Addition
The important rule of addition (“pluscalculation”) is:
$\text{summand} + \text{summand}$ $= \text{sum}$At addition, the operands are designated as summand. The sum is the result.
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The sign
 If the summands have the same sign, you set the common sign and add the contributions.
 If the summands have different signs, you set the sign of the larger summand and subtract the smaller amount from the larger one.
Examples

Set the common sign and add the contributions
$(5)+(3)=(5+3)=8$
$(+3)+(+6)=+(3+6)=+9$ 
Set the sign of the larger summand and subtract the smaller amount
$(8)+(+3)=(83)=5$
$(+7)+(9)=(97)=2$
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Mathematical laws
If $a$, $b$ and $c$ are rational numbers, you have to consider these following mathematical laws:
 Commutative law: $a+b=b+a$
 Associative law: $a+(b+c)=(a+b)+c$ $=a+b+c$