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 the first fraction by the reciprocal of the second fraction. For example, $$\frac{3}{4} \text{ divided by } \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8}$$ .

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

Simplifying a fraction means reducing it to its simplest form, where the numerator and denominator have no common factors other than 1. For example, $$\frac{8}{12}$$ simplifies to $$\frac{2}{3}$$ .

The simplest form of $$\frac{6}{9}$$ is $$\frac{2}{3}$$ .

The result of $$\frac{3}{4} \times \frac{5}{9}$$ is $$\frac{15}{36}$$ , which simplifies to $$\frac{5}{12}$$ .

$$\frac{7}{8} \text{ divided by } \frac{2}{5} = \frac{7}{8} \times \frac{5}{2} = \frac{35}{16}$$ .

$$\frac{25}{8}$$ can be converted to a mixed number by dividing 25 by 8, which gives 3 with a remainder of 1. So, it is written as 3 $$\frac{1}{8}$$ .

The product of $$\frac{4}{5} \text{ and } \frac{10}{11}$$ is $$\frac{40}{55}$$ , which simplifies to $$\frac{8}{11}$$ .