In mathematics, PEMDAS is an acronym used to mention order of operations to be followed while solving expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition and S- Subtraction. There are different acronyms used for order of operations in different countries. For example, in Canada, order of operations is stated as BEDMAS (Brackets, Exponents, Division, Multiplication, Addition and Subtraction). Some people prefer to say BODMAS (B- Brackets, O- Order or Off), while few others call it GEMDAS (G- Grouping).

In this lesson, you will be learning about PEMDAS rule to solve arithmetic expressions followed by solved examples and practice questions.

**Table of Contents**

- Introduction to PEMDAS
- What is PEMDAS?
- BODMAS vs. PEMDAS
- When to use PEMDAS?
- Common Mistakes while using PEMDAS rule
- FAQs on PEMDAS
- Solved Examples
- Practice Questions

## Introduction to PEMDAS

PEMDAS or order of operations is a set sequence to perform operations in an arithmetic expression. There are different scenarios where everything goes through various steps in a fixed sequence. Consider the following scenario. Ryan and Ruhi visited a toy factory. They both observed the processes followed in the factory to manufacture toys. Toys are first designed. Next, they are built and packed in boxes. Finally, they are checked for quality before being shipped to stores. Everything is done in a set order.

Similarly, arithmetic operations are performed in a well-ordered manner. Let us learn the order of operations in Mathematics. Finding the answer to mathematical operations is fairly simple when only one operator is involved. What if multiple operators are involved? This could get a little trickier! Let’s see how.

Ryan and Ruhi solved a mathematical expression 5+2×3 separately. This is how they solved it.

Ruhi's Method | Ryan's Method |

5+2×3 = 7×3 = 21 |
5+2×3 = 5+6 = 11 |

As you can observe, Ryan and Ruhi got different answers. There can only be one correct answer to this expression in mathematics! Can you decide who is correct?

Don’t worry! **PEMDAS** is here to help you find the correct answer.

## What is PEMDAS?

PEMDAS is an order of operation used in mathematics to deal easily with complex calculations. It states that we start solving any arithmetic expression by solving the terms written in parentheses or brackets and then we simplify exponential terms and move ahead to multiplication and division operations and then at last, we can find the answer by solving addition and subtraction operations.

**PEMDAS: Definition**

PEMDAS is a set of rules which are followed while solving mathematical expressions. This rule starts with **Parentheses**, and then operations are performed on the **exponents **or powers. Next, we perform operations on **multiplication or division** from left to right. Finally, operations on **addition or subtraction** are performed from left to right.

P | [{( )}] | Parentheses |

E | x^{2} |
Exponents |

M
D |
× OR ÷ |
Multiplication OR Division |

A
S |
+ OR - |
Addition OR Subtraction |

If you stick to this order of operations in the PEMDAS rule, you will always get the correct answer. The following acronym will help you remember the PEMDAS Rule.

**P**lease **E**xcuse **M**y **D**ear **A**unt **S**ally

Let us understand PEMDAS with the help of an example.

## BODMAS vs. PEMDAS

The** **PEMDAS** **rule is similar to the BODMAS** **rule. There is a difference in the abbrevation because certain terms are known by different names at different locations.

## When to use PEMDAS?

When there is more than one operation in a mathematical expression, we use the PEMDAS method. PEMDAS in Math gives you a proper structure to produce a unique answer for every mathematical expression. There is a sequence of certain rules that need to be followed when using the PEMDAS method. Once you get the hang of these rules, you can do multiple steps at once.

**Points to Remember**

- Operations in brackets should be carried out first.
- Next, solve the exponents in the expression.
- Move from left to right and carry out multiplication or division, whichever comes first.
- Move from left to right and carry out addition or subtraction, whichever comes first.

## Common Mistakes while using PEMDAS rule in Math

The presence of multiple brackets usually causes confusion. If we don't know which bracket to solve first, it could lead to an incorrect answer. We will now learn how to solve this expression with multiple brackets.

4+3[8-2(6-3)]÷2

We will begin with working from the inside of the brackets. We will solve the inner-most bracket first and then move outside.

- Starting with 6 – 3 = 3, we get: 4 + 3[8 – 2(3)] ÷ 2
- Next, multiplying 2(3)=6 or 2×3=6, we get: 4 + 3[8 – 6] ÷ 2
- There is one bracket left, [8 – 6] = 2, we get: 4 + 3[2] ÷ 2
- Solving 3[2] or 3 × 2 = 6, we have: 4 + 6 ÷ 2

We can observe that all the expressions in the brackets are solved. Based on PEMDAS, we know that division comes next, hence, 6 ÷ 2 = 3, that is, 4 + 3. And lastly, addition 4 + 3 = 7.

## FAQs on PEMDAS

### What does PEMDAS Mean?

PEMDAS means the order of operations for mathematical expressions involving more than one operation. It stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition and S- Subtraction.

### How does Pemdas Work?

In any arithmetic expression, if there are multiple operations used then we have to solve the terms written in parentheses first. After getting rid of parentheses, we solve multiplication and division operation, whatever comes first in the expression from left to right. Then, we will get a simplified expression with only addition and subtraction operations. We solve addition and subtraction in left to right order, whatever comes first and get the final answer. This is how PEMDAS work.

### How to do Pemdas with Fractions?

In an expression with fractional terms, there is no change in the use of PEMDAS rule. It is to be done in the same way as any whole number expression.

### What does the P stand for in Pemdas?

In PEMDAS, P stands for parentheses or brackets. The order for solving brackets is given as [{()}]. It means we always solve the innermost bracket first and then we move forward to curly brackets and square brackets.

### Do you Multiply or Divide First in PEMDAS?

In PEMDAS rule, we solve operations on multiplication and division from left to right. We can perform any operation, multiplication or division, whatever comes first in the expression.

### When do we Apply the PEMDAS Rule?

PEMDAS Rule is applied for solving difficult mathematical expression involving more than one operations like addition, subtraction, multiplication or division.

### What is the Rule for PEMDAS?

The PEMDAS rule gives us the correct sequence for solving a mathematical expression. In PEMDAS rule, operations are performed in parentheses first. Next, operations are performed on exponents or powers. This is followed by the operations on multiplication or division from left to right, whichever comes first. Finally,the operations on addition or subtraction are performed from left to right, whichever comes first.

## Solved Examples on PEMDAS

**Example 1:**

Simplify the expression by using PEMDAS rule: 18÷(8-2×3).

**Solution:**

Given expression: 18÷(8-2×3)

According to PEMDAS rule, we have to solve parentheses first. But, here, inside the parentheses, we have two operations, multiplication and subtraction. So, we have to multiply first before it comes first in PEMDAS. So, (8-2×3)= 8-6 = 2

Now, we can rewrite the expression as: 18÷2 as 18÷2= 9

∴ 18÷(8-2×3)= 9.

**Example 2:**

Simplify the expression by using the PEMDAS rule: (4×3÷6+1)×3^{2}

**Solution:**

- Step 1- First, we need to multiply 4 by 3 in the given expression, (4×3÷6+1)×3
^{2}, we get, (12÷6+1)×3^{2} - Step 2- Now, we need to divide 12 by 6 inside the bracket, so, we get, (2+1)×3
^{2} - Step 3- Remove parentheses after adding 2 and 1, we get, 3×3
^{2} - Step 4- Solve exponent, i.e 3
^{2}, which is 9, 3×9 - Step 5- Multiply 3 by 9 to get the final answer, which is, 3×9= 27

∴ (4×3÷6+1)×3^{2}= 27.

## Practice Questions on PEMDAS

**Here are a few activities for you to practice. **

**Select/Type your answer and click the "Check Answer" button to see the result.**