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 Rational numbers Reciprocals and multiplicative inverses If the product of two numbers is 1, the numbers are called reciprocals, or multiplicative inverses, of each other. 8 is the multiplicative inverse of $\frac{1}{8}$, and $\frac{1}{8}$ is the multiplicative inverse of 8, because $8\;\cdot\;\frac{1}{8}=1$ Strategy. To find the reciprocal of a fraction, we invert the numerator and the denominator. Find the reciprocal of $\frac{2}{3}$. The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$ because $\frac{2}{3}(\frac{3}{2})=1$ All real numbers, except 0, have a multiplicative inverse. Exercises