# Inverse Property of Multiplication

**Inverse property of multiplication**:

`huge color(purple)(a times 1/a=1/a times a=1) `

`1/a` is called the **multiplicative inverse** of `a`.

Inverse property is true for any real number `a`.

Notice, that we wrote, that `a times 1/a=1/a times a`. This is true, according to the commutative property of multiplication.

Actually, we already discussed the multiplicative inverse.

Yes, yes. Multiplicative inverse is just another name for reciprocal!

**Example 1**. Multiplicative inverse of `5/3` is `3/5`, because `5/3 times 3/5=1`.

**Example 2**. Multiplicative inverse of `-sqrt(2)` is `-1/sqrt(2)`, because `(-sqrt(2))*(-1/sqrt(2))=1`.

**Example 3**. `2.57*1/2.57=1/2.57*2.57=1` (recall, that both `times` and `*` denote multiplication).

**Conclusion**. Multiplicative inverse (reciprocal) of the number (`a`) is a number, that is turned upside down, i.e. `1/a`.