Order of Operations

Welcome to the Math Salamanders PEMDAS rule page.

Here you will find help in using PEMDAS with some simple instructions and lots of worked examples.

Mathway.

PEMDAS is usually introduced around about 5th grade and changes the way that you look at and read calculations.

However, it is not as simple a rule as it seems - there are several pitfalls which are addressed below!

PEMDAS (sometimes referred to as PEMDAS, BEDMAS or BODMAS) is a mathematical acronym to help you understand how calculations work.

The acronym refers to the order in which any calculation shold be done, and is typically introduced at around the 5th grade level.

The acronym stands for the following:

- P = Parentheses (Brackets)
- E = Exponents
- M = Multiplication
- D = Division
- A = Addition
- S = Subtraction

One popular way to remember the PEMDAS rule is the saying:

'Please Excuse My Dear Aunt Sally'.

PEMDAS looks quite simple from the above example.

It is saying that you have to do calculations in parentheses (brackets) first, then exponents next, and so on...

However, the PEMDAS rule is not quite so straightforward as it seems.

This is because some of the operations have equal weighting, like multiplication and division, or addition and subtraction.

This is why some people call the rule PEDMAS instead.

A good way of looking at the rule is the diagram below.

This clearly shows that multiplication and division have equal weighting. It also shows addition and subtraction also have the same level of importance.

PEMDAS in 4 Simple Steps

Step 1) Do the parentheses (brackets).

Step 2) Do any exponents.

Step 3) Do any Multiplication OR Division left to right

Step 4) Do any Addition OR Subtraction left to right

So now we know what PEMDAS is, it is time to see how it works...

Here are the

3 + 4 x 5

The operations are addition and multiplication.

In PEMDAS, multiplication comes before addition.

So 3 + 4 x 5 = 3 + 20 = 23

4 x (2 + 3)

The operations are multiplication and addition, there are also parentheses (brackets).

Using PEMDAS, the part in Parentheses must come first.

So 4 x (2 + 3) = 4 x 5 = 20

2^{4} - (3 x 4)

There are Exponents, and Parentheses, as well as subtraction and multiplication.

Using PEMDAS, the part in Parentheses must come first.

So 2^{4} - (3 x 4) = 2^{4} - 12

Using PEMDAS, Exponents comes next.

So 2^{4} - 12 = 16 - 12 = 4

12 ÷ 3 x 4

The operations are division and multiplication which have equal weighting.

So we just do the operations left to right.

So 12 ÷ 3 x 4 = 4 x 4 = 16

4 - 5 + 3

The operations are addition and subtraction which have equal weighting.

Just do the operations from left to right.

So 4 - 5 + 3 = -1 + 3 = 2

4 x (1 + 2)^{2}

There are exponents and parentheses as well as as addition and multiplication.

Using PEMDAS, the part in Parentheses must come first.

So (1 + 2) = 3

Next comes the exponent part:

3^{2} = 9

Finally comes the multiplication:

4 x 9 = 36

So 4 x (1 + 2)^{2} = 4 x (3)^{2} = 4 x 9 = 36

6 x 4 ÷ 3 + 12 - 27 ÷ 3

There are all four operations here, so we need to do multiplication and division first.

6 x 4 ÷ 3 we can do left-to-right as multiplication and division have equal weighting.

6 x 4 ÷ 3 = 24 ÷ 3 = 8

This gives us 8 + 12 - 27 ÷ 3

We need to do the division first.

27 ÷ 3 = 9

This leaves us with 8 + 12 - 9.

We can do this calculation left-to-right as all the operations have the same weighting.

8 + 12 - 9 = 20 - 9 = 11

So 6 x 4 ÷ 3 + 12 - 27 ÷ 3 = 24 ÷ 3 + 12 - 9 = 8 + 12 - 9 = 20 - 9 = 11

The sheets in this section involve using parentheses and exponents in simple calculations.

There are also lots of worksheets designed to practice and learn about PEMDAS.

Using these worksheets will help your child to:

- know and understand how parentheses works;
- understand how exponents work in simple calculations.
- understand and use PEMDAS to solve a range of problems.

Take a look at some more of our worksheets similar to this theme.

The sheets in this area will help your child understand the use and purpose of the equals sign (=) in an equation.

It will also help children learn to start manipulating and calculating numerical expressions so that they are equivalent.

This will stand them in good stead for when they start to learn algebra, and manipulate algebraic equations.

Here you will find a range of printable mental math 5th grade quizzes for your child to enjoy.

Each worksheet tests the children on a range of math topics from number facts and mental arithmetic to geometry, fraction and measures questions.

A great way to revise topics, or use as a weekly math quiz!

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