# Addition and Subtraction

OpenMaths | ||
---|---|---|

Basics | Addition and Subtraction | Multiplication and Division | Brackets | |

Algebra | Rearranging Equations | | |

Number | Rational Numbers | |

Addition ([math]+[/math]) and subtraction ([math]-[/math]) are the most basic operations between numbers but they are
very closely related to each other. You can think of subtracting as being the opposite of adding
since adding a number and then subtracting the same number will not change what you started
with. For example, if we start with a and add b, then subtract b, we will just get back to a again:

- [math]a + b - b = a[/math]
- [math]5 + 2 - 2 = 5[/math]

If we look at a number line, then addition means that we move to the right and subtraction means that we move to the left.

The order in which numbers are added does not matter, but the order in which numbers are subtracted does matter. This means that:

- [math]a + b = b + a[/math]
- [math]a - b \neq b - a[/math] if [math]a \neq b[/math]

The sign [math]\neq[/math] means “is not equal to”. For example,

- [math]2 + 3 = 5[/math] and [math]3 + 2 = 5[/math], but
- [math]5 - 3 = 2[/math] and [math]3 - 5 = -2[/math]. (-2 is a negative number, which is explained in detail in another section)

The fact that a + b = b + a, is known as the commutative property for addition.

Content from this page was originally sourced from http://www.fhsst.org/ which is licenced under the GFDL 1.2:

"Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled “GNU Free Documentation License”.