# 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.
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!)