Just the facts: Properties of real numbers A GEMS/ALEX Submission Submitted by: Elizabeth Thompson, PhD Summer, 2008

Part 2: Properties of Real Numbers (A listing) Associative Properties Associative Properties Commutative Properties Commutative Properties Inverse Properties Inverse Properties Identity Properties Identity Properties Distributive Property Distributive Property All of these rules apply to Addition and Multiplication

Associative Properties Associative Properties Associate = group Rules: Associative Property of Addition (a+b)+c = a+(b+c) Associative Property of Multiplication (ab)c = a(bc) It doesn’t matter how you group (associate) addition or multiplication…the answer will be the same! Samples: Associative Property of Addition (1+2)+3 = 1+(2+3) Associative Property of Multiplication (2x3)4 = 2(3x4)

Commutative Properties Commutative Properties Commute = travel (move) Rules: Commutative Property of Addition a+b = b+a Commutative Property of Multiplication ab = ba It doesn’t matter how you swap addition or multiplication around…the answer will be the same! Samples: Commutative Property of Addition 1+2 = 2+1 Commutative Property of Multiplication (2x3) = (3x2)

Stop and think! Does the Associative Property hold true for Subtraction and Division? Does the Commutative Property hold true for Subtraction and Division? Is 5-2 = 2-5? Is 6/3 the same as 3/6? Is (5-2)-3 = 5-(2-3)? Is (6/3)-2 the same as 6/(3-2)? Properties of real numbers are only for Addition and Multiplication

Inverse Properties Think: Opposite Rules: Inverse Property of Addition a+(-a) = 0 Inverse Property of Multiplication a(1/a) = 1 Samples: Inverse Property of Addition 3+(-3)=0 Inverse Property of Multiplication 2(1/2)=1 What is the opposite (inverse) of addition? What is the opposite of multiplication? Subtraction (add the negative) Division (multiply by reciprocal)

Identity Properties Rules: Identity Property of Addition a+0 = a Identity Property of Multiplication a(1) = a Samples: Identity Property of Addition 3+0=3 Identity Property of Multiplication 2(1)=2 What can you add to a number & get the same number back? What can you multiply a number by and get the number back? 0 (zero) 1 (one)

Distributive Property Rule: a(b+c) = ab+bc Samples: 4(3+2)=4(3)+4(2)=12+8=20 2(x+3) = 2x + 6 -(3+x) = -3 - x If something is sitting just outside a set of parenthesis, you can distribute it through the parenthesis with multiplication and remove the parenthesis.

Take time to practice

Homework Log on to class wiki / discussion thread Follow the directions given: Give an example of each of the properties discussed in class, do not duplicate a previous entry.