What Is Pemdas? - Definition and Examples

A mathematical expression requires performing multiple operations to reach a correct solution. There are certain PEMDAS rule which state the particular sequence in which these operations are to be done.

PEMDAS rule

One of the best and most convenient methods to remember the sequence of operations is called the PEMDAS rule. This is basically the short form for the order of operations to be used while solving the mathematical expressions. The full form of PEMDAS is given as follows:

P – Parentheses

E – Exponents (Powers and Roots)

M - Multiplication

D - Division

A - Addition

S – Subtraction

PEMDAS rule provides a simple way for learning the order of operations that needs to be followed. The PEMDAS method makes the calculations easier and gives the correct solution.

Explanation

• P: The first step is to perform the operation within the parentheses or brackets. There can be different types of brackets so the priority is given to small brackets ( ), then curly brackets { } and then big brackets [ ].
• E: The second operation is to solve the exponential expressions expressed in power or roots.
• MD: The next step is to perform the multiplication and division operations, whichever comes first in the equation while going from left to right.
• AS: Then the addition and subtraction are performed whichever operation comes first while moving from left to right.

 Points of PEMDAS

• P is the first letter which means the calculation starts with operations enclosed within the parentheses.
• E is the second letter that stands for exponents which are to be solved next.
• The third and fourth letters are ‘M’ and ‘D’ respectively which means multiplication and division but it does not mean that multiplication is to be done before division. We have to follow the order from left to right whichever operation comes first.
• The fifth letter is A (addition) and the sixth letter is S (subtraction) which are to be carried out next in the order that appears first from left to right.

Order of Operations

Any mathematical expression contains various terms and different operators like addition, subtraction, multiplication, division, etc. The order of operations is a rule that states that these operations are to be performed in a particular sequence while solving an expression.
The order of operations defines the method of performing operations in the specified order while solving any mathematical expression involving multiple operations. The rule to be applied for doing the operations mentions the sequence to be followed:
· Brackets ( ), { }, [ ]
· Exponents or order of powers, roots
· Division (÷) and Multiplication (×)
· Addition (+) and Subtraction (-)

Explanation of Order of Operations Rule

• The first operation is to solve the expression present inside the parentheses or brackets. There is a particular order to solve the parentheses, First, solve the round brackets ( ), then curly brackets { } and then box brackets [ ].
• The next step is to perform operations for any term involving exponents or roots.
• Next, the operation of multiplication or division is to be done in the order whichever comes first from left to right in the expression.
• Then the operation of addition and subtraction is to be performed in the sequence from left to right whichever comes first.

The easiest way to learn the order of operation is to follow the PEMDAS or BODMAS rule which is the acronym of the operations to be performed in sequence. This is explained as follows:

• First the brackets (B) or parentheses (P).
• Next is the order (O) of power or roots or exponential (E) terms.
• Then perform division (D) or multiplication (M)
•  Lastly, perform addition (A) or subtraction (S).

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