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1.3 Properties of Numbers 8/24/16 Common Core State Standards • Interpret complicated expressions by viewing one or more of their parts as a single entity. • Use the structure of an expression to identify ways to rewrite it. New Terms • Equivalent expressions • Additive identity • Multiplicative identity • Multiplicative inverse • Reflexive property • Symmetric property • Transitive property • Substitution property Equivalent expressions • The expression 4k + 8k and 12k are called equivalent expressions because they represent the same number. • IE 2 x + 5x and 7x Additive identity • The sum of any number and 0 is equal to the number. Thus, 0 is called the additive identity. • IE 4 + 0 = 4 • 99 + 0 = 99 Multiplicative identity • The solution of the equation is 1. Since the product of any any number and 1 is equal to the number 1. • IE 8 • n = 8 , 4 • x = 4 Multiplicative inverse • Two numbers whose product is 1. Zero has no reciprocal because any number times 0 is 0. • IE • 1 • 2 = 1 2 1 1 Reflexive property • Any quantity is equal to itself. • IE 5 = 5 4 + 7 = 4 + 7 11 = 11 Symmetric property • If one quantity equals a second quantity, then the second quantity equals the first. • IE If 8 = 2 + 6 then 2 + 6 = 8 Transitive property • If one quantity equals a second quantity and the second quantity equals a third quantity the the first quantity equals the third quantity. • IE If 6 + 9 = 3 + 12 and 3 + 12 = 15 then • 6 + 9 = 15 Substitution property • A quantity may be substituted for its equal in any expression. • IE If n = 11 then 4n = 4 • 11 4(11) = 4 • 11 44 = 44 Commutative and Associative Property • Commutative Property of Addition The order in which you add or multiply does not change their sum or product. • a + b = b + a •2 + 3 = 3 + 2 • Commutative Property of Multiplication • a• b = b• a •4• 6 = 6• 4 Associative Property of Addition and Multiplication • When you group 3 or more numbers when adding or multiplying, does not change their sum or product. ( a + b) + c = a + (b + c) (a • b) • c = a • (b • c) Evaluate the expression then name a property in the process. • 7( 16 ÷ 42 ) • 7(16 ÷ 16) Substitution • 7(1)Multiplicative Identity •= 7 • 2[5 – ( 15 ÷ 3)] • 2(5 – 5) Substitution • 2(0) Mult. Prop. of Zero •= 0 Evaluate each expression and name a property in any step • 16 + 8 + 14 + 12 • Ticket Out the Door 2•4•5•3