Fractions

A fraction such as $\frac{3}{4}$ means three equal parts, each of size $\frac{1}{4}$. Equivalent fractions name the same amount, for example $\frac{1}{2}=\frac{2}{4}=\frac{3}{6}$. To add, subtract, or compare fractions, the parts must be the same size, so first rewrite the fractions with a common denominator. Then add or subtract the numerators, or compare the numerators directly. The word “of” means multiplication: $\frac{1}{2}$ of $\frac{3}{4}$ is $\frac{1}{2}\times \frac{3}{4}$. To divide by a fraction, multiply by its reciprocal: $\frac{2}{3}÷\frac{4}{9}=\frac{2}{3}\times \frac{9}{4}$. Simplify the final fraction whenever possible.