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Order of Operations

The order of operations dictates the sequence in which mathematical operations should be performed to ensure consistent results.



PEMDAS is an acronym used to remember the order of operations in mathematics. 


It stands for:


- Parentheses

- Exponents (including roots, such as square roots)

- Multiplication

- Division

- Addition

- Subtraction


The order of operations dictates the sequence in which mathematical operations should be performed to ensure consistent results. 



Here’s a detailed explanation of each step:

 

1. Parentheses (P)

Operations inside parentheses (or brackets) should be performed first. This includes nested parentheses, which are handled from the innermost to the outermost.


Example:



(3+2) × 5

First, solve the expression inside the parentheses:


5×5=25



2. Exponents (E)

Next, calculate all exponents (powers and roots).


Example:


23 + 4

8+4=12



3. Multiplication and Division (MD)

These operations are handled from left to right, whichever comes first. Multiplication does not always come before division.


Example:


20 ÷ 4 × 2 

First, perform the division:


5×2=10

 



4. Addition and Subtraction (AS)

These operations are also handled from left to right, whichever comes first. Addition does not always come before subtraction.



10−3+2

First, perform the subtraction



7 + 2 = 9




Practice:

Let’s solve a complex example step-by-step:



3 + 6 × (5 + 4) ÷ 323^2

    

Parentheses


3+6×9÷32     Exponents
3+6×9÷9    Multiplication and Division (from left to right):

3

3+54÷9    
3+6 Addition

3+6=9



Thus, the final result is 9.



Understanding and applying PEMDAS ensures that mathematical expressions are interpreted and solved correctly.