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Graphing Calculator by Mathlab: User Manual
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  • Home
    • Introduction
    • PRO Features vs. FREE Version
    • Frequently Asked Questions, FAQs >
      • 1. How to Change the Number Format?
      • 2. How to Set Up the Separators Between Thousands?
      • 3. How to Set Precision?
      • 4. How to Send Feedback with Comments?
      • 5. How to import/export the library?
      • 6. How to Print Results?
      • 7. How to Make the Calculator Show the Results?
      • 8. How to Transport Calculation Results to other Programs?
      • 9. How to Transport Table to Other Platforms?
      • 10. How to Turn Off (or on) Vibration?
      • 11. How to Change the Language?
  • 1. Basics
    • 1.1. Navigation
    • 1.2. UI Elements
    • 1.3. Keyboard
    • 1.4. Input, Enter, Delete, Clear and UNDO Buttons
    • 1.5. Workspace Area
    • 1.6. Editing the Expression/Equation
    • 1.7. Using the Last Answer
    • 1.8. Writing Comments
    • 1.9. Clear, Copy & Paste Commands
    • 1.10. Rearranging Rows
  • 2. Settings
    • 2.1. General
    • 2.2. Calculator
    • 2.3. Graph
  • 3. Library
    • 3.1. Constants
    • 3.2. Functions
    • 3.3. How to Save Calculation Result/Graph to Library?
  • 4. Graph Mode
    • 4.1. 2D Graphing
    • 4.2. 3D Graphing
    • 4.3. Enlarging the Graph Area
    • 4.4. Changing to White Background
    • 4.5. Hide Keyboard
    • 4.6. Degree and Radian Scales
    • 4.7. Fixed Scale
    • 4.8. R-axis Scale
    • 4.9. Logarithmic Scale
    • 4.10. Tracing Values and Slopes
    • 4.11. Special Points: Roots and Criticals
    • 4.12. Intersections of Graphs
    • 4.13. Set Domain
    • 4.14. Show All - Roots, Critical Points and Intersections
    • 4.15. Fullscreen
  • 5. Table Mode
    • 5.1. Sharing of Functions
    • 5.2. 2D Table
    • 5.3. 3D Table
    • 5.4. Edit Functions
    • 5.5. Scroll Results
    • 5.6. Results Precision
    • 5.7. Zoom Controls
    • 5.8. Save and Load Table
    • 5.9. Table of Trigonometric Functions
  • 6. Numbers and Number Sense
    • 6.1. Decimals
    • 6.2. Fractions >
      • 6.2.1. Mixed Fractions
      • 6.2.2. Complex Fractions
      • 6.2.3. Converting Decimals to Fractions
      • 6.2.4. Converting Fractions to Decimals
    • 6.3. Percents
    • 6.4. Scientific Notation
    • 6.5. Engineering Notation
    • 6.6. Rounding Numbers
    • 6.7. Integer and Fractional Parts >
      • 6.7.1. Integer Part of a Number >
        • 6.7.1.1. Ceiling
        • 6.7.1.2. Floor
        • 6.7.1.3. Half Down
        • 6.7.1.4. Half to Even
        • 6.7.1.5. Half to Infinity
        • 6.7.1.6. Half to Odd
        • 6.7.1.7. Half to Zero
        • 6.7.1.8. Half Up
        • 6.7.1.9. Truncate
      • 6.7.2. Greatest Integer is the Floor Function
      • 6.7.3. Least Integer is the Ceiling Function
      • 6.7.4. Fractional Part of a Number
    • 6.8. Order of Operations
    • 6.9. Least Common Multiple
    • 6.10. Greatest Common Divisor
    • 6.11. Modulo
    • 6.12. Binary, Octal, Decimal, Hexadecimal Numbers
    • 6.13. Complex Numbers
    • 6.14. The Polar Form of Complex Numbers
    • 6.15. Polar to Rectangular Coordinates
  • 7. Introductory Algebra
    • 7.1. Arithmetic Operations
    • 7.2. Exponents
    • 7.3. Absolute Values
    • 7.4. Variables
    • 7.5. Evaluating Expressions
    • 7.6. Polynomials
    • 7.7. Roots
    • 7.8. Logarithms
  • 8. Equations in One Variable
    • 8.1. Linear Equation
    • 8.2. Absolute Value Equation
    • 8.3. Quadratic Equation
    • 8.4. Cubic Equation
    • 8.5. Polynomial Equation
    • 8.6. Rational Equation
    • 8.7. Radical Equation
    • 8.8. Exponential Equation
    • 8.9. Logarithmic Equation
  • 9. Inequalities in One Variable
    • 9.1. Inequality Symbols
    • 9.2. Linear Inequalities
    • 9.3. Absolute Value Inequalities
    • 9.4. Quadratic Inequality
    • 9.5. Polynomial Inequalities
    • 9.6. Rational Inequalities
    • 9.7. Compound Inequalities
    • 9.8. Inequalities with Constants
  • 10. Equations and Inequalities in Two Variables
    • 10.1. Linear Equations
    • 10.2. Systems of Linear Equations
    • 10.3. Graphing Inequalities
    • 10.4. Multiple Graphing of Inequalities
    • 10.5. Graphing Systems of Inequalities
    • 10.6. Solving Implicit Equations
  • 11. Algebraic Functions and Graphs
    • 11.1. Plotting Points
    • 11.2. How to Graph Functions?
    • 11.3. Setting the Applied Domain
    • 11.4. Linear Function
    • 11.5. Absolute Value Function
    • 11.6. Quadratic Function
    • 11.7. Polynomial Functions
    • 11.8. Rational Functions
    • 11.9. Radical Functions
    • 11.10. Logarithmic Functions
    • 11.11. Exponential Functions
    • 11.12. Sign Function
    • 11.13. Multiple Graphing
    • 11.14. Piecewise Functions
  • 12. Matrices and Vectors
    • 12.1. Matrix Operations
    • 12.2. Editing Matrix Entries
    • 12.3. Matrix Variables
    • 12.4. Matrix and Vector Forms
    • 12.5. Variable Matrix to System of Linear Equations
    • 12.6. Solving Systems of Linear Equations Using Matrix Equations
  • 13. Trigonometric Functions and Their Inverses
    • 13.1. Degrees and Radians >
      • 13.1.1. Degrees, Minutes and Seconds
      • 13.1.2. Bradis Table
    • 13.2. Trigonometric Function Keys
    • 13.3. Trigonometric Values of Special Angles >
      • 13.3.1. The 45- 45 - 90 Triangle
      • 13.3.2. The 30-60-90 Triangle
      • 13.3.3. Quadrantal Angles
      • 13.3.4. Coterminal Angles
    • 13.4. Trigonometric Values of 15 Degrees and Its Multiples
    • 13.5. Hyperbolic Function Keys
    • 13.6. Graphing Trigonometric Functions
    • 13.7. Graphing Hyperbolic Functions
    • 13.8. Graphing Inverse Functions
  • 14. Analytic Geometry
    • 14.1. Conic Sections
    • 14.2. Parametric Equations
    • 14.3. Polar Graphs >
      • 14.3.1. Limacon
      • 14.3.2. Cardioid
      • 14.3.3. Lemniscate
      • 14.3.4. Rose
      • 14.3.5. Other Polar Graphs
    • 14.4. 3D Graphing
  • 15. Limits
    • 15.1. Right - hand Limit
    • 15.2. Left - hand Limit
    • 15.3. Limit of a Function
    • 15.4. Limit of a Polynomial Function
    • 15.5. Limit of a Rational Function
    • 15.6. Limit of a Radical Function
    • 15.7. Limit of an Absolute Value Function
    • 15.8. Limit of a Trigonometric Function
    • 15.9. Limit of an Exponential and Logarithmic Function
    • 15.10. Limit of a Piece-wise Function
    • 15.11. Limits at Infinity
    • 15.12. Indeterminate Forms
    • 15.13. Limit of a Hyperbolic Function
  • 16. Derivatives
    • 16.1. First Derivative Key
    • 16.2. Second Derivative Key
    • 16.3. Third and Higher Derivative Keys
    • 16.4. Rules of Differentiation
    • 16.5. Derivatives of Polynomial Functions
    • 16.6. Derivatives of Rational Functions
    • 16.7. Dervatives of Trigonometric, Logarithmic and and Exponential Functions
    • 16.8. More on Derivatives
  • 17. Partial Derivatives
    • 17.1. Increments
    • 17.2. Dervative of a Function df (or dy))
    • 17.3. Derivative of a Function df (f not in terms of x)
    • 17.4. Partial Derivatives
    • 17.5. Higher Order Partial Derivatives
    • 17.6. Total Derivates
  • 18. Definite Integral
    • 18.1. Definite Integral of Algebraic Functions
    • 18.2. Definite Integral of Trigonometric Functions
  • 19. Basic Statistics
    • 19.1. Summation Notation
    • 19.2. Product Notation
    • 19.3. Minimum and Maximum
    • 19.4. Factorial, nCr and nPr
    • 19.5. Measures of Central Tendency >
      • 19.5.1. Mean from Ungrouped Data Set
      • 19.5.2. Mean from Frequency Distribution Table
      • 19.5.3. Median from Ungrouped Data Set
      • 19.5.4. Mode
    • 19.6. Measures of Variability >
      • 19.6.1. Range
      • 19.6.2. Interquartile Range and Quartile Deviation
      • 19.6.3. Mean Absolute Deviation
      • 19.6.4. Variance and Standard Deviation
      • 19.6.5. Coefficient of Variation
    • 19.7. Measures of Position
    • 19.8. Bivariate Data Analysis >
      • 19.8.1 Covariance
      • 19.8.2. Correlation Coefficient
      • 19.8.3. Scatterplot and Regression Line
  • 20. Special Functions
    • 20.1. Gamma Function
    • 20.2. Logarithmic Gamma Function
    • 20.3. Digamma Function
  • 21. List of ALL Functions
    • 21.1. Arithmetics
    • 21.2. Algebra
    • 21.3. Trigonometry
    • 21.4. Statistics
    • 21.5. Calculus

6.8. Order of Operations

Simplifying expressions requires knowing the order of operations which is listed below. You can remember it according to the acronym GEMDAS.

1) G - Perform the operations inside a grouping symbol starting from the innermost to the outermost grouping symbols. Braces,
          brackets and parentheses are the most commonly used grouping symbols in mathematics.
2) E - Simplify expressions involving exponents.
3) M - Perform multiplication from left to right (as the order appears in the problem).
4) D - Perform division from left to right (as the order appears in the problem).
5) A - Perform addition from left to right (as the order appears in the problem).
6) S - Perform subtraction from left to right (as the order appears in the problem).

Reminders 
1) You can enter brackets [ ] and braces {  } but it may be easier to use parentheses (  ) instead. You can enter as many parentheses as needed to group terms or arguments.

Note: The app uses square brackets [ ] for matrices and ordered pairs, braces {  } for systems of equations and (  ) for grouping terms in a sequence of operations. 
        
2) You can do multiplication and division simultaneously or by whichever operation comes first.
3) You can do addition and subtraction simultaneously or by whichever operation comes first.

The app uses GEMDAS. To simplify expressions that involve a series of operations, enter the expression as it appears in the problem and enter parentheses instead of brackets or braces. Use the operation keys (+, −, ×, ÷). You can access the division symbol (÷) by tapping the fraction bar (/) twice. If you want to use a dot for multiplication, tap the multiplication sign (×) twice.

Illustration

Simplify the expression below using GEMDAS.
Solution
Step 1: Observe that there two grouping symbols: brackets and parentheses.
            The innermost grouping contains 3^2 + 6 ÷ 2.
            First, simplify 3^2 into 9.
            Then, divide 6 by 2 to get 3.
            Add 9 to 3 (the quotient of 6 and 2).
            Thus 3^2 + 6 ÷ 2 is equal to 12.

Step 2: Replace the group (3^2 + 6 ÷ 2) with 12 found in Step 1 and proceed to the next step.
            The original expression now becomes: 24 - 2 [5 - 6 ×  12].
            The square brackets can be replaced with parentheses.
            The new expression is 24 - 2 (5 - 6 ×  12).

Step 3: Simplify the terms within the parentheses.
            Multiply 6 and 12. Then subtract the product from 5.
            5 - 6 ×  12 = 5 - 72 = - 67

Step 4: Replace the 2nd group of terms (5 - 6 ×  12) with -67 found in Step 3.
            24 - 2 ( 5 - 6 ×  12) = 24 - 2(-67)
 
Step 5: Perform the multiplication.
           Multiply 2 and -67.
           24 - (-134)

Step 6: Perform the subtraction.
           Subtract -134 from 24. Note that a negative number is being subtracted.
           24 - (-134) = 24 + 134

Final answer: 158

To see the answer in the calculator, type in the entire expression.
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If you decide to use brackets instead of parentheses, the answer is still 158 but it is expressed as a 1 x 1 matrix. A 1 x 1 matrix can be considered as a number or a scalar, so numerically, the two results are the same. It is a matter of preference whether you want to use brackets or parentheses.
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Examples
Perform the indicated operation.
Solutions

1) Enter the expression as it appears in the problem: 10 + 3^2 - (6 * 2 ÷ 4)
Picture
2) Enter the expression as it appears in the problem: 42 - 2*4^2 ÷ (4​÷2+3)
Picture
3) Enter the expression as it appears in the problem: 15 ​÷ 3*4 - 6 + 2
Picture
4) Enter the expression as it appears in the problem: 15 ​÷ 3*4^3 - (6+2)^2
Picture
5) Enter the expression as it appears in the problem: (15​÷3)^2 * (4^3 - (6+2)^2)
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If you want to use brackets, tap the parentheses key twice. The answer will be expresses in a 1 x 1 matrix.

Enter the expression as it appears in the problem: (15 ÷ 3) * [4^3 - (6+2)^2]
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