Multiplying and Dividing Rational Numbers

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

To multiply two fractions, multiply the numerators together and the denominators together. For example, $$\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$$ .

The result is a negative rational number.

The result is a positive rational number.

To divide two fractions, multiply the first fraction by the reciprocal of the second fraction. For example, $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}$$ .

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

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

$$\frac{15}{8}$$ .

$$1$$ .

$$-\frac{7}{8}$$ .