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 1/2, 1 is the numerator and 2 is the denominator.

To multiply fractions, multiply the numerators together and the denominators together. For example, $$\frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4} = \frac{3}{8}$$ .

To divide fractions, multiply by the reciprocal of the second fraction. For example, $$\frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3}$$ .

Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator have no common factors other than 1. For example, $$\frac{8}{24} = \frac{1}{3}$$ .

The product of a positive number and a positive number is always positive.

The product of a negative number and a negative number is always positive.

The product of a positive number and a negative number is always negative.

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place that result over the original denominator. For example, $$2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$$ .

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

To divide a fraction by a whole number, multiply the denominator of the fraction by that whole number. For example, $$\frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$$ .