What Is PEMDAS? Explained for Elementary School Students

Math expressions can be confusing, especially when they consist of several different operations.

Which one should you do first, and which comes next?

Whether you're just starting to learn the order of operations, or you are helping your student with their homework, PEMDAS can make solving most math expressions a piece of cake.

Read on to find everything you need to know about PEMDAS: when and how we use it, tips for remembering it, examples to practice with, and a fun quiz to test your skills.

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What Is PEMDAS?

PEMDAS is an acronym that helps us remember the order of operations in math.

It stands for:

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

We use this acronym in the United States.

In other countries, you are more likely to encounter different, but similar acronyms:

• In the UK, Australia, India, Pakistan, and Bangladesh, this order is known as BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction)
• In Canada, it's called BEDMAS (Brackets, Exponents, Division, Multiplication, Addition, Subtraction).

When Do We Use PEMDAS?

We use PEMDAS when we come across math problems with multiple operations in one expression.

To solve these expressions correctly, we follow PEMDAS.

This means we handle:

• Parentheses first
• Exponents second
• Multiplication and division next 
• Addition and subtraction last 

Let’s put PEMDAS into action with a simple example:

6 + 3 x (2 + 1)

Without PEMDAS, we may make a mistake and start solving the expression from left to right like so:

9 x (2 + 1) --> 9 x 3 = 27

Using PEMDAS, we can remember that we need to start with parenthesis, then do the multiplication, and finally do the addition, like so:

First, we solve the expression inside the parentheses:

(2 + 1) = 3

After we’ve solved the parentheses, our expression looks like this: 6 + 3 x 3

Then, we do the multiplication:

3 x 3 = 9 

Now, our expression looks like this: 6 + 9 

Finally, when we add the two, we get:

6 + 9 = 15

So, the correct answer is 15. 

Let's see all that in one sequence:

6 + 3 x (2 + 1)  --> 6 + 3 x 3 --> 6 + 9 = 15

A Trick to Memorizing PEMDAS Rules

Sometimes, students struggle to memorize the order of operations in PEMDAS.

To make it easier, they use playful mnemonics. A mnemonic is a tool that helps you remember something by using a pattern of letters, ideas, or associations.

One popular mnemonic for PEMDAS is: "Please Excuse My Dear Aunt Sally." Each word in this phrase helps remember the steps:

• Please (Parentheses)
• Excuse (Exponents)
• My (Multiplication)
• Dear (Division)
• Aunt (Addition)
• Sally (Subtraction)

Examples of PEMDAS

Here are a couple more challenging examples to help you understand how to use order of operations better.

Example 1

3² + 4 x 5 + 22

Let's break it down using PEMDAS:

1. First, we do the exponent (in this case multiply 3 by itself):

3² = 9

So, the expression becomes: 

9 + 4 x 5 + 22

2. Next, multiply

4 x 5 = 20 

So, the expression becomes: 

3. Finally, add: 

So, the answer is 51.

Example 2

12² – 4 x 2 ÷ (3 + 1) 

Let's use PEMDAS step-by-step:

1. First, do the addition inside the parentheses:

(3 + 1) = 4

So, the expression becomes: 

12² – 4 x 2 ÷ 4

2. Next, do the exponent: 

12² = 144

So, the expression becomes: 

144 – 4 x 2 ÷ 4

3. Then, multiply: 

4 x 2 = 8

So, the expression becomes: 

144 – 8 ÷ 4

4. After this, divide: 

8 ÷ 4

So, the expression becomes: 

144 – 2

5. Finally, subtract: 

144 – 2 = 142

So, the answer is 142.

Quiz Time! Recap What You've Learned About PEMDAS

Ready to show what you’ve learned about PEMDAS? Try our 2-minute quiz.

PEMDAS FAQs

PEMDAS is especially helpful when we’re working with more complicated math problems. Here are a couple of tricky examples to help you understand better.

Can PEMDAS be applied to all mathematical problems?

Yes, PEMDAS is a universal rule for solving mathematical expressions with multiple operations. It ensures consistency and accuracy in calculations.

Can the order of operations change in different countries?

No, PEMDAS (or its equivalents, such as BODMAS, BEDMAS, etc.) is universally recognized and used in mathematical operations worldwide.

How does PEMDAS help us in everyday life?

Whether you’re doing a science experiment, budgeting, or solving puzzles that involve mathematical expressions, PEMDAS helps ensure that anyone, anywhere in the world can look at an expression and know how to simplify it.

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