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Algebra II Chapter 2 2012

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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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P Parenthesis E Exponents MD Multiplication and Division AS Addition and Subtraction In order from left to right

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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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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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P Parenthesis E Exponents M Multiplication D Division A Addition S Subtraction

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Can you fill in the missing operations? 1. 2 - (3+5) + 4 = -2 2. 4 + 7 * 3 ÷ 3 = 11 3. 5 * 3 + 5 ÷ 2 = 10

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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

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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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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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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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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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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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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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ALGEBRAIC PROPERTIES. Commutative Property An operation is commutative if a change in the order of the numbers does not change the results. This means.

ALGEBRAIC PROPERTIES. Commutative Property An operation is commutative if a change in the order of the numbers does not change the results. This means.

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