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