Texas Instruments TI-73 EXPLORER, TI-73

Chapter 2: Math Operations 37

7302ENG.DOC CH2 Math Operations, English Julie Hewlett Revised: 07/29/98 11:58 AM Printed: 05/19/99 8:58

AM Page 37 of 32

gcd(valueA,valueB)

Find the greatest common divisor for the fraction, 27/36.

1. Find the GCD of 27/36.

27¡36Eb

2. Simplify the fraction

completely using the GCD

(without using the

calculator).

3. Verify your answer by

simplifying 27/36 by 9 on the

calculator. You must be in

Mansimp mode setting.

.####"

b-l

27=36"B9

3 3

Calculates the cube of n, which is equivalent to n Q n Q n of

any real number, expression, or each element in a list.

Calculate 53.

513

36 P 9

9 = 3

GCD=9

53 = 5 Q 5 Q 5 = 125

Contents

Main ti T TTTI 333E 7773 ---7 Important Information US FCC Information Concerning Radio Frequency Interference Table of ContentsTable of Contents iv Page vi Operating the Operating the TITIN 7373 2 Preparing to Use Your TIN 7373 TITIN Turning the Turning the 4 Adjusting the Display ContrastAdjusting the Display Contrast Resetting Memory and All DefaultsResetting Memory and All Defaults The Home Screen 6 Entering Numbers and Other Characters Entering a Negative Number Entering a Negative Number a Entering a Number in Scientific Notation Entering a Number in Scientific Notation - { Entering Text Entering Text - Entering Secondary Functions Entering Secondary Functions - t 8 Test and Logic (Boolean) Operators 10 Entry Line Common Display CursorsCommon Display Cursors Editing Numbers and CharactersEditing Numbers and Characters 12 Functions and Instructions Accessing Functions and Instructions from MenusAccessing Functions and Instructions from Menus Displaying a Menu Accessing and Selecting Menu Items Exiting a Menu without Making a Selection 14 Instructions from theInstructions from the Accessing FunctionsAccessing Functions CATALOGCATALOG Entering Expressions 16 Grouping Parts of Expressions with ParenthesesGrouping Parts of Expressions with Parentheses Using Implied Multiplication in ExpressionsUsing Implied Multiplication in Expressions Entering Multiple Expressions on One LineEntering Multiple Expressions on One Line Retrieving Previous Entries - 18 Recalling and Storing the Last Answer - Continuing a Calculation with AnsContinuing a Calculation with Ans Using Ans as a Variable in an ExpressionUsing Ans as a Variable in an Expression 20 Storing Values to a Variable Storing Values to a Variable X Recalling Variable Values Recalling Variable Values - P 22 Mode Settings Numeric Notation ModeNumeric Notation Mode 24 Decimal Notation ModeDecimal Notation Mode Angle ModeAngle Mode Display Format ModeDisplay Format Mode Simplification ModeSimplification Mode Math OperationsMath Operations Page Keyboard Math Operations , , M , , T Basic Operations Basic Operations \ , , F 28 Integer Division Integer Division - - p Percent Percent C 30 Inverse Function Inverse Function - Square Square 6 Power Power 7 Square Root Square Root - z 32 Test Operations Test Operations - t Relational Operators Logic (Boolean) Operators 34 MATH Menu lcm( lcm( 1 1 1 36 gcd( gcd( 1 2 2 Page 38 ( ( 1 Solver Solver 1 1 4 4 The EQUATION SOLVER Screen The Equation Variables Screen 40 Equation Equation Variables bound Solve Solving Equations with Only One Possible Answer 42 Solving Equations with More Than One Answer Page 44 NUM Menu " abs( abs( 1 1 1 round( round( 1 " 2 2 46 " iPart( and fPart( iPart( and fPart( 1 3 and 4 3 and 4 min( and max( min( and max( 1 " 5 and 6 5 and 6 48 " remainder( remainder( 1 7 7 1 610 8 4 PRB Menu " rand rand 1 1 1 50 " randInt( randInt( 1 2 2 nPr nPr 1 " nCr nCr 1 " 3 3 52 " ! ! 1 5 5 coin( coin( 1 " dice( dice( 1 " 6 6 LOG Menu " log( log( 1 1 1 10^( 10^( 1 " ln( ln( 1 " 2 2 56 " e^( e^( 1 4 4 FractionsFractions 58 Entering Fractions Simple Fractions Mixed Numbers 12 Using Fractions in Calculations 60 Fraction Modes Display Format Mode SettingsDisplay Format Mode Settings Simplification Mode SettingsSimplification Mode Settings Autosimp SettingAutosimp Setting 62 Mansimp SettingMansimp Setting Letting the Calculator Choose the Simplification Factor Choosing the Simplification Factor } Recalling the Factor - 6:Factor 64 Converting Between Fractions and Decimals Converting Between Mixed Numbers and Simple Fractions Page Page 68 Area Area - Length Length - Page 70 Converting a Unit of MeasureConverting a Unit of Measure Constants 72 Single ModeSingle Mode Defining Constants in Single Mode Single Mode Constant Calculations Recalling a Constant in a Series of Calculations 74 Multiple ModeMultiple Mode Defining Constants in Multiple Mode Recalling Constants in Multiple Mode 76 ListsLists 78 Steps for Creating a List The List Editor 3 Naming a List 80 Entering List Elements Numerical Lists 82 Entering Fractional Elements Dependent Numerical Lists 84 Categorical Lists 86 Editing Lists in the List Editor Inserting or Deleting a New ListInserting or Deleting a New List 88 Deleting Lists from Calculator MemoryDeleting Lists from Calculator Memory Inserting or Deleting One Element in a ListInserting or Deleting One Element in a List Editing an Existing ElementEditing an Existing Element 90 Clearing All Elements in a ListClearing All Elements in a List Clearing All Elements in All ListsClearing All Elements in All Lists Editing a List FormulaEditing a List Formula Deleting a List Formula v Ls Menu 92 v OPS Menu SortA( and SortD( SortA( and SortD( - " v 1 and 2 1 and 2 Sorting One List 94 Sorting Multiple Lists ClrList ClrList - " v dim( dim( - v 96 @ " v List( List( - 5 5 98 " v Select( Select( - 6 6 seq( seq( - " v 7 7 100 " v augment( augment( - 8 8 List Commands from the Home Screen Creating a ListCreating a List Copying One List to AnotherCopying One List to Another Displaying One List ElementDisplaying One List Element 104 Inserting or Changing a List ElementInserting or Changing a List Element Using Math Functions with ListsUsing Math Functions with Lists 106 Statistical PlotsStatistical Plots 108 Steps for Defining a Stat Plot Defining Statistical Data in Lists Y Deselecting Functions Defining a Stat Plot 110 The Stat Plot Menu Screen e PlotsOff and PlotsOn - 4 and 5 Selecting Stat Plot Types 112 Defining Stat Plot Options Page 114 Adjusting Window Values and Format Scatter Plot Scatter Plot Displaying the Stat Plot Stat Plot Examples and xyLine Plot and xyLine Plot Page 116 Pictograph Pictograph 118 Bar Graph Bar Graph Page 120 Pie Chart Pie Chart Histogram Histogram 122 Box Plot Box Plot 124 Modified Box Plot Modified Box Plot Page Page StatisticalStatistical AnalysesAnalyses 128 v " v min( and max( min( and max( - MATH Menu Page 130 mean(, median(, and mode(mean(, median(, and mode( " v 3, 4, and 5 3, 4, and 5 stdDev( stdDev( - " v 6 6 132 " v sum( sum( - 7 7 v CALC Menu CALC CALC v Using Frequency Lists with Using Frequency Lists with - 134 ! v 1-Var Stats and 2-Var Stats 1-Var Stats and 2-Var Stats - 1 and 2 1 and 2 Page 136 What Do the Results Mean? n (number of data points) freq (Frequency Lists) , Q Q , and Med 138 ! v Manual-Fit Manual-Fit - 3 3 Page 140 ! v Med-Med Med-Med - 4 4 Page 142 ! v LinReg(ax+b) LinReg(ax+b) - 5 5 Page 144 ! v QuadReg QuadReg - 6 6 Page 146 ! v ExpReg ExpReg - 7 7 Page Page TablesTables 150 What Is a Table? Steps for Creating a Table 152 Defining and Selecting Functions in the Y= Editor & Setting Up the Table - f 154 Displaying the Table - i Indpnt=Auto and Depend=AutoIndpnt=Auto and Depend=Auto 156 Indpnt=Auto and Depend=AskIndpnt=Auto and Depend=Ask Indpnt=AskIndpnt=Ask 158 Editing X Values from the Table Screen 160 YY Editing Editing from the Table Screen from the Table Screen Table Setup from the Home Screen Page Function GraphingFunction Graphing 164 Steps for Graphing a Function Example of Function Graphing 166 Defining Functions in the Y= Editor & Entering FunctionsEntering Functions 168 Editing FunctionsEditing Functions Selecting FunctionsSelecting Functions Exiting the Y= EditorExiting the Y= Editor Selecting a Graph Style 170 Setting the Window Format - g 172 Defining Window Values Y X cos (X) 174 The Window Values Screen The Window Values Screen ' Determining Window Values for a Specific GraphDetermining Window Values for a Specific Graph 176 Displaying a Graph * 178 Smart GraphSmart Graph Exploring the Graph with the Free-Moving CursorExploring the Graph with the Free-Moving Cursor Exploring a Function Graph with Exploring a Function Graph with ) Using QuickZoom Controlling the Increments of a TraceControlling the Increments of a Trace 180 Adjusting Window Values with the ( ZOOM Menu 182 ZBox ZBox ( 1 1 Zoom In and Zoom Out Zoom In and Zoom Out ( 2 and 3 2 and 3 184 ZStandard ZStandard ( ZInteger ZInteger ( 6 6 0 0 The ( " ZPrevious ZPrevious ( MEMORY Menu 1 1 186 " SetFactors SetFactors ( 2 2 DrawingDrawing 188 DRAW Menu ClrDraw ClrDraw 2 1 1 Line( Line( 2 2 2 Line( from the Graph Screen 190 Line( from the Home Screen or Program Editor Horizontal and Vertical Horizontal and Vertical 2 3 and 4 3 and 4 192 Horizontal and Vertical from the Graph Screen Horizontal and Vertical from the Home Screen or Program Editor Shade( Shade( 2 5 5 194 Circle( Circle( 2 6 6 Circle( from the Graph Screen 196 Circle( from the Home Screen or Program Editor Text( Text( 2 7 7 Text( from the Graph Screen 198 Text( from the Home Screen or the Program Editor Pen Pen 2 8 8 200 POINTS Menu 202 Pt-On(, Pt-Off(, and Pt-Change(Pt-On(, Pt-Off(, and Pt-Change( " 1, 2, and 3 1, 2, and 3 Pt-On(, Pt-Off( and Pt-Change( from the Graph Screen Page 204 Pt-On(, Pt-Off(, and Pt-Change( from the Home Screen and Program Editor Pxl-On(, Pxl-Off(, and Pxl-Change(Pxl-On(, Pxl-Off(, and Pxl-Change( " 4, 5, and 6 4, 5, and 6 206 " STO Menu StorePic StorePic 2 " 1 1 208 " RecallPic RecallPic 2 2 2 Deleting a Graph PictureDeleting a Graph Picture TrigonometryTrigonometry 210 u u Trig Functions Trig Functions - TRIG Menu 1, 3, and 5 1, 3, and 5 Inverse Trig Functions Inverse Trig Functions - u 2, 4, and 6 2, 4, and 6 Angle Mode SettingsAngle Mode Settings 212 Page 214 Graphing Trig Functions u ANGLE Menu 216 r " u and and Converting between Degrees and RadiansConverting between Degrees and Radians 218 Entering Angles in DMS NotationEntering Angles in DMS Notation 3010'23" " u Page 220 8 " u DMS DMS - ProgrammingProgramming 222 What Is a Program? Steps for Creating a Program 224 Creating and Naming a New Program " Create New Create New 8 1 1 The Program EditorThe Program Editor 226 Entering Program Commands Entering Functions, Instructions, and Variables Exiting the Program Editor The 8 CTL Menu 228 If If 8 1 1 If-Then If-Then 8 1 and 2 1 and 2 230 If-Then-Else If-Then-Else 8 1, 2, and 3 1, 2, and 3 For( For( 8 4 4 232 While While 8 Repeat Repeat 8 5 5 6 6 End End 8 7 7 Pause Pause 8 8 8 234 Lbl and Goto Lbl and Goto 8 9 and 0 9 and 0 IS>( IS>( 8 A A DS<( DS<( 8 B B 236 Menu( Menu( 8 C C SetMenu( SetMenu( 8 D D 238 prgm prgm 8 E E Return Return 8 F F Stop Stop 8 G G 240 DelVar DelVar 8 GraphStyle( GraphStyle( 8 H H I I The 8 I/O Menu 242 Input 8 " 1 Storing to a Variable Displaying the Current Graph 244 " Disp Disp 8 Prompt Prompt 8 2 2 DispGraph DispGraph 8 " Output( Output( 8 " DispTable DispTable 8 246 " Key Code Diagram 73 TIN ClrScreen and ClrTable 8 " 8 and 9 GetCalc( 8 " 0 Get( and Send( 8 " A and B 248 Editing Program Commands Inserting, Deleting, and Editing Command LinesInserting, Deleting, and Editing Command Lines Copying and Renaming a ProgramCopying and Renaming a Program 250 Calling a Program from Another ProgramCalling a Program from Another Program Notes about Calling Programs Executing a Program 252 Breaking Out of a ProgramBreaking Out of a Program Debugging a Program Communication Link the CBL/CBR and Application 254 TI-73 Link Capabilities Linking to Another Calculator Linking to the CBL 2/CBL System or CBR The Link SEND Menu 9 Linking to a PC or Macintosh 1 256 The Link RECEIVE Menu 9 1 " 258 Transmitting Data Items Repeating a Transmission to an Additional TI-73 DuplicateName Menu 260 Transmission Error Conditions Backing Up Memory 262 Upgrading your Graph Explorer TI-73 Software Graph Explorer Software Upgrades The APPLICATIONS Menu 9 264 Steps for Running the CBL CBR Application Selecting the CBL/CBR Application Specifying the Data Collection Method 266 Specifiying Data Collection Options GAUGE TYPE 268 MIN and MAX UNITS DIRECTNS (Directions) Data Collection Comments and Results DATA LOGGER 270 #SAMPLES INTRVL (SEC) UNITS PLOT Ymin and Ymax DIRECTNS (Directions) 272 Data Collection Results RANGER Collecting the Data 274 Stopping Data Collection MemoryMemory ManagementManagement 276 About About - MEMORY Menu 1 1 Check RAM Check RAM - Check APPs Check APPs - 2 2 3 3 278 Delete Delete - 4 4 List - Clear Home Clear Home - Apps and AppVars - 280 Reset Reset - ClrAllLists ClrAllLists - 6 6 Resetting All Memory - 7 1 282 Resetting Defaults - 7 2 Function and AA Instruction Reference 284 L Appendix A: Function and Instruction Reference 285 286 Appendix A: Function and Instruction Reference 287 288 Appendix A: Function and Instruction Reference 289 290 Appendix A: Function and Instruction Reference 291 292 Appendix A: Function and Instruction Reference 293 L 23.45) b L L 294 Appendix A: Function and Instruction Reference 295 296 Appendix A: Function and Instruction Reference 297 L 5) b L L 5.2, L 5.3) b L 298 Appendix A: Function and Instruction Reference 299 300 Appendix A: Function and Instruction Reference 301 L 302 Appendix A: Function and Instruction Reference 303 304 Appendix A: Function and Instruction Reference 305 306 Appendix A: Function and Instruction Reference 307 308 Appendix A: Function and Instruction Reference 309 310 Appendix A: Function and Instruction Reference 311 312 Appendix A: Function and Instruction Reference 313 314 Appendix A: Function and Instruction Reference 315 316 Appendix A: Function and Instruction Reference 317 318 B 320 The 73 TIN Menu Map Appendix B: Reference Information 321 - f- f (in Program editor) ( - g. 322 1 2 - u - v Appendix B: Reference Information 323 8 8 (in Program editor) 324 - | 9 Appendix B: Reference Information 325 - } - } 1:Window - } - } 326 - } 4:Picture - } 5:Table Appendix B: Reference Information 327 - - (in Program editor) Set Constant: Single Multiple - - 2:Check RAM - 328 - 4:Delete - 7:Reset The VARS Menu - } 330 Equation Operating System (EOS ) Appendix B: Reference Information 331 In Case of Difficulty If Suggested Action 332 Correcting an Error Error Messages Appendix B: Reference Information 333 334 Appendix B: Reference Information 335 336 Appendix B: Reference Information 337 338 C CCC 340 Battery Information When to Replace Batteries Effects of Replacing the Batteries Replacing the Batteries Battery Precautions Page Appendix C: Service and Warranty Information 343 Customers in the U.S. and Canada Only One-Year Limited Warranty for Commercial Electronic Product 344 One-Year Limited Warranty for Commercial Electronic Australia & New Zealand Customers only IndexIndex A A B 346 C C D Index 347 D E 348 E F F G Index 349 G H I I 350 L M Index 351 M N O P 352 P Q R Index 353 R S S 354 S T T U Index 355 U V W X 356