Additive Inverse
Pronunciation: /ˈæd.ɪ.tɪv ˈɪn.vɜrs/ Explain
The additive inverse of a number is the number
that, when added to the original number, gives zero. The additive inverse of
a is
^{-}a.^{[3]}
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
- McAdams, David E.. All Math Words Dictionary, additive inverse. 2nd Classroom edition 20150108-4799968. pg 11. Life is a Story Problem LLC. January 8, 2015. Buy the book
- additive inverse. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/12/2018. http://www.merriam-webster.com/dictionary/additive inverse. Buy the book
- Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 59-60. Thomson, Brooks/Cole. 2005. Last Accessed 6/12/2018. Buy the book
More Information
- McAdams, David E.. Inverse. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/19/2018. https://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. 4/11/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/a/additiveinverse.html.
Image Credits
Revision History
4/11/2019: Changed equations and expressions to new format. (
McAdams, David E.)
4/9/2019: Updated formatting of math objects. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
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.)