Addition

Pronunciation: /əˈdɪ ʃən/ ?

Addition is joining two or more quantities together to make a sum.[see references] Figure 1 gives an example of integer addition. In the addition statement 4 + 3 = 7, 4 and 3 are addends and 7 is the sum. Addends are what is being added together, and the sum is the result of the addition. The symbol '+' is called the addition sign.

4 dots and 3 dots and 7 dots representing 4 + 3 = 7
Figure 1: Representation of 4 + 3 = 7

Real numbers can also be added. Figure 2 gives a representation of 2 + 1 = 3.

Number line showing 2 + 1 = 3
Figure 2: Representation of 2 + 1 = 3

Manipulative 3 represents the addition of real numbers. Click on the blue points and drag them to change the figure.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)
Manipulative 3: Addition of real numbers Created with GeoGebra.

Addition is also defined for many types of math entities such as vectors and matrices.

Subtraction

Mathematicians usually define subtraction as addition of the additive inverse of a value. Subtraction is defined this way so that subtraction of vectors and matrices and other math entities makes more sense. Stated mathematically, a - b ≡ a + -b. A difference is the result of subtracting one number from another. For example, in the equation 7 - 4 = 3, 3 is the difference.

A example of this is 5 - 4 = 5 + -4 = 1

Properties of Addition of Real and Complex Numbers

Property NameExampleDescription
Additive property of zero
Additive identity
a + 0 = 0 + a = aAny number plus zero equals the original number. 0 is the additive identity for real and complex numbers.
Additive inversea + (-a) = 0The additive inverse of any real or complex number is the negative of that numbers.
Associative property of additiona + ( b + c ) = ( a + b ) + cThe order of in which multiple additions of real and complex numbers are performed does not change the result.
Commutative property of additiona + b = b + aIt doesn't matter which of two numbers come first in addition of real and complex numbers.
Distributive Property of Multiplication over Addition and Subtractiona ( b + c ) = ab + ac, a ( b - c ) = ab - acMultiplication is distributive over addition and subtraction.
Additive property of equalityIf a = b then a + c = b + c.The additive property of equality states that any number can be added to both sides of an equation without changing the truth value of the equation.
Subtractive property of equalityIf a = b then a - c = b - c.The subtractive property of equality states that any number can be subtracted from both sides of an equation without changing the truth value of the equation.
Table 1: Properties of Addition

Addition Facts

Addition facts are two operands and the result of adding those two operands. The following table gives the addition facts for 0 through 10.

+012345678910
0012345678910
11234567891011
223456789101112
3345678910111213
44567891011121314
556789101112131415
6678910111213141516
77891011121314151617
889101112131415161718
9910111213141516171819
101011121314151617181920

Adding complex numbers

To add two complex numbers, add the corresponding parts. Given two complex numbers a + bi and c + di, (a + bi) + (c + di) = (a + c) + (b + d)i. Example: (3 - 2i) + (-1 + 3i) = (3 + (-1)) + (-2 + 3)i = 2 + 1i = 2 + i.

Educator Resources

Cite this article as:


Addition. 2010-10-12. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/addition.html.

Translations

Image Credits

Revision History


2010-10-12: Added "Adding complex numbers", additive identity, additive inverse, and additive property of equality (McAdams, David.)
2010-01-04: Added "References" (McAdams, David.)
2009-03-03: Added discussion of difference to the section on subtraction (McAdams, David.)
2008-09-16: Changed figure 3 to a manipulative (McAdams, David.)
2008-06-07: Corrected spelling errors (McAdams, David.)
2008-05-14: Initial version (McAdams, David.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2005-2011 Life is a Story Problem LLC. All rights reserved.
Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License