# What does pemdas mean?

Apr 11, 2016

P.E.M.D.A.S. is an acronym that lists the operations which should be done first. It stands for:

P arentheses
E xponents
M ultiplication
D ivision
A ddition
S ubtraction

Order of Operations
Since the acronym starts with "P" first, it implies that in a mathematical problem, the parentheses should be dealt with first before moving on to the next step in the problem.

For example, in the following problem, you should get $20$.

$5 \times \left(1 + 3\right)$

$= 5 \times 4$

$= 20$

If you did the following, it would be considered wrong, since the parentheses must always be dealt with first.

$5 \times \left(1 + 3\right)$

$\ne 5 \times 1 + 3$

$\ne 5 + 3$

$\ne 8$

Once you finish dealing with the parentheses, you move onto the following letter, E, which stands for exponents, and so on. If a mathematical problem does not have an operation, you move onto the next letter.

For instance, in the following problem, there are no parentheses, so we skip to exponents.

$2 \times {5}^{2}$

$= 2 \times 25$

$= 50$

Equally-Ranked Operations
If you come across a problem where division appears before multiplication, you can deal with division first, since division and multiplication are ranked equally, as long as you remember to solve the problem from left to right. This also applies for addition and subtraction.

For example, in the following problem, you should get $18$.

$2 \times 15 \div 5 \times 3$

$= 30 \div 5 \times 3$

$= 6 \times 3$

$= 18$

If you did the following, it would be considered wrong, since you must work from left to right.

$2 \times 15 \div 5 \times 3$

$\ne 2 \times 15 \div 15$

$\ne 30 \div 15$

$\ne 2$

Other Names for P.E.M.D.A.S.
Outside of the U.S., P.E.M.D.A.S. may be referred to as the following. They all mean the same thing, but are just different ways of describing the order of operations.

• B.O.D.M.A.S. in the United Kingdom

B rackets
O rders
D ivision
M ultiplication
A ddition
S ubtraction