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12.2: Properties of Real Numbers

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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


This page titled 12.2: Properties of Real Numbers is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Denny Burzynski & Wade Ellis, Jr. (OpenStax CNX) .

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