Five Fundamental Math Operations

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Topics

• Five Fundamental Math Operations
• Precedence of Math Operations
• Using Parentheses to override precedence
• Writing and Interpreting VB Calculation
  Statements
• Mathematical Functions

A computer lets you make more mistakes faster
than any invention in human historywith the
possible exceptions of handguns and
tequila Mitch Ratcliffe
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Numeric Operations in Computer Code

• Computers were invented to process large
  quantities of numeric data
• Computers perform arithmetic operations on
  numeric values incredibly rapidly
• All computer operations can be performed using
  the basic operations of addition, subtraction,
  multiplication, and division.
• Most computer languages also provide for
  exponentiation
• Most also provide built in functions for more
  complex operations

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Objectives

• Understand the five fundamental arithmetic
  operations in VB
• Understand how to write and interpret
  mathematical calculations in VB
• Understand the precedence of mathematical
  operations in computers and how parenthetical
  grouping affects calculation order
• Understand the use of predefined mathematical
  functions available in VB

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Five Fundamental Arithmetic Operations

• VB supports five built-in arithmetic operations
• Operation Conventional Notation Computer
  Symbol
• Addition 3 4 3 4
• Subtraction 3 - 4 3 - 4
• Multiplication 3 x 4 3 4
• Division 3 ??? 3 / 4
• Exponentiation 34 3 4

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The Assignment Operation

• Many times the results of a calculation or other
  operation are assigned to a variable, property,
  or other value holder
• iSum iFirstValue iSecondValue
• iSum Val(txtFirst.Text) Val(txtSecond.Text)
• MainMenu.Top (Screen.Height - MainMenu.Height)
  / 3
• The calculation on the right of the equal sign is
  performed first and assigned to the location on
  the left
• The Equal Sign is an assignment operator

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Using Numeric Calculations

• Legal statements
• x 4
• y 2
• z x 5
• t x 2
• txtPrice.Text x y
• Const Pi 3.14
• dblDiameter Pi sglRadius
• dSqrt x .5

• Illegal statements
• 4
• x y
• z x txtInput.Text
• sglPrice 1,456.98

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Precedence of Numeric Calculations

• Q What is the result of 3 5 2?A
• Numeric operations have a defined hierarchy or
  precedence of calculation
• 1. Exponentiation
• 2. Multiplication and division
• 3. Addition and subtraction
• 4. Left to right within categories
• Because multiplication precedes addition 5 is
  multiplied by two giving 10 first after which the
  three is added to give 13

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Precedence Exercises
What are the results of the following
calculations if x 12 and y 4?

• x y / 2
• y 3 / 4
• x 2 y - 2 x
• 8 x y / 3
• -8 y -2
• 16 (1 / 4)

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Using Parentheses to Group Calculations

• Operations grouped in parentheses are performed
  first, regardless of the natural order of
  calculation3 5 2 13(3 5) 2 16
• Parentheses may be nested((3 5) 8) / (2 4)
  ?
• Parentheses may be used to visually format
  mathematical expressions even if no change to the
  calculation order is needed

Inner parentheses are evaluated first
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More Precedence Exercises
Write computer expressions for each mathematical
expression
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Numeric Functions

• VB (and most other programming languages) provide
  predefined numeric calculations in the form of
  functions
• Functions often operate on a value and return
  some transformation of the value
• E.g. in x 25 y Sqr(x)Sqr( ) is a
  predefined function which returns the square root
  of its argument (x in this case)

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Functions and Expressions as Arguments

• Functions may be nested
• E.g., in Math.Sqr(Math.Abs(x))
• the absolute value of x is determined first and
  then becomes the argument of the square root
  function
• A calculation may be performed inside the
  argument of a function
• E.g., in Math.Sqr(x 2)
• the value of x is first squared and then the
  square root of the result is taken
• Functions are always calculated from the inside
  out

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Empty Variables in Mathematical Operations

• Variables which have never been assigned a value
  are said to be empty
• If a mathematical operation is performed on an
  empty variable the variable behaves as if its
  value is zero
• Be very careful as division by zero results in a
  runtime error which will crash the program.
• NB Variables loaded from databases may sometimes
  contain a null value which is different from
  empty.

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Converting Data Types
Introduces inefficiency

• VB will automatically convert many numeric data
  types before performing calculations
• Single precision values can be multiplied by
  integers, assigned to currency variables etc.
• Some conversions cannot take place
• String values cannot be assigned to explicitly
  declared numeric variables (non variants)
• Commonly arises when using text boxes, list
  boxes, grid controls, etc.

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The Val( ) Function

• Val( ) returns the numeric value of its argument
• Argument is typically a string but may be a
  number
• Val converts strings to numbers
• A common use of Val is to convert values which
  must be treated as text into numbersintQty
  Val(txtQty.Text)intCourse Val(cboCourseNumber.T
  ext)sglPrice Val(InputForm.Tag)
• Or use the Convert method

Some properties always contain characters
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The Val ( ) Function Examples

• Val (123.54) 123.54
• Val () 0
• Val(123A45) 123
• Val(A123) 0
• Val( 123 456) 123456

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Methods of the Math Class
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