Multiplying and Dividing Fractions and Mixed Numbers

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

You should simplify the fractions if possible before multiplying.

A mixed number is a whole number combined with a fraction, such as $$2\frac{1}{2}$$ .

Multiply the whole number by the denominator and add the numerator. For example, $$2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$$ .

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

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

Convert the mixed numbers to improper fractions before dividing.

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

The least common multiple of two numbers is the smallest number that is a multiple of both.