Inverse Properties

Additive Inverse: $a + ( a) = 0$. This is also called the opposite. Multiplicative Inverse: $a \cdot \frac{1}{a} = 1$, for $a \neq 0$. This is also called the reciprocal.

a. The additive inverse (opposite) of $ 9b$ is $9b$, since $ 9b + 9b = 0$. b. The multiplicative inverse (reciprocal) of $\frac{7x}{15y}$ is $\frac{15y}{7x}$, because their product is $1$. c. The multiplicative inverse of $ 8$ is $ \frac{1}{8}$.

Think of inverses as the ultimate 'undo' buttons for numbers. The additive inverse zaps any number back to zero, its starting point. The multiplicative inverse resets any number back to one, the master identity of multiplication. Every number has a secret agent partner to bring it back to baseline.