Opposite number

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In mathematics, the opposite or additive inverse of a number is a number which, when added to , results in 0. The opposite of is .[1][2] 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.[3]

  1. The opposite of 0 is 0.
  2. 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 .
  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
  6. The division of two non-zero opposite numbers is always , because
  7. Each number has a unique opposite number.

Related pages[change | change source]

References[change | change source]

  1. Weisstein, Eric W. "Additive Inverse". mathworld.wolfram.com. Retrieved 2020-08-27.
  2. "Additive Inverse". www.learnalberta.ca. Retrieved 2020-08-27.
  3. Ghosh, N. "Opposite Numbers: Definition, Examples, and Properties". Mathstoon. Retrieved 6 February 2022.