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Lesson 12 - Order of Operations, Median

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Order of Operations

Look at "". How do you know which to do first? Should you add 4 plus 5 and then multiply by 2, or multiply first and then add?

Natural Order

There is a "natural" order of operations to mathematics:
  1. If there’s any parentheses ( ) then do them first.
  2. Then do exponents and powers and square roots.
  3. Then do multiplication and division
  4. And then do any addition and subtraction from left to right.
It may help to remember them as P.E.M.D.A.S. using their first letters.

Thus in the example , we would multiply first.
 
Example: 8 - 4 - 1 = ?

Since we have more than one subtraction, we do the left one first:
(8 - 4) - 1 = 3

What if we wanted to tell someone to do the subtraction in a different order? Use parentheses to change the natural order. Expressions in parentheses are always done first.
 
Example: 8 - (4 - 1) = ?

Since we have parentheses we must do "four minus one" first:
8 - (4 - 1) = 5

Suppose you have an expression with both subtraction and exponents. You should do the exponent first (unless commanded otherwise by parentheses).
 
Example:

Since there’s no ( ) we must do "two to the fourth power" first:

Last modified: June19, 2000, by DeVondria Brady for use in EDU 506