# Addition and Subtraction

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# Preknowledge

 List here

Addition ($+$) and subtraction ($-$) 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:

• $a + b - b = a$
• $5 + 2 - 2 = 5$

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:

• $a + b = b + a$
• $a - b \neq b - a$ if $a \neq b$

The sign $\neq$ means “is not equal to”. For example,

• $2 + 3 = 5$ and $3 + 2 = 5$, but
• $5 - 3 = 2$ and $3 - 5 = -2$. (-2 is a negative number, which is explained in detail in another section)

# Extension exercise

 Commutativity for Addition.

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

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