12.2: Properties of Real Numbers
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
\(-(-a) = a\)