# Opposite of a number

The opposite of a number is a number that is the same distance from 0 as another number, but in the opposite direction. Given a number, the opposite of that number can also be thought of as the number that needs to be added in order for the result to be 0.

The number line above shows that positive three and negative three are opposites of each other. They have the same value, but in opposite directions. This is true for all positive numbers; the opposite of a positive number is its negative value. The same is also true for negative numbers; the opposite of a negative number is its positive value. The opposite of zero is itself.

Examples

Find the opposite of the following numbers.

1. 7:

The opposite of 7 is -7.

2. -12:

The opposite of -12 is 12.

3. (3 + 4 + 2):

-(3 + 4 + 2) = -9

The opposite of (3 + 4 + 2) is -9.

The opposite of a number is also referred to as its additive inverse, a concept that is also used in algebra to apply to variables and other expressions, not just positive and negative numbers. In an algebraic context, finding the additive inverse involves multiplying a given expression by -1.

Note that a negative number is not the same thing as an additive inverse. A negative number is only the additive inverse of its respective positive value.