12.2: Properties of Real Numbers

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Jun 12, 2021
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- 12.1: Table of Symbols
- 12.3: Important and Useful Rules/Formulas

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Commutative Property

Addition

$a + b = b + a$

$3 + 4 = 4 + 3$

Multiplication

$ab = ba$

$4 \cdot 3 = 3 \cdot 4$

Associative Property

Addition

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

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

Multiplication

$a(bc)=(ab)c$

$4(3⋅5)=(4⋅3)5$

Distributive Property

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

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

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

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

Properties of Zero

$a \cdot 0 = 0$

$0 \cdot a = 0$

If $a =\not = 0$ , then $\dfrac{0}{a} = 0$ and $\dfrac{a}{0} = 0$ is undefined.

Double Negative Property

$-(-a) = a$

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Commutative Property

Associative Property

Distributive Property

Properties of Zero

Double Negative Property

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