1. Properties of Real Numbers
COMMUTATIVE: if you change the order of the numbers being added, the answer does not change. This also works for multiplying. The following are examples of this property…
Add: = ½ + ¾ = ¾ + ½
Multiply: (5)(-10) = (-10)(5) (x + 3) = (x + 3)6
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ASSOCIATIVE: changing the grouping in an addition problem will not affect the answer. This also works for multiplication. The following are examples…
Add: (-2 + 5) = ( ) ( ) = ( )
Multiply: (3 · 5) · 2 = 3 · (5 · 2)
IDENTITY: of Addition or Additive Identity…any number plus zero is itself (adding zero to a number doesn’t change the number (identity)) = -5; c = c
of Multiplication or Multiplicative Identity…any number multiplied by one is itself (multiplying by one doesn’t change the number (identity)). (8)(1) = 8; 1 · y = y
INVERSE: of Addition or Additive Inverse…a number added to its additive inverse (opposite) gives zero = 0; ½ + - ½ = 0
of Multiplication or Multiplicative Inverse…any number multiplied by its multiplicative inverse (reciprocal) gives one · ½ = 1; − 𝟑 𝟒 ∙− 𝟒 𝟑 =𝟏
DISTRIBUTIVE: the factor outside the parentheses is distributed (multiplied) to each of the terms inside the parentheses. a(b + c) = ab + ac; 4(2x + 7) = 8x + 28