PEMDAS Explained – How Does PEMDAS Work?

When solving math problems with multiple operations, it’s important to follow the correct order to get the right answer. That’s where PEMDAS comes in. PEMDAS is the fundamental rule of calculations in maths to find out which operations to do first, so your answer is always accurate.

Without a clear order of operations, two people solving the same equation could end up with completely different answers. PEMDAS is a standard mathematical process to follow, starting with parentheses and ending with addition and subtraction. Let’s learn everything about PEDMAS in this article.

What is PEMDAS?

PEMDAS stands for:

• P: Parentheses
• E: Exponents (powers or square roots)
• M: Multiplication
• D: Division
• A: Addition
• S: Subtraction

PEMDAS is used to first solve anything inside parentheses, then move to exponents, followed by multiplication or division (from left to right), and finally, addition or subtraction (also from left to right). By following PEMDAS, we ensure we solve it in the right order.

PEMDAS Rules Explained

The PEMDAS rules are a standard set of guidelines that tell us the correct order in which to solve mathematical expressions. Without these rules, calculations could be done in the wrong order, leading to different or incorrect answers. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

P – Parentheses: Solve anything inside parentheses or brackets first.

E – Exponents: Next, calculate powers or square roots.

M – Multiplication

D – Division

→ Solve from left to right, whichever comes first.

A – Addition

S – Subtraction

→ Also solve from left to right, whichever comes first.

Let’s understand this with an example –

Expression:
(6 + 3) ² ÷ 3 − 2 × 2 + 5

1. Step 1: Parentheses
   Evaluate inside the parentheses:
   6 + 3 = 9
   Now the expression becomes:
   9² ÷ 3 − 2 × 2 + 5
2. Step 2: Exponents
   Apply the exponent to the result from the parentheses:
   9² = 81
   Now the expression becomes:
   81 ÷ 3 − 2 × 2 + 5
3. Step 3: Division
   Perform the division from left to right:
   81 ÷ 3 = 27
   Now the expression becomes:
   27 − 4 + 5
4. Step 4: Multiplication
   Now do the multiplication:
   2 × 2 = 4
   Now the expression becomes:
   27 − 4 + 5
5. Step 5: Subtraction
   Now subtract:
   27 − 4 = 23
   Now the expression becomes:
   23 + 5
6. Step 6: Addition
   Finally, add:
   23 + 5 = 28
7. Final Answer: 28

BODMAS vs PEMDAS: What is the Difference

Both PEMDAS and BODMAS help in solving math expressions correctly. The difference lies in the terminology used in different regions. While PEMDAS is common in the United States, BODMAS is widely used in the UK, India, and other countries.

Element	BODMAS Term	PEMDAS Term
B / P	Brackets	Parentheses
O / E	Orders (powers/roots)	Exponents
D	Division	Division
M	Multiplication	Multiplication
A	Addition	Addition
S	Subtraction	Subtraction

When to Use PEMDAS

PEMDAS should be used every time you are solving a mathematical expression that has more than one operation. Without using it, you might do the steps in the wrong order and get an incorrect answer. It’s especially helpful in algebra, word problems, and multi-step equations.

You should use PEMDAS when:

• Solving expressions with multiple operations
• Working through algebraic equations
• Handling word problems with calculations
• Evaluating formulas in science and engineering
• Completing multi-step math problems in school or on exams

Common Mistakes While Using PEMDAS Rule

Even when students remember the PEMDAS acronym, small misunderstandings can lead to big calculation errors. Below are some of the most frequent mistakes and how to avoid them.

• Ignoring parentheses: Skipping operations inside parentheses is a major error. Always start with what’s inside the brackets, no matter what follows.
• Treating PEMDAS as a strict order: Many people mistakenly think multiplication always comes before division, or addition before subtraction. In reality, multiplication and division (M/D) are done from left to right, whichever comes first. The same goes for addition and subtraction (A/S).
• Combining steps too quickly: Trying to do multiple operations at once, especially without writing them down, can be confusing. Process the calculation step by step.
• Not using the left-to-right rule: For M/D and A/S, operations must be carried out from left to right. Doing them out of order breaks the rule and changes the answer.
• Skipping re-checks: It is important to check your calculation once you are done with this. Rushing through without checking work can lead to missed signs or forgotten steps, especially with negatives or exponents.

Conclusion

PEMDAS is a simple yet powerful tool that brings order to mathematical problems. It helps you solve expressions correctly by guiding you through each operation in the right sequence. Mastering PEMDAS builds confidence, improves accuracy, and prepares you to handle more advanced math with ease.