Additive Inverse
Pronunciation: /ˈæd ɪ tɪv ɪnˈvɜrs/ Explain
The additive inverse of a number is the number that, when added to the
original numbers, gives zero. The additive inverse of
a is ^{-}a.^{[1]} This is because
a + ^{-}a = 0, where 0 is the
additive identity
for real numbers.
Examples
The additive inverse of 5 is ^{-}5 since 5 + ^{-}5 = 0.
The additive inverse of ^{-}5 is 5 since ^{-}5 + 5 = 0.
The additive inverse of ^{-}3 is 3 since ^{-}3 + 3 = 0.
The additive inverse of 3 is ^{-}3 since 3 + ^{-}3 = 0.
The additive inverse of x is ^{-}x since x + ^{-}x = 0.
The additive inverse of ^{-}p is p since ^{-}p + p = 0.
Understanding Check
Click on the check box of the correct answer.
- What is the additive inverse of 8?
a a No, 8 + a ≠ 0. The additive inverse of 8 is ^{-}8.
^{-}a ^{-}a No, 8 + ^{-}a ≠ 0. The additive inverse of 8 is ^{-}8.
8 8 No, 8 + 8 ≠ 0. The additive inverse of 8 is ^{-}8.
^{-}8^{-}8 Yes! 8 + ^{-}8 = 0. The additive inverse of 8 is ^{-}8.
- What is the additive inverse of ^{-}4?
x x No, ^{-}4 + x ≠ 0. The additive inverse of ^{-}4 is 4.
^{-}x ^{-}x No, ^{-}4 + ^{-}x ≠ 0. The additive inverse of ^{-}4 is 4.
4 4 Yes! ^{-}4 + 4 = 0.
^{-}4^{-}4 No, ^{-}4 + ^{-}4 ≠ 0. The additive inverse of ^{-}4 is 4.
- What is the additive inverse of r?
r r No, r + r ≠ 0. The additive inverse of r is ^{-}r.
^{-}r ^{-}r Yes! r + ^{-}r = 0.
4 4 No, r + 4 ≠ 0. The additive inverse of r is ^{-}r.
^{-}4^{-}4 No, r + ^{-}4 ≠ 0. The additive inverse of r is ^{-}r.
Other Additive Inverses
The additive inverse is defined for a number of math entities, including
vectors,
and
matrix.
The additive inverse for vector <a,b> is
<^{-}a,^{-}b>. This is because
<a,b> + <^{-}a,^{-}b> = <0,0>.
<0,0> is the
additive identity
for vectors.
The additive inverse
for a matrix A is found by multiplying matrix
A by the scalar ^{-}1:
^{-}1·A. The result of this operation is a
zero matrix.
References
- additive inverse. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 8/6/2018. http://www.merriam-webster.com/dictionary/additive inverse.
- Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 59-60. Thomson, Brooks/Cole. 2005. Buy the book
More Information
- McAdams, David E.. Inverse. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/19/2018. http://www.allmathwords.org/en/i/inverse.html.
- Definition of Additive Inverse. www.mathsisfun.com. Math Is Fun. 6/18/2018. https://www.mathsisfun.com/definitions/additive-inverse.html.
Cite this article as:
McAdams, David E. Additive Inverse. 6/12/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/additiveinverse.html.
Image Credits
Revision History
6/18/2018: Added More Information entry. (
McAdams, David E.)
6/12/2018: Removed broken links, updated license, implemented new markup. (
McAdams, David E.)
12/24/2009: Added "References". (
McAdams, David E.)
10/5/2008: Expanded 'More Information'. (
McAdams, David E.)
5/14/2008: Added additive inverse of vectors and matrices. Corrected typo changing 'additive identity' to 'additive inverse' (
McAdams, David E.)
4/17/2008: Initial version. (
McAdams, David E.)