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

\(-(-a) = a\)

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