VB Lecture Notes - Evaluating Expressions

Objective #1: Evaluate mathematical expressions.Use the order of operations to evaluate expressions and to write proper expressions.

• Expressions are groups of operators such as the plus symbol ( + ) and operands such as the numbers 1 and 2 or variables like x and y that can be evaluated or simplified. Examples:
  
  1 + 2 
  4 + 2 - 2
  12 / 2 * 2    
  x + 3
  
  
• Operators

  -  is the negative sign

  ^    is the exponent operator. For example, 2 ^ 3 evaluates to 8 since 2 to the third power is 8. Later in this course, you will learn how to use the Pow method from the Math class to perform exponentiation.

  *    is the multiplication operator

  /    is the division operator

  Mod    is the modulus operator. It computes the remainder of a division problem. For example, 10 Mod 3 evaluates to 1 since the remainder of 10 divided by 3 is 1.               Examples: 12 Mod 5 = 2      4 Mod 3 = 1     4 Mod 2 = 0     10 Mod 10 = 0

  +    is the addition operator

  -    is the subtraction operator
  

Objective #2: Use the order of operations to evaluate expressions.

• Visual Basic automatically follows the the order of operations which some students learn as PEMDAS ( "Please Excuse My Dear Aunt Sally" ). In Visual Basic, the order of operations is:
  
  parentheses
  exponents
  multiplication & division
  Mod
  addition & subtraction
  
  
• Note that multiplication and division are tie according to the order of operations so they should be evaluated from left to right in the order that they appear. For example, the expression 12 / 3 * 4 evaluates to 16 and not 1.
  
  The same goes with addition and substraction. The expression 4 - 2 + 2 evaluates to 4 and not 0.
  
  The Mod operation fits in between multiplication/division and addition/subtraction. The expression 10 Mod 4 * 2 evaluates to 2 since the multiplication is performed first before Mod.
  
  
• More examples:
  •   10 / 5 * 2 evaluates to 4 (not 1)
  •    24 / 8 * 4 evaluates to 12 (not 0.75)
  •    20 / 2 * 5 evaluates to 50 (not 2)
  •    2 * 2 * 2 / 2 * 2 evaluates to 8 (not 2)
  •    TRY THIS ONE: 36 / 18 * 2 evaluates to ?
  •    10 - 5 + 5 evaluates to 10 (not 0)
  •    100 - 3 + 97 evaluates to 194 (not 0)
  •    50 + 60 - 3 + 100 evaluates to 207 (not 7)
  •    TRY THIS ONE: 100 - 5 + 5 - 5 + 5 evaluates to ?

Objective #3: Write proper mathematical expressions.

• Mathematical notation must be written in lines of code. For example, in computer programming, you must represent the fraction one half as 1/2 rather than writing it with a fraction bar as you would in a mathematics classroom.
  
  
• You can refer to a negative number by using a hyphen as in
  
  -2 + 5
  
  which simplifies to 3
  
  
• Insert parentheses where necessary in order to preserve the correct evaluation. The rule-of-thumb is to add extra parenthesis when you are in doubt if they are required or not. If you want the addition to occur before the subtraction in the following expression
  
  4 - (2 + 2)
  
  you must use the parentheses so the answer is 0 and not 4.
  
  
• Note that sometimes two expressions can result in the same answer even if they are written differently as in:
  

  2 * 10 / 5 + 4
  
  10 / 5 * 2 + 4
  
  which both simplify to 8
  

• Do not use commas when typing numbers in the thousands. For example
  
  1,000 + 3
  
  would cause an error. It must be written as
  
  1000 + 3
  
  in Visual Basic.