# 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, addition *and* subtraction, or subtraction *and* multiplication—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 the **order of operations.** The order in which operations should be done is abbreviated as **PEMDAS**:

**P**arentheses**E**xponents**M**ultiplication and**D**ivision*(from left to right)***A**ddition and**S**ubtraction*(from left to right)*

(One way to memorize this is to think of the phrase **P**lease **E**xcuse **M**y **D**ear **A**unt **S**ally.)

- In the above example, we're dealing with multiplication and subtraction.
**M**ultiplication comes a step before**S**ubtraction, 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 no
**P**arentheses. - There are no
**E**xponents. - We start with the
**M**ultiplication and**D**ivision, 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 with**6 x 2 + 1 = ?****6 x 2 = 12**, leaving us with**12 + 1 = ?**- We then do the
**A**ddition:**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**, leaving**30 ÷ 10 + 1 = ?****30 ÷ 10 = 3**, leaving**3 + 1 = ?****3 + 1 = 4***(off by 9!)*

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

__Example #3__: 5 + (4 – 2)^{2} x 3 ÷ 6 – 1 = ?

- Start with the
**P**arentheses:**4 – 2 = 2**. (Even though subtraction is usually done in the last step, because it's in parentheses, we do this first.) That leaves**5 + 2**^{2}x 3 ÷ 6 – 1 = ? - Then
**E**xponents:**2**. We now have^{2}= 4**5 + 4 x 3 ÷ 6 – 1= ?** - Then
**M**ultiplication and**D**ivision, starting from the left:**4 x 3 = 12**, leaving us with**5 + 12 ÷ 6 – 1 = ?** - Then moving to the right:
**12 ÷ 6 = 2**, making the problem**5 + 2 – 1 = ?** - Then
**A**ddition and**S**ubtraction, starting from the left:**5 + 2 = 7**, leaving**7 – 1 = ?** - Finally, moving to the right:
**7 – 1 = 6**

(For more practice, try our Operation Order game!)

**See also:**