Order of Operations

When simplifying problems many people use the acronym PEMDAS to remember the order of operations.  The problem is that if a person always multiplies before they divide or added before they subtract they will frequently get the wrong answer.

dr-math-juggling-1In this video we look at a different way to remember the order of operations: Please Excuse Dr. Math’s Silly Actions (PEDMSA). While conceptually it is important to realize that division and multiplication (and subtracting and adding) are done from left to right, if you forget and divide first (or subtract first) you will still get the correct answer.

To print a poster about Order of Operations go to the Notes section.

 

Lets look at the Order of Operation.

You may have heard this term before, but lets think about it.
 
As the name implies, we are asking in what order should we do the operations, such as multiplying, subtracting, and exponents, when we are solving a problem. What are the rules we need to follow to insure that the answer makes sense and that all people solving a problem will get the same answer.

 

So how do we know how to proceed?

Well, there are some simply rules, that says that when we are solving a problem we first look for:
 
      Parentheses (or any other grouping symbols)
 
      Exponents
 
      Divide and Multiply from left to right
 
      Subtract and Add from left to right
 
To better under stand how to apply these rules lets look at a few examples.



Ex. 1 $9-2+3+10*5=$
First we multiply $10*5$ $9-2+3+50 =$
Then we subtract and add $7+3+50 =$
from left to right $10+50 =$
$60$



 
Now lets look at a more complex problem, where we can apply all our rules.



Ex. 2 $3^2 \div 109 * 0 + 3(-33.9 + 2.8) =$
Parentheses $3^2 \div 109 * 0 + 3(-31.1) =$
Exponents $9 \div 109 * 0 + 3(-31.1) =$
Divide and Multiply $9  \div 109 * 0 + 3(-31.1) =$
from left to right $\tfrac {9}{109} * 0 +3(-31.1) =$
$0 + -93.3 =$
$-93.3$



                                                       
 

order of operationsTo help us remember the order of operations we can just use the first letter of each operation: PEDMSA

You can create your own mnemonic to help you remember this, or use ours

Please Excuse Dr. Math’s Silly Actions

This can help you remember the order you should perform the
                          operations.

 

Dr. Math's Order of Operations

 

When we simplify expressions using the order of operations, why do we subtract and add from left to right? Why do we divide and multiply from left to right?

 
So we could have shortened PEDMSA to PEMA (Please Excuse Math Antics), since multiplying and dividing are related, and adding and subtracting are related.


A little confused?

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