Simplifying a fraction means writing it in its lowest terms while keeping the same value. A fraction is fully simplified when the numerator and denominator have no common factor greater than \(1\).

To simplify a fraction, find the highest common factor (HCF) of the numerator and denominator, then divide both by that number.

$$
\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}
$$

Here, the HCF of \(18\) and \(24\) is \(6\).

If the numerator and denominator are both even, you can often start by dividing by \(2\) and repeat until no further common factors remain.

$$
\frac{10}{16} = \frac{5}{8}
$$

Another method is prime factorisation. Write both numbers as products of prime factors, cancel any common factors, then multiply what remains.

$$
\frac{12}{20} = \frac{2^2 \times 3}{2^2 \times 5} = \frac{3}{5}
$$

A fraction is already simplified if the only common factor of the numerator and denominator is \(1\).

Always check your final fraction carefully. Simplifying should change how the fraction is written, not its value.