Addition is joining two or more quantities together to make a sum. 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.
Figure 1: Representation of 4 + 3 = 7 |
Real numbers can also be added. Figure 2 gives a representation of 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.
Click on the points A and B near the top to change the figure. The blue and red arrows on the number line show A added to B. The sum A+B is below them in purple. |
Manipulative 1 - Addition Created with GeoGebra. |
Addition is also defined for many types of math entities such as vectors and matrices.
Mathematicians usually define subtraction as adding 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
Property Name | Example | Description |
---|---|---|
Additive property of zero Additive identity |
a + 0 = 0 + a = a | Any number plus zero equals the original number. 0 is the additive identity for real and complex numbers. |
Additive inverse | a + (-a) = 0 | The additive inverse of any real or complex number is the negative of that numbers. |
Associative property of addition | a + ( b + c ) = ( a + b ) + a | The order of in which multiple additions of real and complex numbers are performed does not change the result. |
Commutative property of addition | a + b = b + a | It doesn't matter which of two numbers come first in addition of real and complex numbers. |
Distributive Property of Multiplication over Addition and Subtraction | a ( b + c ) = ab + ac, and a ( b - c ) = ab - ac | Multiplication is distributive over addition and subtraction. |
Additive property of equality | If 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 equality | If 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 are two operands and the result of adding those two operands. The following table gives the addition facts for 0 through 10.
+ | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|---|
0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
2 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
3 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
4 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
5 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
6 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
7 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
8 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
9 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
10 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
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.
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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