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Properties of Real Numbers Name Closure Property a + b is a unique real number ab is a unique real number Example Commutative a+b=b+a ab = ba 2+3=3+2 (-6)(7) = (7)(-6) Associative (a + b) + c = a + (b + c) (ab)c = a(bc) (-1 + 4) + 9 = -1 + (4 + 9) [(5)(8)]2 = 5[(8)(2)] Distributive a(b + c) = ab + ac 7(3 + 1) = (7)(3) + (7)(1) Identity a+0=0+a=a a(1) = 1(a) = a -3 + 0 = 0 + -3 = -3 24(1) = 1(24) = 24 Inverse a + (-a) = (-a) + a = 0 a (1/a) = (1/a)a = 1 6 + (-6) = (-6) + 6 = 0 5 (1/5) = (1/5)5 = 1 Substitution Replace an expression with an equivalent expression (4+5)(8) = (9)(8) Definition of Subtraction a – b = a + (-b) 8 – 2 = 8 + (-2) Definition of Division a ÷ b = a(1/b) when b 0 10 ÷ 5 = 10(1/5) To add two numbers with the same sign: • Add their absolute values • Use their common sign To add two numbers with different signs: • Subtract their absolute values • Use the sign of the number whose absolute value is larger To subtract two numbers: • Use the definition of subtraction to change to an addition problem (i.e., add the opposite of the second number) To multiply two numbers: (+) · (+) = (+) (+) · () = () () · () = (+) () · (+) = () To divide two numbers: (+) ÷ (+) = (+) (+) ÷ () = () () ÷ () = (+) () ÷ (+) = ()