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 to perform exponentiation.

  *    is the multiplication operator since the letter x would be confusing to use for multiplication

  /    is the division operator

  Mod    is the modulus operator. See the notes below.

  +    is the addition operator

  -    is the subtraction operator
  

Objective #2: Use Mod appropriately to compute the remainder of a division problem.

• Mod is an operator in VB that computes the remainder of a long division problem. For example, if you needed to determine the remainder of 12 divided by 5, you would type      12 Mod 5     in VB.
  
  
• Mod is short for modulus which is a term in mathematics that you may learn later in school.
  
  
• Examples:
  
  4 Mod 3 = 1
  4 Mod 2 = 0
  10 Mod 10 = 0
  8 Mod 3 = 2
  100 Mod 98 = 2
  20 Mod 7 = 6
  
  
• Mod would be used in the real world to figure out how many leftover pieces of pizza there would be if a family of 3 people evenly divided the 8 slices in a whole pizza (answer: 2 pieces). The expression 8 Mod 3 could be used to determine that there are two leftover pieces.
  
  There are many other real world situations where you would need to determine the leftover or remainder of a division problem.

Objective #3: 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.
  
  However, 12 / (3 * 4) would evaluate to 1 since the parentheses require that you do the multiplication before the division.
  
  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 #4: 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.

Objective #5: Evaluate string expressions.

• Strings are words or phrases in computer science. For example "Hello World" is considered to be a string. Even the set of symbols "#$(&>@" is considered to be a string because it is wrapped in double quotes.
  
  
• A set of numbers could be considered to be a string. For example, "19610" is a string since it is surrounded by double quotes. The phone number "6103740739" is a string as well.
  
  
• Two strings can be joined together with concatenation as in       "Wyomissing" + "Spartans"        is equal to        "WyomissingSpartans"
  
  You can even concatenate a blank space between two strings as in              "Wyomissing" + " " + "Spartans"        is equal to        "Wyomissing Spartans"    
  
  Concatenation even applies when something doesn't make logical sense as in                   "4" + "Wyo"        simplifies to                      "4Wyo"   
  
  
• Sometimes you need to turn a string into a number however. The expression      "3" + 4    may lead to an error because a string should not be added or concatenated with a number.
  
  But you can use the Str command to convert a numeric value to a string as in
  
  "3" + Str(4)     which simplifies to       "3" + "4"       which further simplifies to     "34"
  
  In this case, the number 4 is being converted into "4" so that "3" + "4" simplifies to "34"
  
  
• Or you could convert two numeric values into strings and then concatenate them as in
  
  Str(3) + Str(4)    which simplifies to      "3" + "4"      which further simplifies to    "34"
  
  But, because of the order of operations
  
  Str(3 + 4)     simplifies to        Str(7)         which further simplifies to      "7"
  
  
• Sometimes you need to turn a string into a numeric value. The Val command can be used to convert a string into a numeric value as in
  
  Val("3") + 4     which simplifies to       3 + 4         which further simplifies to       7
  
  But, because of the order of operations
  
  Val("3" + "4")        simplifies to       Val("34")        which further simplifies to         34
  
  
• Do not attempt to convert something that is not a number into a numeric value. It could result in an error such as this example
  
  Val("Wyomissing") + 4
  
  which doesn't make any sense since "Wyomissing" isn't a legal numeric value or number.