Multiplying and dividing fractions

A fraction represents a part of a whole and consists of a numerator (top number) and a denominator (bottom number). For example, in the fraction $$\frac{3}{4}$$ , 3 is the numerator and 4 is the denominator.

To multiply fractions, multiply the numerators together and the denominators together. For example, $$\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$$ .

To divide fractions, multiply by the reciprocal of the second fraction. For example, $$\frac{2}{3} \text{ divided by } \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$$ .

A mixed number is a whole number combined with a fraction. For example, $$1 \frac{1}{2}$$ is a mixed number, which represents 1 whole and 1/2.

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder is the new numerator over the original denominator. For example, $$\frac{9}{4} = 2 \frac{1}{4}$$ .

The reciprocal of a fraction is obtained by flipping the numerator and denominator. For example, the reciprocal of $$\frac{3}{4}$$ is $$\frac{4}{3}$$ .

The first step in dividing fractions is to find the reciprocal of the second fraction.

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 result is $$\frac{2 \times 3}{3 \times 5} = \frac{6}{15} = \frac{2}{5}$$ after simplification.

The result is $$\frac{1}{4} \times \frac{1}{8} = \frac{1}{32}$$ .