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.

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

The reciprocal of a fraction $$\frac{a}{b}$$ is $$\frac{b}{a}$$ .

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

Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator have no common factors other than 1.

The simplest form of $$\frac{6}{18}$$ is $$\frac{1}{3}$$ .

The result is $$\frac{2}{12}$$ , which simplifies to $$\frac{1}{6}$$ .

The result is $$\frac{3}{5} \times \frac{2}{1} = \frac{6}{5}$$ or $$1 \frac{1}{5}$$ .

To convert a mixed number, multiply the whole number by the denominator and add the numerator: $$a \frac{b}{c} = \frac{a \times c + b}{c}$$ .

The product is $$\frac{2 \times 3}{3 \times 4} = \frac{6}{12}$$ , which simplifies to $$\frac{1}{2}$$ .