Calculations with real numbers
| [[$ a+b=b+a,\quad ab=ba $]] |
additive commutative property |
| [[$ a +(b+c) = (a+b)+c, \quad a(bc)=(ab)c \quad $]] | additive associative property
|
| [[$ a(b+c)=ab+ac $]] | multiplicative associative property |
| [[$ a+(-a)=0 $]] | number a's opposite number –a |
| [[$ a \cdot \dfrac{1}{a}=1 $]] | number a's reciprocal[[$ \dfrac{1}{a} \quad (a \neq 0) $]] |
| [[$ |a| $]] | absolute value Graphical interpretation: [[$ |a| $]] = number a's points distance from zero  |