Opposite number

In mathematics, the opposite or inverse of a number $k$ is an additive or a subtractive number $n$ which, when added to $k$, results in 0. The opposite of $a$ is $-a$. For example, −7 is the opposite of 7, because $7+-7=0$.

Definition

A number $x$ is called an opposite or inverse number of another number $y$ if $x+y=0$. By definition, $-x$ is the opposite number of $x$. For example, $-2$ is the opposite number of $2$ and vice-versa. This is because $-2+2=0.$

Properties

The opposite numbers satisfy the properties listed below.

1. The opposite of 0 is 0.
2. Two opposite numbers have the same absolute value. This follows from the fact that the $-a$ is the opposite number of $a$ and both have the same absolute value $|-a|=|a|$.
3. The opposite of a positive number is the negative version of the number. The opposite of a negative number is the positive version of the number.
4. opposite numbers are located in the opposite direction on a number line having the same distance from the origin. That is, they are symmetric about the origin on a number line.
5. The sum of two opposite numbers is always zero, because $-a+a=0.$
6. The division of two non-zero opposite numbers is always $-1$, because ${\frac {-a}{a}}={\frac {a}{-a}}=-1.$
7. Each number has a unique opposite number.

Related pages

• Addition
• Reciprocal
• Absolute value
• Operation (mathematics)