Multiplying and Dividing Fractions

A fraction represents a part of a whole and is written as $$\frac{a}{b}$$ , where 'a' is the numerator and 'b' is the denominator.

The numerator is the top number in a fraction and represents how many parts of the whole are being considered.

The denominator is the bottom number in a fraction and indicates the total number of equal parts the whole is divided into.

The reciprocal of a fraction $$\frac{a}{b}$$ is $$\frac{b}{a}$$ , obtained by flipping the numerator and denominator.

To multiply two fractions, multiply the numerators together and multiply the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ .

$$\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6}$$ .

$$\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{3 \times 2}{4 \times 1} = \frac{6}{4} = \frac{3}{2}$$ .

To divide fractions, multiply by the reciprocal of the second fraction: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ .

$$\frac{8}{24} = \frac{1}{3}$$ after dividing both the numerator and denominator by 8.

The first step in simplifying a fraction is to find the greatest common divisor (GCD) of the numerator and denominator.