1. 1.3 Properties of Numbers 8/24/16

2. 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.

3. New Terms Equivalent expressions Additive identity Multiplicative identity Multiplicative inverse Reflexive property Symmetric property Transitive property Substitution property

4. Equivalent expressions The expression 4k + 8k and 12k are called equivalent expressions because they represent the same number. IE 2 x + 5x and 7x

5. 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

6. 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

7. 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

8. Reflexive property Any quantity is equal to itself. IE 5 = 5 4 + 7 = 4 + 7 11 = 11

9. 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

10. 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

11. 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

12. 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

13. 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)

14. Evaluate the expression then name a property in the process. 7( 16 ÷ 4 2 ) 7(16 ÷ 16) Substitution 7(1)Multiplicative Identity = 7 2[5 – ( 15 ÷ 3)] 2(5 – 5) Substitution 2(0) Mult. Prop. of Zero = 0

15. Evaluate each expression and name a property in any step 16 + 8 + 14 + 12 Ticket Out the Door 2 4 5 3