The evaluation of an expression involving numbers is one of the basic tasks in arithmetic. If an expression contains addition ( + ), subtraction ( – ), multiplication ( x ), division (\(\div\)), bracket ( ), and Of( of ) , then the precedence of simplification of the operation is given by “ BODMAS “ rule. First we have to know that what is BODMAS rule? or What is BODMAS formula ? BODMAS rule is a rule or order that is used to simplify the expression involving more operators in mathematics. When an equation involving more operators first we have to know that in which order we have to solve the expression. This problem is solved with the help of BODMAS rule.

The BODMAS acronym is

**B**rackets( Parts of a calculation inside the bracket always come first).

Precedence of brackets are : [ { ( bar ) } ]

**O**rders (powers and square roots)**D**ivision**M**ultiplication**A**ddition**S**ubtraction

Each letter of the word stands for the first letter of an operator. If an expression involving two or more similar operators that appear in succession, then the precedence is from left to right. By using BODMAS, we can evaluate an expression in the correct order of precedence. Anything inside the bracket is done first. Then evaluate any powers or roots. Next do any division or multiplication in an expression working from left to right and then followed by addition and subtraction again from left to right. Here, division and multiplication have the same priority and addition and subtraction have the same priority.

## What is BODMAS in Maths ?

Mathematics is a logic based discipline. In arithmetic, an expression or an equation involves two components namely,

- Numbers – A number is a mathematical value which is used for representing a particular quantity and it is used in counting and making calculations. The symbol that represents a number is called a numeral. According to the property, numbers can be classified as
- Natural Numbers
- Integers
- Rational Numbers
- Irrational Numbers
- Real Numbers
- Complex Numbers
- Imaginary Numbers

- Operators or operations : An operator is a character which combines two numbers and produces an expression or equation. The most common operators used in mathematics are :
- Addition : “ + “
- Subtraction : “ – “
- Multiplication : “ x “
- Division : “ ÷ ”

In mathematics, the order of operations or the operator precedence is given by BODMAS rule. The symbol used for grouping the value is bar. Grouped symbols is treated as a single expression. Since math is the foundation of all the subjects, some rules exist to simplify the process of calculation.

## Sample Example

Problems on BODMAS rule involving integers and decimals values are given below

### Question 1 :

Find the value of 2[2+2{39-2(17+2)}]

### Solution :

Given, 2[2+2{39-2(17+2)}]

By using BODMAS Rule,

First simplify the value inside the brackets ( )

= 2[2+2{39-2(19)}]

= 2[2+2{39-38}]

subtract the value inside the brackets { }

= 2[2+2{1}]

= 2[2+2]

Add the value inside the brackets [ ]

=2[4]

Finally multiply both values which gives 8.

Therefore, the value of 2[2+2{39-2(17+2)}] is 8

### Question 2 :

Find the value of 4.5 – [2 + 0.5 of ( 2.1 – 1.3 x 1.01)]

### Solution:

Given, 4.5 – [2 + 0.5 of ( 2.1 – 1.3 x 1.01)]

By using BODMAS Rule,

First simplify the value inside the brackets ( )

= 4.5 – [2 + 0.5 of ( 2.1 – 1.313)] “ Multiply 1.3 x 1.01 “

= 4.5 – [2 + 0.5 of 0.787 ] “ Subtract 1.313 from 2.1 “

simplify the value inside the brackets [ ]

= 4.5 – [2 + 1.4435 ] “ Multiply 0.5 x 0.787 “

= 4.5 – 3.4435 “ Add two values inside the brackets [ ]

Finally Subtract the values

= 1.0565

Therefore, the value of 4.5 – [2 + 0.5 of ( 2.1 – 1.3 x 1.01)] is 1.0565.

To solve more problems on arithmetic operations using BODMAS rule and other rules that simplify the expressions, register with BYJU’S – The Learning App and also watch interactive videos.