Application of BODMAS

BODMAS is an order in which the mathematical operations are to be applied.The B in BODMAS stands for Bracket . For example in this problem ( 4+3)× 4 we will first solve the operation in the bracket then we will multiply .So B means solving the Operation in the bracket. Then comes O , O in BODMAS stands for order which means the square root order in the problem under consideration.Also the rule of BODMAS is sometimes written as BIDMAS replacing the order by indices . After Order comes Division Operation so that is performed then multiplication , addition and subtraction.

Simply put the problem is solved starting with Bracket and then followed by order , division , multiplication, addition and subtraction.

Importance of BODMAS 

• It is an easy way to solve and tackle complex mathematical problems.
• It helps students in approaching the problem in the right way. 
• It helps in remembering what hierarchy to be followed as the mnemonic or acronym

Exceptions to rule and it’s application

• The rule is not applicable in every problem .It does have some exceptions to it 

Rules 

• Division and multiplication is of equal weightage and importance and  the order to be followed while solving a problem with both Multiplication and division will be from left to right .
• Similar is the case of the addition bags subtraction. They have the same weightage but the order to be followed will be from left to right which comes first . 

Difference between BODMAS and BIDMAS

• BODMAS stands for Bracket Order Division Multiplication Addition and subtraction while BODMAS stands for Bracket Indices Division Multiplication Addition and subtraction.
• Simply a chance of Order by Indices.

Application 

Explanation of application of BODMAS rules with some examples.

The following examples will help in understanding how the simplification of these problems gets easy to deal with one BODMAS rule .

EXAMPLE  : Use of Bracket concept 

Solve – 

• 400+( 60×9) 

Here we will first solve the bracket operation according to the rule followed by addition . So this solution goes like this -: 400+ ( 540)= 940 is the answer

• 10÷ ( 4+8-9 ) 

In this problem we will solve the bracket operation but as in this problem there are multiple bracket operations we will again apply the BODMAS rule from left to right . As addition comes first so we will first add followed by subtraction and then division. So the solution is -: 10÷(12 -9) = 10÷( 3)=3.3approx.

• (12×5+6) -22

In the above problem as the bracket has multiple operations so we will use the rule in the bracket according to which first we will have Multiplication then addition.so the solution is -: 12×5 = 60+ 6 = 66-22 = 44 .

Types of brackets 

In mathematics we have different types of brackets; these are round brackets , square brackets and angular brackets and so on .The three main are as follows -:

1. Round brackets – These brackets are most commonly used and are known as Parentheses.These are represented by the symbol -()
2. Square brackets – These brackets are also known as box brackets as when combined they give a box shape. These are represented by this symbol -[]
3. Curly Bracket – They are called so because of their shape and the other name for curly brackets in braces . They are represented by this symbol – {}

Order of brackets 

When an problem has multiple brackets then the following order is followed for the above mentioned three brackets -:

1. First solve the round  brackets or the parentheses.
2. Second solve the curly brackets or braces 
3. Third, solve the square or box brackets .

Round brackets-Curly Brackets- Square brackets

() Followed by {}followed by []

EXAMPLES : Use of order concept

• 5+72

In this problem we will first do the square of seven and then add it to 5 hence we get 7×7 = 49 followed by adding 5 to it.So 5 + 49 = 54.

• 23+(4×10) +82

In the above mentioned question we have both bracket and order and both of equal importance so in this case we will use the left to right rule . As we can see that the operation for brackets is to the left of order so it will be performed before that .So the solution goes like this -:

23+( 40) +82 = 23+40+64 = 63+64=127

• 18+53×100

As the above mentioned example has a square so the hierarchy of solving starts from square then multiplication follows. Y addition.

The solution is as follows -:

18+125×200= 18+25000=25018

EXAMPLES :Use of division 

• 2+6-8÷2

In the given problem the Operation of division is followed by that of addition then Subtraction.

The solution is -:

2+6-4=8-4=4 is the final answer.

EXAMPLES: Use of Multiplication 

• 12×5+6-8

here multiplication followed by addition then Subtraction

60+6-8=66-8=58

EXAMPLES : Use of Addition and subtraction

• 14-6+8

addition – Subtraction ( order)

14-14=0

If we don’t follow the order the answer will be different .

If we start 14-6 which is 8 plus 8 than answer will be 16 not 0

Some complex problems 

• [ 23+(5-8×9)]×2

In this problem we will first solve the round brackets so we get (5-8×9)=(5-72)=-67 followed bybox brackets – hence we will add 23 +(-67) =23-67= -44 thus will be multiplied by 2 that is -44×2 = -88 which is the answer.

• 30-[23- {3+9-(8+5)}]

So this problem is of Multiple brackets the order is as follows -()-{}-[]

So the round brackets has 8+5= 13 followed by curly brackets {3+9-13} that will be addition followed by Subtraction so we get 12-13 = -1 than box brackets 23-{-1}= 23+1 =24 than finally the outer part 30 – 24 =6 

Conclusion

BODMAS is an logical arrangement of operation like the bracket ,order, division, multiplication addition and subtraction.It is an easy and handy way to tackle complex mathematical problems.

This acronym is easy to remember the order of the operations.