**BODMAS Rule: **A simple arithmetic expression involving two numbers and a single operation is easy to solve. But what about expressions with multiple numbers and operations? While solving expressions with multiple operations, if we work on the operations, for example, as they appear from left to right, you might not get the correct answer. How do we know which particular operation to solve first then? This is where the BODMAS Rule saves us.

In this article, we will tell you what is BODMAS rule and what is the order of arithmetic operations.

## BODMAS Rule: Order Of Arithmetic Operations

Arithmetic operations include mathematical operations like addition, subtraction, multiplication, and division.

While solving expressions that include multiple operations, we cannot just randomly pick up and solve the different operations. This won’t give you the correct answers.

There is a certain order in which arithmetic operations are to be solved in order to arrive at the correct answer. This is where the BODMAS Rule comes to the picture.

### What Is BODMAS Rule?

BODMAS is an acronym that stands for:

B = Brackets

O = Of

D = Division

M = Multiplication

A = Addition

S = Subtraction

This means while solving arithmetic expressions with multiple operations of various types:

- a. First, the expressions within the brackets ( (), {}, []) are to be solved irrespective of the operators inside the brackets.
- b. Next, the square roots and numbers with powers are to be solved. The O in BODMAS stands for Of or Order.
- c. Then, we must solve the division operation, followed by multiplication, addition, and lastly, subtraction.

Note that, ‘()’ is the first bracket, whereas ‘{}’ and “[]” are second and third brackets respectively. While solving expressions with different brackets, expressions with the first bracket should be solved first, followed by send and then third. |

Let us elaborate on it with an example.

Consider the following expression:

*a – (b – c) + d X e ÷ f*

We have to solve this expression in the following order or sequence:

i. **Bracket: **First, we have to find the value of ** (b – c)** which is inside the bracket. Let’s say, it’s A, i.e

**(b – c) = A**.

ii.

**Division:**Then we have to find the value of

**Let’s say, it’s B, i.e**

*e ÷ f.*

*e ÷ f = B.*iii.

**Multiplication:**The resultant value, B is to be multiplied by d. Let’s say,

**B X d = C**.

iv.

**Addition:**Now, we have to add the result of (b – c) that is A to C. Let the result be D.

v.

**Subtraction:**Now, we have to subtract D from a to arrive at the correct answer.

### BODMAS Rule Examples

Let us now go through some of the examples of BODMAS Rule:

**Example 1:** Solve: 5 – 6 X 4

**Solution:**

As multiplication (M) comes before subtraction (S), we have to find the value of 6 X 4 first and then subtract it from 5.

So,

5 – 6 X 4

= 5 – 24

= -19

**Example 2:** Solve: 10 ** ÷** (5 + 5)

**Solution:**

As per BODMAS Rule, the expressions within brackets are to be solved first. So, in this problem, we have to find the addition of 5 and 5 within the bracket first. Then we have to divide 10 by the result of the addition.

10 ** ÷** (5 + 5)

= 10

**10**

*÷*= 1

**Example 3:** Solve: 10 ** ÷** 5 + 5

**Solution:**

This problem may look similar to the one in Example 2 but here there is no bracket. So, as per BODMAS Rule, here we have to solve the division first followed by the addition.

10 ** ÷** 5 + 5

= 2 + 5

= 7

So, you see, the results are entirely different based on the order in which you solve the operations.

**Example 4:** Solve: 10 ** ÷** [(5 + 5) X {(4 X 2) – (5 – 2)}]

**Solution:**

10 ** ÷** [(5 + 5) X {(4 X 2) – (5 – 2)}]Solving the expressions within the first brackets, we get

= 10

**[10 X {8 – 3}]Solving the expression within the second bracket, we get**

*÷*= 10

**[10 X 5]**

*÷*Now, solving the expression within the third bracket, we get

= 10

**50**

*÷*= 0.2

So, now you know how to go about solving arithmetic expressions with more than one operation. We hope this detailed article helps you. Solve more questions involving BODMAS Rule from your textbook and you will get a hang of it.

### Other Articles On Maths

Some other helpful articles by Embibe are provided below:

HCF And LCM | Properties Of Triangles |

Maths is a subject that is important not only for school-level exams and engineering and medical entrance exams for students of the Science stream but also for others. Basic knowledge of Mathematics and numerical ability are tested in other exams as well, for example, various exams for government job recruitment. It is therefore important that you take the subject seriously and get your basics clear.

Students of Class 8, 9, 10, 11, and 12 can solve free Maths questions on Embibe. The links are provided below:

a. Class 8 Maths Practice Questions |

b. Class 9 Maths Practice Questions |

c. Class 10 Maths Practice Questions |

d. Class 11-12 Maths Practice Questions |

So, make the best use of these resources and master the subject.

*If you have any queries, feel free to ask in the comment section below. We will get back to you at the earliest.*

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