Math Order of Operations

We must follow a very specific math order of operations.  In other words, when you have a bunch of operations in a row:  multiply, add, evaluate powers, and so on, you have to do them in a very specific order to get the problem correct.

  Which Solution is Correct?    
5 + 3·2
5 + 3·2
5 + 6 
  Because multiplication comes before addition in the order, 11 is the correct answer.  
  This is what the math order of operations is all about. Just remember, the funny word "PEMDAS" to help you.  

The Four Steps of the Math Order of Operations

Here are the four steps, then GradeA will break them down for you:

  1. Parentheses:  Do all operations inside groupings first.
  2. Exponents:  Evaluate all powers next.
  3. Multiply/Divide:  Perform multiplication and division from left to right.
  4. Add/Subtract:  Perform addition and subtraction from left to right.

Got all that?  Well, in case you don't, here are some nice examples...

Step 1:  Parentheses

It should make sense to you that the operations inside the parentheses for first:  that is what they are there for!  We had to add 2+1 before we could multiply because of the parentheses.

Step 2: Exponents

Because exponents "hover" above the numbers, that should help you remember that they are important.  Do them before you do the normal arithmetic operations of + — x ÷.

Step 3:  Multiplication/Division

** Perform multiplication from left to right.  This means that division can come before multiplication in some problems!.

Ex:  6 ÷ 2·3 = 3·3 = 9  (notice you divided before multiplying!)

Step 4: Addition/Subtraction

** Again, left to right.  Sometimes subtract before addiing!

Ex:  5 ― 3 + 8 = 2 + 8 (notice you subtract before adding!)


How do I Remember the Order of Operations?

The order is:  Parentheses, Exponents, Multiply/Divide, Add/Subtract.

Students often remember the letters as PEMDAS.
And they say it is "Pem Das"

A mnemonic that is often used is the silly phrase:

"Please Excuse My Dear Aunt Sally"

It is supposed to reference a clumsy old aunt - don't mind her...

Know a fancy trick of how you remember?  Tell us!

Practice The Math Order of Operations

Take a try at these examples (answers below):

1.  4+3·8 2.  8÷(5-1) 3.  6+23 4.  9-8+1  

*Tip:  After you have found your answer, check it with your calculator.

Most all calculators (especially scientific and graphing) "understand" the order of operations.  That means that if you put in your problems as they are, your calculator should give the right answer.

*Remember:  Never trust a calculator more than yourself!

Answers:  1.  28       2.  2        3.  14         4.  2


Do you need help with other pre-algebra problems besides the math order of operations?  Ready to try algebra class?


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