## Inverse Property of Multiplication

Read this section to see examples of how to apply the inverse property of addition. Focus on the examples in the boxes. Note that in the first multiplication example box, we can use the inverse property for fractions as well as whole numbers.

### Use the Inverse Properties of Addition and Multiplication

What number multiplied by $\frac {2}{3}$ gives multiplicative identity, $1$? In other words, two-thirds times what results in $1$?

 $\frac {2}{3} \cdot \text{____} =1$ We know $\frac{2}{3} \cdot \frac{3}{2}=1$

What number multiplied by $2$ gives the multiplicative identity, $1$? In other words two times what results in $1$?

 $2 \cdot \text{____} =1$ We know $2 \cdot \frac{1}{2}=1$

Notice that in each case, the missing number was the reciprocal of the number.

We call $\frac {1}{a}$ the multiplicative inverse of $a(a≠0)$. The reciprocal of a number is its multiplicative inverse. A number and its reciprocal multiply to $1$, which is the multiplicative identity.

#### INVERSE PROPERTIES

Inverse Property of Addition for any real number $a,$

$a+(−a)=0$

$-a \text { is the additive inverse of a.}$

Inverse Property of Multiplication for any real number $a ≠ 0,$

$a \cdot \frac {1}{a} = 1$

$\frac {1}{a} \text { is the multiplicative inverse of a.}$

Source: Rice University, https://openstax.org/books/prealgebra/pages/7-4-properties-of-identity-inverses-and-zero