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: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ .

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

Divide the numerator by the denominator. The quotient is the whole number, and the remainder over the original denominator is the fraction.

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 multiplying.

To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD).

$$\frac{3 \times 2}{4 \times 5} = \frac{6}{20} = \frac{3}{10}$$ after simplification.

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