Order of Operations

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Welcome to the Math Salamanders PEMDAS rule page.

Here you will find help in using PEMDAS and also a chance to practise using the rule with our PEMDAS worksheets.

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!

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At Fifth Grade, children enjoy exploring Math with these free 5th Grade Math problems and Math games.
Children will enjoy completing these 5th Grade Math Worksheets and playing these
Math games whilst learning at the same time.

During Fifth Grade, children learn about factors and prime numbers. They build on their learning of long division
and can divide numbers up to 1000 by two digit numbers.
They are able to multiply decimals by whole numbers, and are able to work out powers of a number.

Children are able to add and subtract fractions, decimals and mixed numbers, and learn to
multiply and divide fractions. They are able to solve multi-step problems
involving whole numbers, fractions and decimals.

These free printable Fifth Grade Math Games, and other Math Worksheets for fifth grade
will help your child to achieve their Elementary Math benchmark set out by Achieve, Inc.

In the UK, 5th Grade is equivalent to Year 6.

PEMDAS RULE

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 explained!

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

PEMDAS in Action!

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

Here are the

Example of the PEMDAS rule

Example 1

3 + 4 x 5

The operations are addition and multiplication.

In PEMDAS, multiplication comes before addition.

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

Example 2

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

Example 3

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

Example 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

Example 5

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

PEMDAS worksheets

The sheets below use PEMDAS to work out a range of calculations.

The first series of sheets are a great resource for students who are just learning the rule.

The second series of sheets are good for stretching and challenging more able students.

Order of Operations worksheets

PEMDAS Challenges Worksheets

PEMDAS RULE GAME

The PEMDAS rule game is a game which involves using brackes, multiplication and addition or subtraction.

The aim of the game is to place digit cards in the pemdas game boards to get as close to the given target as possible.

PEMDAS GAME

Grade: 5th Grade +

Number of players: any.

Learning skills: learning PEMDAS and reasoning skills.

Using Parentheses and Exponents

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

Knowledge of the PEMDAS rule is not essential to complete the sheets in this section.

Using these sheets will help your child to:

- know and understand how parentheses affects a calculation;
- understand how exponents work in simple calculations.

Balancing Math Equations Worksheets

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.

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