# How do you find the additive and multiplicative inverse of -4 3/5?

Jul 6, 2017

Additive inverse: $+ 4 \frac{3}{5}$

Multiplicative inverse (reciprocal) $- \frac{5}{23}$

#### Explanation:

This means that the numbers are the same, but they have opposite signs.

$\left(- 3\right) + \left(+ 3\right) = 0 \text{ or } \left(+ x\right) + \left(- x\right) = 0$

So in this case, the additive inverse of $- 4 \frac{3}{5} \text{ is } + 4 \frac{3}{5}$

The multiplicative inverse is also known as the reciprocal.

Multiplicative inverses multiply to give $1$

$\frac{2}{3} \times \frac{3}{2} = 1 \text{ or } \frac{a}{b} \times \frac{b}{a} = 1$

In this case:

$- 4 \frac{3}{5} = - \frac{23}{5} \text{ } \leftarrow$ write as an improper fraction

$- \frac{23}{5} \times - \frac{5}{23} = 1$