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

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Important things toremember Important things to remember Parenthesis – anything grouped… including information above or below a fraction bar. Exponents – anything in the same family as a power… this includes radicals (square roots). Multiplication- this includes distributive property (discussed in detail later). Some items are grouped!!! Multiplication and Division are GROUPED from left to right (like reading a book- do whichever comes first. Addition and Subtraction are also grouped from left to right, do whichever comes first in the problem.

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So really it looks like this….. PParenthesis EExponents MDMultiplication and Division ASAddition and Subtraction In order from left to right

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SAMPLE PROBLEM #1 Parenthesis Exponents This one is tricky! Remember: Multiplication/Division are grouped from left to right…what comes 1 st ? Division did…now do the multiplication (indicated by parenthesis) More division Subtraction

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SAMPLE PROBLEM Subtraction Exponents Remember the division symbol here is grouping everything on top, so work everything up there first….multiplication Parenthesis Division – because all the work is done above and below the line

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Order of Operations-BASICS Think: PEMDAS Order of Operations-BASICS Think: PEMDAS Please Excuse My Dear Aunt Sally PParenthesis EExponents MMultiplication DDivision AAddition SSubtraction

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Take time to practice

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Assignment #1 Assignment #1 (When all assigned problems are finished – do for Homework as needed) Remember PEMDAS and Please Excuse My Dear Aunt Sally? Make up your own acronym for PEMDAS and post it on the class wiki. Write it on White Paper and Illustrate your acronym. Make sure it is school appropriate.

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Lesson Extension Can you fill in the missing operations? (3+5) + 4 = * 3 ÷ 3 = * ÷ 2 = 10

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Assignment #2 Create a Puzzle Greeting Fold a piece of paper (white or colored) like a greeting card. On the cover: Write an equation with missing operations (like the practice slide) In the middle: Write the equation with the correct operations On the back: Put your name as you would find a companies name on the back of a greeting card.

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

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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 doesnt 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)

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Commutative Properties Commutative Properties Commute = travel (move) Rules: Commutative Property of Addition a+b = b+a Commutative Property of Multiplication ab = ba It doesnt 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)

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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

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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)

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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)

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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.

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Take time to practice

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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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