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Just the facts: Properties of real numbers

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 Commutative Properties Inverse Properties Identity Properties Distributive Property.

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Just the facts: Properties of real numbers

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

  2. 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

  3. Associative PropertiesAssociate = 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)

  4. Commutative PropertiesCommute = 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)

  5. 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)-3 = 5-(2-3)? Is (6/3)-2 the same as 6/(3-2)? Is 5-2 = 2-5? Is 6/3 the same as 3/6? Properties of real numbers are only for Addition and Multiplication

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

  7. Identity Properties Rules: Identity Property of Addition a+0 = a Identity Property of Multiplication a(1) = a 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) Samples: Identity Property of Addition 3+0=3 Identity Property of Multiplication 2(1)=2

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

  9. Take time to practice

  10. 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.

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