Basic Identities

  • Closure Axiom of Addition
        Sum (or difference) of 2 real numbers equals a real number.
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  • Additive Identity
        a + 0 = a
        e.g. 5 + 0 = 5 and 0 + 5 = 5
  • Additive Inverse
        a + (-a) = 0
        e.g. 3 + (-3) = 0
  • Associative of Addition
        (a + b) + c = a + (b + c)
        e.g. (2 + 3) + 5 = 2 + (3 + 5)
  • Commutative of Addition
        a + b = b + a
        e.g. 3 + 4 = 4 + 3
  • Definition of Subtraction
        a - b = a + (-b)
        e.g. 4 - 6 = 4 + (-6)
  • Closure Axiom of Multiplication
        Product (or quotient if denominator is not equal to 0) of 2 real numbers equal to a real number.
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  • Multiplicative Identity
        a กม 1 = a
        e.g. 6 กม (1) = 6 and 1กม (6) = 6
  • Multiplicative Inverse
        a กม (1/a) = 1 (a is not equal to 0)
        e.g. 6 กม (1/6) = 1
  • Multiplication Times Zero
        a กม 0 = 0
        e.g. 7 กม 0 = 0
  • Associative of Multiplication
        (a กม b) กม c = a กม(b กม c)
        e.g. (2 กม 3) กม 6 = 2 กม (3 กม 6)
  • Commutative of Multiplication
        a กม b = b กม a
        e.g. 4 กม 6 = 6 กม 4
  • Distributive Law
        a (b + c) = ab + ac
        e.g. 2 (3 + x) = 2(3) + 2(x)
  • Definition of Division
        a/b = a(1/b)
        e.g. 3/5 = 3(1/5)


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