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Sign Operations 07/27/12lntaylor ©

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Table of Contents Learning Objectives Signs and symbols mean different things Memorizing Opposite symbols Practice 07/27/12lntaylor ©

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LO1: LO2: Define and differentiate signs and symbols Eliminate 80% of your mistakes by focusing on signs and symbols 07/27/12lntaylor © TOC Learning Objectives

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Def1: Def2: Sign – there are only two signs + and - Symbols in math tell you what to do (operations) 07/27/12lntaylor © TOC Definitions

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PK1:Knowledge of mathematical symbols 07/27/12lntaylor © TOC Previous Knowledge

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07/27/12lntaylor © TOC SignsMeaning +Positive number to the right of 0 -Negative number to the left of 0 Note1: Note 2: There are only 2 signs They are seldom used properly It is true!!

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07/27/12lntaylor © TOC SymbolsOperations Meaning +Do not change the following sign(s) Also means go right -Change the following sign(s) Also means go left x,*,( )Multiply numbers next to symbol /, − Divide numbers next to symbol Root of the number under the symbol =Left side is exactly the same as the right side

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Signs and Symbols 07/27/12lntaylor © TOC

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Step1: Step2: Sign – there are only two signs + and - There are no signs in this problem There are only symbols telling you what to do 07/27/12lntaylor © TOC 3 + 1 = 4 These are symbols Step3:Where are the signs? Let me show you The signs are in red and the symbols in gold + 3 + + 1 = + 4 Step4:The first + is a symbol telling you not to change the second + Let me show you Do not change the positive number! Note:The + means start at 3 and go to the right 1 Hard to believe? Let me show you more. 3 + 1 = 4

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Step1: Step2: Sign – there are only two signs + and - There are no signs in this problem There are only symbols telling you what to do 07/27/12lntaylor © TOC 3 - 1 = 2 These are symbols Step3:Where are the signs? Let me show you The signs are in red and the symbols in gold + 3 - + 1 = + 2 Step4:The first - is a symbol telling you to change the second + Let me show you Change the positive number! Note: 3 - 1 = 2 The - means start at 3 and go to the left 1 Hard to believe? Let me show you more.

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Step1: Step2: Sign – there are only two signs + and - There is an extra sign in this problem And a symbol telling you what to do 07/27/12lntaylor © TOC 3 - - 1 = 4 This is a symbol Step3:Where are the signs? Let me show you The signs are in red and the symbols in gold + 3 - - 1 = + 4 Step4:The - is a symbol telling you to change the - Let me show you Change the negative number! Note:See/ there are no positive and negative signs…only symbolic operations 3 + 1 = 4 This is a sign

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Step1: Step2: Sign – there are only two signs + and - There are no signs in this problem There are only symbols telling you what to do 07/27/12lntaylor © TOC -3(4) + 2 = -10 These are symbols Step3:The first – says start at 0, go left 3 times (4 units each time or 12 units) The next symbol + says go to the right 2 from where you were The last symbol says you will end up 10 left of 0 - 12 + 2 = - 10 Note:Do you see that symbols tell you what to do and signs tell you where you are? -12 -10 0

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Step1: Step2: Sign – there are only two signs + and - There are no signs in this problem There are only symbols telling you what to do 07/27/12lntaylor © TOC -3(4x + 5) + 2 = -12x - 13 Step3:The first symbol – says start at 0, go left 3 times (4x + 5 each time) This is why - ( )means change the signs in the ( ) after you multiply The next symbol + says do not change the sign - 3( + 4x + 5) + 2 = - 12x - 13 Note:Do you see that symbols tell you what to do and signs tell you where you are? – 12x – 15 + 2 = – 12x – 13

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07/27/12lntaylor © TOC Note1: Note2: Now you know the difference between signs and symbols What you thought was a sign is really a symbol telling you go left or right -12 - 4 0 6 10 12 -12 + 18 – 10 + 14= 10 Start at 0 Go left 12 Go right 18 Go left 10 Go right 14 You will end up at 10 to the right of 0

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07/27/12lntaylor © TOC Memorizing opposite symbols

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07/27/12lntaylor © TOC SymbolWhat is its opposite? + - * / xexe > - > > > > > + / * xexe clear answers

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07/27/12lntaylor © TOC Practice

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07/27/12lntaylor © TOC Sign ProblemAnswer 3(4x – 5) = ? 9 - -12 = ? -4(-5 + 3x) = ? -3(3x – 3) – 2(3x + 6) = ? -4(-5 -6x) = ? -4(4x 2 + 5) = ? > 12x - 15 > > > > > 21 20 – 12x - 15x - 3 20 + 24x - 16x 2 - 20 clear answers

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