what is additive inverse

An additive inverse of a number is the number you add to it to get a sum of 0.

Core idea

• If a number is xxx, its additive inverse is −x-x−x.

• When you add a number and its additive inverse, you always get 0: x+(−x)=0x+(-x)=0x+(−x)=0.

• They are the same distance from 0 on the number line, but on opposite sides.

Simple examples

• Additive inverse of 5 is −5-5−5, because 5+(−5)=05+(-5)=05+(−5)=0.

• Additive inverse of −9-9−9 is 9, because −9+9=0-9+9=0−9+9=0.

• Additive inverse of 34\frac{3}{4}43​ is −34-\frac{3}{4}−43​.

• Additive inverse of 0 is 0 itself (0 is its own additive inverse).

Quick formula

• For any real number nnn: additive inverse of nnn = −1×n=−n-1\times n=-n−1×n=−n.

• For −n-n−n, the additive inverse is nnn.

Think of it this way: to “undo” adding a number, you add its additive inverse, which is just the same number with the opposite sign.

TL;DR: Additive inverse means “opposite number”: change + to − or − to + so that adding the two gives 0.