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Opposite number

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In mathematics, the opposite or inverse of a number <math>k</math> is an additive or a subtractive number <math>n</math> which, when added to <math>k</math>, results in 0. The opposite of <math>a</math> is <math>-a</math>.[1][2] For example, −7 is the opposite of 7, because <math>7+-7 = 0</math>.

Definition[change]

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

Properties[change]

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 <math>-a</math> is the opposite number of <math>a </math> and both have the same absolute value <math>|-a|=|a|</math>.
  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 <math>-a+a=0.</math>
  6. The division of two non-zero opposite numbers is always <math>-1 </math>, because <math>\frac{-a}{a}=\frac{a}{-a}=-1.</math>
  7. Each number has a unique opposite number.

Related pages[change]

References[change]

  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. (6 February 2022). "Opposite Numbers: Definition, Examples, and Properties". Mathstoon. Retrieved 6 February 2022.