What is BODMAS Rule – Full Form, Formula, Example in Mathematics

BODMAS Rules Definition

In mathematics, the order of operations or operator precedence is defined to solve a mathematic expression to determine which procedure or function takes priority. That order of operations takes the form of the BODMAS rule in mathematics. The BODMAS convention is to ensure that there is no ambiguity while solving an expression.

BODMAS full form

The BODMAS full form is

• Brackets(the expressions and operator inside the bracket takes preference.)
  Rule of order for brackets is: [ { ( bar ) } ]
• Orders ( square roots and powers) and ‘of’
• Division
• Multiplication
• Addition
• Subtraction

BODMAS Rule	BODMAS: The order of precedence	Operators
B	Brackets	[ { ( bar ) } ]
O	Of (order)	of
D	Division	‘/’ or ‘÷ ‘
M	Multiplication	‘*’ or ‘x’
A	Addition	+
S	Subtraction	–

BODMAS Rule full form explains the rule of order for simplification expressions. An individual letter of the term stands for the first letter of an operator. When a mathematical expression and has two or more similar operators, then the precedence is to follow from left to right.

Also Read: Basics of Simplification with important concepts & new pattern questions

Any mathematical expression contains two major things, numbers, and operators. Let’s understand the type of numbers and operators that can be solved using the BODMAS formula.

Numbers or Numerals are values that denote a particular magnitude or quantity. In mathematics, there are categorized into two major sections: Counting Numbers and Scalars.

Counting Numbers are whole numbers and no fractional part is included. Scalars are a more accurate representation of numbers as it contains a decimal part. There are :

• Real numbers
• Integers
• Positive and negative numbers
• Rational and Irrational numbers
• Imaginary numbers
• Complex numbers
• Prime numbers and composite numbers

An operator is also used for expressing the symbol of a mathematical operation. They are used to convert a number into an expression. When two or more numbers are used along with an operator, it is called a mathematical expression. There are as follows:

• Addition: “ + “
• Subtraction: “ – “
• Multiplication: “ x “
• Division: “ ÷ ”

BODMAS Rule Formula & Examples

Let’s understand the use of the BODMAS rule with some BODMAS examples:

Simplication of brackets

Like the letter, ‘B’ in BODMAS stands for Brackets and there are multiple types of brackets, there is an order of precedence for the brackets. The rule of precedence is: [ { ( bar ) } ].

BODMAS Example: Simplify: 78 – [24 – {16 (5 – 4 – 1)}]

Solution:

78 – [24 – {16 – (5 – 4 – 1)}]

= 78 – [24 – {16 – (5 – 3)}] [Removing vinculum]

= 78 -[24 – {16 – 2}] [Removing parentheses]

= 78 – [24 – 14] [Removing braces]

= 78 – 10

= 68.

BODMAS Example: Solving the given expression 52 – 4 of (17 – 12) + 4 × 7 using BODMAS formula

Solution:

52 – 4 of (17 – 12) + 4 × 7

= 52 – 4 of 5 + 4 × 7, (as per the BODMAS rule, solving the bracket first )

= 52 – 4 × 5 + 4 × 7, (BODMAS rule : solving Order -‘of’)

= 52 – 20 + 4 × 7, (BODMAS rule : Solving multiplication 4 × 5 = 20)

= 52 – 20 + 28, (BODMAS rule : Solving multiplication 4 × 7 = 28)

= 32 + 28, (BODMAS rule : Solving subtraction 52 – 20 = 32)

= 60, (BODMAS rule : Solving addition 32 + 28 = 60)

You must practice BODMAS rule examples to get good conceptual clarity and usage of the rule. The BODMAS rule is highly relevant for the upcoming examinations like SBI PO, IBPS PO, SBI Clerk, IBPS Clerk, and many other Banking Exams.

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