Simplifying a fraction means writing it in its lowest terms by dividing the numerator and denominator by their highest common factor (HCF).
$$\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}$$
A fraction is fully simplified when the numerator and denominator share no common factor other than 1.
Method: find the HCF of the numerator and denominator, then divide both by it.
$$\frac{24}{36}: \quad \text{HCF}(24, 36) = 12, \quad \frac{24}{36} = \frac{2}{3}$$
You can also simplify in steps (cancel by 2, then 3, etc.) if you can't spot the HCF immediately — just make sure you've fully simplified at the end.
In algebra: the same principle applies — cancel common factors from the numerator and denominator. $$\frac{6x^2}{9x} = \frac{2x}{3}$$
Common error: cancelling only the numerators or only part of the expression — the same factor must divide both numerator and denominator.