Topic: Real Number Systems MI: Properties Do Now:Handout

What are properties???? 1. Properties describe how numbers behave during mathematical operations.

Commutative Property: Commutative Property - interchange or switch the elements. Addition Multiplication x+ y = y+ x     (x) (y)= ( y) (x)                               6 + 3 = 3 + 6 3 x 6 = 6 x 3 Think of the elements as "commuting" from one location to another.  "They get in their cars and drive to their new locations."  This explanation will help you to remember that the elements are "moving" (physically changing places). 

Associative Property Associative Property- regroup the elements. Addition    Multiplication                                                             (X + Y) + Z = X + (Y + Z) (X . Y). (Z) = X. ( Y. Z) The associative property can be thought of as illustrating "friendships"  (associations).  The parentheses show the grouping of two friends.  Always have parenthesis on both sides.

Distributive Property: Distributive Property- multiply across the parentheses.  Each element inside the parentheses is multiplied by the element outside the parentheses.                      a (b + c) = a •b + a •c 2(3+ 4) = 2x3 + 2x4 Hint: Includes addition and multiplication in same example. Can also work for subtraction: a(b – c) = ab-ac

Identity Property of Addition: Identity Property- Think identical Additive Identity is zero!!!!!                           a + 0 = a “ 0” is the identity element for addition 6 + 0 = 6

Identity Property of Multiplication: Multiplicative identity (identical) a x ? = a “ ” is the identity element for multiplication. 6 x ? = 6

Inverse Property of Addition: Inverse Property- What brings you back to the identity element using addition?                     X +  -X = 0  Additive Inverse 6 + -6 = 0 Inverse of addition uses negatives!!!!!

Inverse Property of Multiplication Inverse Property- What brings you back to the identity element using multiplication? x . 1/x = 1 6 . 1/6 = 6 Inverse of multiplication uses reciprocals (flips)

Multiplicative Property of Zero Any number times “0” is zero!!!!!