Multiplying and Dividing Fractions - Review

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 $$\frac{b}{a}$$ . It is obtained by flipping the numerator and denominator.

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 $$\frac{6}{24}$$ is $$\frac{1}{4}$$ .

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

To convert a mixed number like $$1\frac{1}{3}$$ to an improper fraction, multiply the whole number by the denominator and add the numerator: $$1\frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3}$$ .

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

The result is $$\frac{5 \times 2}{8 \times 5} = \frac{10}{40} = \frac{1}{4}$$ .