In mathematics, the opposite or additive inverse of a number is a number which, when added to , results in 0. The opposite of is . For example, −7 is the opposite of 7, because .
Definition[change | change source]
A number is called an opposite number of another number if . By definition, is the opposite number of . For example, is the opposite number of and vice-versa. This is because
Opposite numbers are also known as additive inverses.
Properties[change | change source]
The opposite numbers satisfy the properties listed below.
- The opposite of 0 is 0.
- Two opposite numbers have the same absolute value. This follows from the fact that the is the opposite number of and both have the same absolute value .
- 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.
- 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.
- The sum of two opposite numbers is always zero, because
- The division of two non-zero opposite numbers is always , because
- Each number has a unique opposite number.
Related pages[change | change source]
References[change | change source]
- ↑ Weisstein, Eric W. "Additive Inverse". mathworld.wolfram.com. Retrieved 2020-08-27.
- ↑ "Additive Inverse". www.learnalberta.ca. Retrieved 2020-08-27.
- ↑ Ghosh, N. "Opposite Numbers: Definition, Examples, and Properties". Mathstoon. Retrieved 6 February 2022.