PEMDAS

PEMDAS is the guideline that helps us to understand the correct order for solving math problems. It reminds us to first work on anything inside the Parentheses, then solve the Exponents, then substitute the Multiplication or Division (from left to right), and finally complete the Addition or Subtraction (also from left to right). Following PEMDAS helps us to get the correct answer, even for long or tricky expressions.

Let’s see a PEMDAS example:

Question:

Use the PEMDAS rule to simplify the expression:

\(8 + (3 × 4)² ÷ 6\)

Answer:

Use PEMDAS in step-by-step

Step 1: Start with parentheses

\((3 × 4) = 12\)

Now the expression becomes:

\(8 + 12² ÷ 6\)

Step 2: Substitute exponents

\(12² = 144\)

Now:

\(8 + 144 ÷ 6\)

Step 3: Multiplication/Division (left to right)

\(144 ÷ 6 = 24\)

Now:

\(8 + 24\)

Step 4: Addition/Subtraction

\(8 + 24 = 32 \)

Answer: 32

BODMAS and PEMDAS are two important rules in solving complex expressions involving different arithmetic operations. The differences between BODMAS and PEMDAS is given below:
 

When a math expression includes multiple operations like addition, subtraction, multiplication, division, exponents, or parentheses, we must follow a specific order to get the correct answer. This fixed sequence is known as PEMDAS.

PEMDAS stands for:

P stands for Parentheses:

Solve anything inside brackets first: ( ), { }, [ ]. These always get the highest priority.

E stands for Exponents:

Next, simplify powers and roots (e.g., 2², 4³, √16).

M and D stand for Multiplication and Division:

Then perform multiplication or division, moving left to right. These two are on the same level; whichever comes first from left to right is solved first.

A and S stand for Addition and Subtraction:

Finally, add or subtract, again working left to right. These also share the same level of priority.
 

The PEMDAS rule helps us to follow the correct order of operations when solving math problems that contain more than one operation. It tells us which steps to do first, ensuring the final answer is correct.
A key point to remember is that:
 

• Multiplication and division are inverse operations,
   
• Addition and subtraction are also inverse operations.
   

Because each pair works together, they are treated equally in the order of operations.

So, instead of thinking “multiplication before division” or “addition before subtraction,” we solve them from left to right in the order they appear.

That’s why teachers often show PEMDAS with:
 

• M/D on the same level
   
• A/S on the same level
   

This makes it clear that these operations are performed according to their left-to-right position, not by strict priority.

 

Now, let’s learn when to use PEMDAS. It is used to solve expressions that contain more than one operation.

We use PEMDAS in math to provide a structured approach to finding the correct answer. When applying PEMDAS, we first solve the operations within the parentheses or brackets, and next, we solve the exponential expression. For operations of equal precedence, perform calculations from left to right.

Understanding PEMDAS becomes much easier when you know a few smart techniques. These tips and tricks help students remember the order of operations, avoid common mistakes, and solve expressions correctly.
 

• Don’t try to solve everything at once. Circle or highlight each part (parentheses → exponents → MD → AS) as you complete it.
   
• Multiplication/Division and Addition/Subtraction are equal pairs. Always solve them from left to right, not by strict order.
   
• If an expression has multiple types of brackets, follow this order: ( ) → [ ] → { }.
   
• Check for hidden multiplication; expressions like 2(3 + 4) mean 2 × (3 + 4). Always look for multiplication next to parentheses.
   
• A PEMDAS calculator helps students to check their answers and understand where they made errors. It should be used only after they have tried solving it manually.
   
• Show how the order matters in daily activities, like following steps in cooking or assembling a toy. This helps kids understand why the PEMDAS rule is essential in solving math problems correctly.
   
• Regular practice using a PEMDAS worksheet helps children to understand the order of operations better. Worksheets also help them spot errors and build accuracy.

In daily life, there are many situations where we need to solve the sequence of operations in math. Now let’s learn how PEMDAS is used in various sectors. 
 

• In construction, to calculate the loads and stresses for designing structures, we use PEMDAS.  
   
• In computer science, to ensure algorithms follow correct logic in calculation, we use PEMDAS.
   
• To calculate accurate medication dosages, pharmacists use the PEMDAS rule.
   
• PEMDAS is essential for solving multi-step mathematical problems..