Addition and Subtraction

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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.

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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)

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Extension exercise

Commutativity for Addition.

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

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