Oops... Use Care When Evaluating A - B + C

A mathematical expression came up during class that GDT should have spent more time discussing.

   Evaluate:  20 - 10 + 6

   Subtraction and addition have equal precedence; 
   therefore, evaluate left-to-right.

   step 1) 20 - 10 = 10  
   step 2) 10 + 6 = 16

   20 - 10 + 6 = 16

Order of operations are still applicable when processing operators of equal precedence.

   Evaluate:  20 - 10 + 6

   If the addition is done before the subtraction, then 
   the expression becomes 20 - (10 + 6).

   step 1)  10 + 6 = 16
   step 2)  20 - 16 = 4

   20 - 10 + 6 != 20 - (10 + 6)

   In English, 20 minus 10 plus six is not equal to
   20 minus the quantity 10 + 6.

Writing subtraction as addition can help ensure operations are executed in the correct order.

   20 - 10 + 6 = 20 + (-10) + 6

   Because the commutative and associative properties hold 
   true for addition, order of operations is not significant.

   Commutative property:  a + b = b + a
   Associative property:  a + (b + c) = (a + b) + c

   Some examples...

   20 + ((-10) + 6) = (20 + (-10)) + 6
   20 + ((-10) + 6) = 20 + (6 + (-10)) = ((-10) + 6) + 20
Exercises
  1. Evaluate: 24 / 12 * 6

  2. Evaluate: 30 - 10 + 20 - 10

  3. Evaluate: 50 - 10 + (10 - 5)


Creator: Gerald Thurman [gthurman@gmail.com]
Created: 07 February 2007

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