# How do you find the additive and multiplicative inverse of 5/9?

Feb 10, 2017

Additive inverse of $\frac{5}{9}$ is $- \frac{5}{9}$ and multiplicative inverse of $\frac{5}{9}$ is $\frac{9}{5}$

#### Explanation:

Additive inverse of a number is the number which when added to it makes the sum zero $0$ - the additive identity element . Observe that $0$ is known as additive identity element as when this is added to any number, it results in the same number.

Obviously additive inverse of $x$ is $- x$ and hence additive inverse of $\frac{5}{9}$ is $- \frac{5}{9}$.

Multiplicative inverse of a number is the number which when multiplied to it makes the product one $1$ - the multiplicative identity element . Observe that $1$ is known as multiplicative identity element as when this when multiplied to any number, results in the same number.

Obviously multiplicative inverse of $x$ is $\frac{1}{x}$ and hence additive inverse of $\frac{5}{9}$ is $\frac{1}{\frac{5}{9}} = \frac{9}{5}$.