Just the facts Properties of real numbers A

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

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

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

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

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

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

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

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

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.