one with the fewest pieces is the simplest form.

Watch it work

Question: Simplify 1824\frac{18}{24}.

Have a go

Q1. Simplify 812\frac{8}{12}.

Q2. Simplify 1525\frac{15}{25}.

Q3. Simplify 3648\frac{36}{48}.

Q4. Is 715\frac{7}{15} already in its simplest form? Explain.