When working with algebra reciprocal numbers are common, and when working in algebra inverse numbers are too. Get help with both here.

Every number has an **opposite**. In fact, every number has **two** opposites: the **additive inverse** and the** reciprocal**—or **multiplicative inverse**. Don't be intimidated by these technical-sounding names, though. Finding a number's opposites is actually pretty straightforward.

The first type of opposite is the one you might be most familiar with: **positive numbers** and **negative numbers**. For example, the opposite of 4 is -4, or **negative four**. On a number line, 4 and -4 are both the same distance from 0, but they're on opposite sides.

This type of opposite is also called the **additive inverse**.** Inverse** is just another word for **opposite**, and **additive** refers to the fact that when you **add** these opposite numbers together, they always equal 0.

-4 + 4 = 0

In this case, **-4 + 4** equals 0. So does **-20 + 20** and **- x + x**. In fact, any number you can come up with has an additive inverse. No matter how large or small a number is, adding it and its inverse will equal 0 every time.

If you've never worked with positive and negative numbers, you might want to review our lesson on negative numbers.

**For positive numbers or variables, like 5 or**Add a negative sign (-) to the left of the number: 5 → -5.*x*:x → -x 3y → -3y **For negative numbers or variables, like -5 or**Remove the negative sign: -10 → 10.*-x*:-y → y -6x → 6x

The main time you'll use the additive inverse in algebra is when you **cancel out** numbers in an expression. (If you're not familiar with cancelling out, check out our lesson on simplifying expressions.) When you cancel out a number, you're eliminating it from one side of an equation by performing an **inverse action** on that number on **both** sides of the equation. In this expression, we're cancelling out -8 by adding its **opposite:** 8.

x | - 8 | = | 12 |

+ 8 | + 8 |

Using the additive inverse works for cancelling out because a number added to its inverse **always** equals** 0**.