Order of Operations

Updated February 21, 2017 | Factmonster Staff

The information below explains PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction

When you have a math problem that involves more than one operation?for example, additionandsubtraction, or subtractionandmultiplication?which do you do first?

Example #1: 6 ? 3 x 2 = ?

  • Do you do the subtraction first (6 ? 3 = 3) and then the multiplication (3 x 2 =6)?
  • Or do you start with the multiplication (3 x 2 = 6) and then subtract (6 ? 6 =0)?

PEMDAS

In cases like these, we follow theorder of operations.The order in which operations should be done is abbreviated asPEMDAS:

  1. Parentheses
  2. Exponents
  3. Multiplication andDivision(from left to right)
  4. Addition andSubtraction(from left to right)

(One way to memorize this is to think of the phrasePleaseExcuseMyDearAuntSally.)

  • In the above example, we're dealing with multiplication and subtraction.Multiplication comes a step beforeSubtraction, so first we multiply 3 x 2, and then subtract the sum from 6, leaving 0.

Example #2: 30 5 x 2 + 1 = ?

  • There are noParentheses.
  • There are noExponents.
  • We start with theMultiplication andDivision, working from left to right.
    NOTE:Even though Multiplication comes before Division in PEMDAS, the two are done in the same step, from left to right. Addition and Subtraction are also done in the same step.
  • 30 5 = 6, leaving us with6 x 2 + 1 = ?
  • 6 x 2 = 12, leaving us with12 + 1 = ?
  • We then do theAddition:12 + 1 = 13

Note that if we'd done the multiplication before the division, we'd have ended up with the wrong answer:

  • 5 x 2 = 10, leaving30 10 + 1 = ?
  • 30 10 = 3, leaving3 + 1 = ?
  • 3 + 1 = 4(off by 9!)

One last example for advanced students, using all six operations:

Example #3: 5 + (4 ? 2)2x 3 6 ? 1 = ?

  • Start with theParentheses:4 ? 2 = 2. (Even though subtraction is usually done in the last step, because it's in parentheses, we do this first.) That leaves5 + 22x 3 6 ? 1 = ?
  • ThenExponents:22= 4. We now have5 + 4 x 3 6 ? 1= ?
  • ThenMultiplication andDivision, starting from the left:4 x 3 = 12, leaving us with5 + 12 6 ? 1 = ?
  • Then moving to the right:12 6 = 2, making the problem5 + 2 ? 1 = ?
  • ThenAddition andSubtraction, starting from the left:5 + 2 = 7, leaving7 ? 1 = ?
  • Finally, moving to the right:7 ? 1 = 6

(For more practice, try ourOperation Ordergame!)