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Just the facts: Order of Operations and Properties of real numbers

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## Just the facts: Order of Operations and Properties of real numbers

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**Just the facts: Order of Operations and Properties of real**numbers Algebra II Chapter 2 2012**Important things toremember**• 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.**So really it looks like this…..**• Parenthesis • Exponents • Multiplication and Division • Addition and Subtraction In order from left to right In order from left to right**SAMPLE PROBLEM #1**Parenthesis Exponents This one is tricky! Remember: Multiplication/Division are grouped from left to right…what comes 1st? Division did…now do the multiplication (indicated by parenthesis) More division Subtraction**SAMPLE PROBLEM**Exponents Parenthesis Remember the division symbol here is grouping everything on top, so work everything up there first….multiplication Division – because all the work is done above and below the line Subtraction**Order of Operations-BASICSThink: PEMDAS Please Excuse My**Dear Aunt Sally • Parenthesis • Exponents • Multiplication • Division • Addition • Subtraction**Lesson Extension**• Can you fill in the missing operations? • 2 - (3+5) + 4 = -2 • 4 + 7 * 3 ÷ 3 = 11 • 5 * 3 + 5 ÷ 2 = 10**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 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)**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)**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**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**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**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) = 2x + 6 • -(3+x) = -3 - x