How To Use PEMDAS & Solve With Order Of Operations (Examples)

Running into a math problem that mixes different operations such as multiplication, addition and exponents can be puzzling if you don't understand PEMDAS. The simple acronym runs through the order of operations in math, and you should remember it if you need to complete calculations on a regular basis. PEMDAS means parentheses, exponents, multiplication, division, addition and subtraction, telling you the order in which you tackle different parts of a long expression. Learn how to use this and you'll never be confused by problems such as 3 + 4 × 5 – 10 that you may encounter.

​Tip:​ PEMDAS describes the order of operations:

P – Parentheses

E – Exponents

M and D – Multiplication and division

A and S – Addition and subtraction.

Work through any problems with different types of operations according to this rule, working from the top (parentheses) to the bottom (addition and subtraction), noting that operations on the same line can just be tackled from left to right as they appear in the question.

The order of operations tells you which parts of a long expression to calculate first to get the right answer. If you just approach questions from left to right, for example, you will end up calculating something completely different in most cases. PEMDAS describes the order of operations as follows:

P – Parentheses

E – Exponents

M and D – Multiplication and division

A and S – Addition and subtraction.

When you're tackling a long math problem with numerous operations, first calculate anything in parentheses, and then move to the exponents (i.e., the "powers" of numbers) before doing multiplications and division (these work in any order, simply work left to right). Finally, you can work on addition and subtraction (again just work left to right for these).

Remembering the acronym PEMDAS is probably the most difficult part of using it, but there are mnemonics you can use to make this easier. The most common is Please Excuse My Dear Aunt Sally, but other alternatives are People Everywhere Made Decisions About Sums and Pudgy Elves May Demand A Snack.

Answering problems involving the order of operations just means remembering the PEMDAS rule and applying it. Here are some order of operations examples to clarify what you have to do.

\(4 + 6 × 2 – 6 ÷ 2\)

Go through the operations in order and check for each. This doesn't contain parentheses or exponents, so move onto the multiplication and division. First, 6 × 2 = 12, and 6 ÷ 2 = 3, and these can be inserted to leave an easy problem to solve:

\(4 + 12 – 3 = 13\)

This example includes more operations:

\((7 + 3)^2 – 9 × 11\)

The parenthesis comes first, so 7 + 3 = 10, and then this is all under an exponent of two, so 10² = 10 × 10 = 100. So this leaves:

\(100 – 9 × 11\)

Now the multiplication comes before the subtraction, so 9 × 11 = 99 and

\(100 – 99 = 1\)

Finally, look at this example:

\(8 + (5 × 6^2 + 2)\)

Here, you tackle the section in parentheses first: 5 × 6² + 2. However, this problem also requires you to apply PEMDAS. The exponent comes first, so 6² = 6 × 6 = 36. This leaves 5 × 36 + 2. Multiplication comes before addition, so 5 × 36 = 180, and then 180 + 2 = 182. The problem then reduces to:

\(8 + 182 = 190\)

Watch the video below for another example:

Practice applying PEMDAS using the following problems:

\(5^2 × 4 – 50 ÷ 2\)
\(3 + 14 ÷ (10 – 8)\)
\(12 ÷ 2 + 24 ÷ 8\)
\((13 + 7) ÷ (2^3 – 3) × 4\)

The solutions are listed below in order, so don't scroll down until you've attempted the problems.

\(\text{Problem 1} \
\,\)
\(\begin{aligned}\)
\(5^2 × 4 &- 50 ÷ 2\)
\(&= 25 × 4 – 50 ÷ 2\)
\(&= 100 – 25\)
\(&= 75
\end{aligned}\)

\(\text{Problem 2} \
\,\)
\(\begin{aligned}\)
\(3 + 14 &÷ (10 – 8)\)
\(&= 3 + 14 ÷ 2\)
\(&= 3 + 7\)
\(&= 10
\end{aligned}\)

\(\text{Problem 3} \
\,\)
\(\begin{aligned}\)
\(12 ÷ 2 &+ 24 ÷ 8\)
\(&= 6 + 3\)
\(&= 9
\end{aligned}\)

\(\text{Problem 4} \
\,\)
\(\begin{aligned}\)
\((13 + 7) ÷ &(2^3 – 3) × 4\)
\(&= 20 ÷ (8 – 3) × 4\)
\(&= 20 ÷ 5 × 4\)
\(&= 16
\end{aligned}\)