0When 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:
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
(One way to memorize this is to think of the phrase Please Excuse My Dear Aunt Sally.)
- In the above example, we're dealing with multiplication and subtraction. Multiplication comes a step before Subtraction, 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 Parentheses.
- There are no Exponents.
- We start with the Multiplication and Division, 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 Addition: 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 Parentheses: 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 + 22 x 3 ÷ 6 – 1 = ?
- Then Exponents: 22 = 4. We now have 5 + 4 x 3 ÷ 6 – 1= ?
- Then Multiplication and Division, 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 Addition and Subtraction, starting from the left: 5 + 2 = 7, leaving 7 – 1 = ?
- Finally, moving to the right: 7 – 1 = 6
