BODMAS

BODMAS stands for Brackets of Division, Multiplication, Addition, Subtraction. BODMAS is an arithmetic expression taught in the primary classes of their school life.

It sets the order for solving an equation that consists of various techniques of calculations. Some arithmetic scholars also call BODMAS as PEMDAS. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

BODMAS act as a guiding order of operation for solving an equation. The BODMAS rule says “To solve an equation, one must follow the following steps

  • Check whether the equation has any brackets (() [] {} ). In case the equation has any of these brackets, one must solve them in the mentioned order. 
  • The second thing one must solve in an equation is powers and roots.
  • After getting derived numbers, one must apply division, multiplication, addition, and then subtraction in the last.
  • The number you get after solving the equation in this order is the correct answer to the equation.

Let’s look into some examples –

  • 12 ˣ (10 +3)  

Now according to the BODMAS rule, the first step is to solve brackets.

So,

12ˣ (10+3)

 = 12ˣ (13)

 = 156

  • 1000 ÷ 10 {( 10-5) + (12 -6)}

The previous example had one simple bracket. In case the example has more than one brackets and two or different types of brackets. One must solve them in order of the BODMAS rule.

1000 ÷ 10 {( 10-5) + (12 -6)}

= 1000 ÷ 10 {5 + 6}

= 1000 ÷ 10 {11}

In the next step, we will again apply the BODMAS rule by first solving the division. 

Note – When there is a single number in the bracket after solving, multiplication has to be done.

= 1000 ÷ 10 {11}

= 100 {11}

=1100

After the understanding of the basics of BODMAS, one must also understand the certain rules and conditions that are applied in BODMAS. The failure to understand these rules and conditions will derive the wrong answer.

  • In case there is only one elementary arithmetic symbol in the equation, one can open the brackets first and then solve the equation.

For example, in the given condition –

4 + (6 + 1) 

There is only one elementary arithmetic symbol, hence according to BODMAS rule, one can open the brackets and solve it. Thus 

4 + (6 + 1)

= 4 + 6 + 1

= 11

  • In case there is a negative arithmetic symbol before the bracket, the numbers in the brackets will get multiplied with the negative arithmetic symbol. Here, BODMAS follows the basic rules of symbols –
+++
+
+
+

For example, in the given situation –

½ [{-2 (2+2)}10]

We will solve the brackets first, as per the BODMAS rule.

 ½ [{-2 (2+2)}10]

= ½ [{-2 (4)}10]

=½ [{- 8)}10]

=½ [- 80]

= -40

  • In case there are more than two or more terms inside the bracket, each term gets multiplied with the number outside the bracket, and then it will be solved. This rule of BODMAS is generally applied in the algebraic equations, where the characters are also associated with numbers.

For example, in the following condition, the equation will be solved as –

a ( b + c) + 2

= ab +ac + 2

BODMAS is a simple formula that helps people to solve complex equations and arithmetic expressions. Following the order of operation, one can solve any question without any difficulty.

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About the Author

Piyush values education and has studied from the top institutes of IIT Roorkee, IIM Bangalore, KTH Sweden and Tsinghua University in China. Post completing his MBA, he has worked with the world’s # 1 consulting firm, The Boston Consulting Group and focused on building sales and marketing verticals for top MNCs and Indian business houses.

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