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12.2: Properties of Real Numbers

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Addition

$a + b = b + a$

$3 + 4 = 4 + 3$

Multiplication

$a b = b a$

$4 \cdot 3 = 3 \cdot 4$

Addition

$a + (b + c) = (a + b) + c$

$4 + (3 + 5) = (4 + 3) + 5$

Multiplication

$a (b c) = (a b) c$

$4 (3 \cdot 5) = (4 \cdot 3) 5$

$a (b + c) = a b + a c$

$4 (x + 3) = 4 x + 12$

$(b + c) a = a b + b c$

$(x + 3) 4 = 4 x + 12$

$a \cdot 0 = 0$

$0 \cdot a = 0$

If $a =\neq 0$ , then $\frac{0}{a} = 0$ and $\frac{a}{0} = 0$ is undefined.

$- (- a) = a$