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|
|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.|
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
|Additive property of zero
|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.
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.
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