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Order of Operations

Up until 5th grade, most math problems only had one operation (such as 2 + 3 = 5) to complete within a problem.  However, now we have problems that contain more than one operation, and we must do the operations in the correct order.

Watch the video below to help you understand why we need to follow the Order of Operations.

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Operations

"Operations" means things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation (such as the chart below).

.

But, when you see something like ...

7 + (6 × 52 + 3)

... what part should you calculate first? 

Start at the left and go to the right? 
Or go from right to left?

Warning: Calculate them in the wrong order, and you will get a wrong answer !

So when we talk about the Order of Operations we need to remember PEMDAS!

What is PEMDAS? 

It is just a silly saying to help us remember the order we complete each operation within a problem.  

You can remember PEMDAS by saying "Please Excuse MDear Aunt Sally".
Or ... Pudgy Elves May Demand A Snack
Popcorn Every Monday Donuts Always Sunday
Please Eat Mom's Delicious Apple Strudels
People Everywhere Made Decisions About Sums

 

Please

Parenthese, Braces, and Brackets

Excuse

Exponents

Three to the fourth power with the exponent of four written as a small number above and to the right of the base number three.

MDear

Multiply or Divide (from left to right)

         

or

     

÷     /      —    

Aunt Sally

Add or Subtract (from left to right)

+   —


Do things in Parentheses First. Example:

yes   6 × (5 + 3) = 6 × 8 =
48
 
no   6 × (5 + 3) = 30 + 3 =
33
(wrong)

Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract. Example:

yes   5 × 22 = 5 × 4 =
20
 
no   5 × 22 = 102 =
100
(wrong)

Multiply or Divide before you Add or Subtract. Example:

yes   2 + 5 × 3 = 2 + 15 =
17
 
no   2 + 5 × 3 = 7 × 3 =
21
(wrong)

Otherwise just go left to right. Example:

yes   30 ÷ 5 × 3 = 6 × 3 =
18
 
no   30 ÷ 5 × 3 = 30 ÷ 15 =
2
(wrong)

Divide and Multiply rank equally (and go left to right).

Add and Subtract rank equally (and go left to right)

So do it this way:

After you have done "P" and "E", just go from left to right
doing any "M" or "D" as you find them.

Then go from left to right doing any "A" or "S" as you find them.

 

Try this Order of Operations Game to help you better understand this concept.

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