# Algebra/Chapter 3/Inverses

What are Equations? | Algebra Chapter 3: Solving Equations Section 2: Inverses of Numbers |
Properties of Equality |

Numbers have two inverses: additive inverses, or opposites, and multiplicative inverses, or reciprocals. All real numbers besides 0 have both of these inverses.

## Additive Inverses

[edit | edit source]The additive inverse of a number is such that a number added to its additive inverse is zero. It is also called an opposite. To find a number's additive inverse, find if the number is positive, negative, or neither. If a number *n* is positive, then its additive inverse is *-n*. Likewise, the additive inverse of *-n* is *n.* 0 is the additive inverse of itself.

## Multiplicative Inverses

[edit | edit source]The multiplicative inverse of a number is such that a number multiplied by its multiplicative inverse is 1; that is, unity. It is also called a reciprocal. The multiplicative inverse of a number *n* is 1/n. To find a number's multiplicative inverse you may also write it as a fraction and reverse its numerator and denominator; recall that any number divided by 1 is itself. 0 has no multiplicative inverse; it would be 1/0, but numbers can not be divided by zero.