What is Opposite number?
In [[mathematics]], the '''opposite''' or '''inverse''' of a [[number]] <math>k</math> is an additive or a subtractive number <math>n</math> which, when [[addition|added]] to <math>k</math>, results in 0. The opposite of <math>a</math> is <math>-a</math>.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Additive Inverse|url=https://mathworld.wolfram.com/AdditiveInverse.html|access-date=2020-08-27|website=mathworld.wolfram.com|language=en}}</ref><ref>{{Cite web|title=Additive Inverse|url=http://www.learnalberta.ca/content/memg/Division03/Additive%20Inverse/index.html|access-date=2020-08-27|website=www.learnalberta.ca}}</ref> For example, −7 is the opposite of 7, because <math>7+-7 = 0</math>. == Definition == 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 == The opposite numbers satisfy the properties listed below.<ref>{{Cite web|last=Ghosh|first=N.|title=Opposite Numbers: Definition, Examples, and Properties|url=https://www.mathstoon.com/opposite-numbers/|access-date=6 February 2022|website=Mathstoon|date=6 February 2022 |language=en}}</ref> # The opposite of [[Zero|0]] is 0. # 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>. # 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 <math>-a+a=0.</math> # The division of two non-zero oppos