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BODMAS Rule

We all have dealt with this term in our maths class. Wonder why do we need a BODMAS rule to perform calculations, when we all are aware of how to go about adding, subtracting, multiplying, and dividing? 

Do we need this concept to assist in calculations? 

Well yes we do. Not observing the BODMAS will land us in a soup with the maths instructor and also leave us frustrated, with incorrect answers,  despite all our hard work.

What is BODMAS?

The full form of BODMAS is Brackets, Orders, Division, Multiplication, Addition, Subtraction.

When an expression is presented with multiple operations in maths, BODMAS theory is used to stop us from going ahead and just calculating from left to right or in a haphazard manner. It points out the correct order or sequence to be followed while solving the maths problem.

What are the mathematical operations?

The four main operations in maths are:

  • Addition ( + )
  • Subtraction ( – )
  • Multiplication ( x )
  • Division (÷)

Why BODMAS?

Maths is all about logical interpretations and systematic solving of problems. Hence it requires certain set procedures to be observed. It is easy to perform one function, like addition, with two or three numbers. But if a question involves more than one operation, it can be confusing to solve the problem without guidance. And of course, without a rule to assist us, our answers would be a disaster!

It is here that BODMAS steps in. It allows for quick calculations and sequential processing of the expression given. Like, multiplication is given precedence over division .

Example:

( 3 + 4) x 5 = 35 is incorrect. 

3 + ( 4 x 5 ) = 23 is correct

The brackets given like:  ( ), {}, []   signify that the expressions given in them have to be calculated first, followed by any powers or roots provided (called order). Then we must move on to division, multiplication, addition and subtraction. 

The following tables can help you understand better:

BODMAS
Brackets[ ], { }, ( )Ordersx2, √xDivision÷Multiplication×Addition+Subtraction–
BBRACKET10 x ( 2+3)= 10 x 5= 50
OOF4 + 22 = 4 +4 =8
DDIVISION2 + 6 ÷ 3 = 2 + 2 = 4
MMULTIPLICATION12– 5 x 2 = 12 – 10 = 2
AADDITION10 – 2 + 5 =10 – 7 = 3
SSUBTRACTION12 – 4 + 3 = 12 – 7 = 5

Now let us go through  a few examples to see its application:

Example :

Solve 567– 78 (13x 4 – 8 x 12)

Solution:

As per the BODMAS rule, we will  start by dealing with the brackets first. In the bracket itself, we have 2 different operations, subtraction and multiplication. If we follow the rule, multiplication should be performed first.

428 – 60 ( 6 x 7 – 12 x 4)

428 – 60 (42 – 48)

428 – 60 – 6

The property of integers suggests – and – becomes +, therefore

428 – 66

= 362

Therefore, the answer is 362

Example :

Find the value of x in the following equation 3126 + x + 456 = 340

Solution:

3126 + x + 456 = 340

We will first rearrange the equation

3126 + 456 + x = 340

Using the BODMAS rule, we will attempt the addition operation

3582 + x = 340

Shifting 3582 to the other side of the equation, we get

x = 340  –  3582

= – 3242

Therefore, the answer is – 3242.

How to deal with brackets ?

Brackets mean that, simplification of terms inside the brackets can be done directly and first, before any other calculation.  We must perform the operations inside the bracket in the order of division, multiplication, addition and subtraction.

Note: The order of brackets to be simplified is (), {}, [].

The following examples will help you grasp the rule of brackets:

Example :

Solve 160÷10{(5-3)+(6−4)}

Solution:

 160÷10{(5−3)+(6−2)}

Step 1: Simplify the terms in the bracket {}.

Step 2: Then follow DMOS.

160÷10{(5−3)+(6−2)}

160÷10{2+4}

⇒160÷10{6}

= 160÷10×6

= 16×6

= 96

Example :

Solve 1/4[{−4(1+3)}10]

Solution :

Step 1: Simplify the terms inside () followed by {}, then [].

Step 2: Then proceed with other calculations..

1/4[{−4(1+3)}10]

= 1/4 [{–4(4)} 10]

= 1/4 [{–16} 10]

= 1/4 [–160]

= -40

What should you not forget?

Follow the distributive property while working with brackets, which state that a (b + c) = ab + ac. 

Example:

Simplify 6 ( 4 + 3 )

To use the Distributive Property a ( b + c ) = ab + ac

6 ( 4 + 3 ) = 6 x 4 + 6 x 3

= 24 + 18

= 42 is you answer

There is no doubt that it is mandatory to have a stronghold over this concept from the start. All those who are attempting various competitive examinations or preparing for SAT, GMAT or GRE, should have the capability to handle BODMAS. 

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