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Monday, September 23, 2013

How to Apply BODMAS (Order of Operations) Principle / Rule ?

20 comments

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In a problem where more than two operations ('operations' mean add, subtract, multiply and divide etc) are involved, the BODMAS rule is followed. Do you know what each of these letters stands for ?

Look at this
  • B - brackets
  • O - of (multiplication)
  • D - division
  • M - multiplication
  • A - addition
  • S - subtraction
This order should be followed while solving problems with more than one mathematical operation.

Example 1 : Simplify 3 of 4 X 5 % 6

Solution : Three operations need to be done here. According to the BODMAS rule, we begin with 'of', then 'multiplication' and finally we perform 'division'

3 x 4 x 5 % 6  = 12 x 5 % 6 = 60 % 6 = 10

You should remember that if 'BODMAS' rule is not followed in case of one mathematical operation each method may give a different result.

Look at the following example, subtraction is followed by multiplication.

6 - 3 X 2

(6-3) x 2 = 3x 2  = 6
Alternate method (multiplication is followed by subtraction)

6 - 3 x 2

6 - 6 = 0

Although both methods seem correct, there cannot be two different answers to the same problem. There has to be one standard method. Hence the "BODMAS" rule is followed.

Example 2 : Simplify 4 + 5 x 12 - 6

Solution :

Applying the BODMAS rule, we get the following result
4 + 60 - 6

64 - 6 = 58

Example 3 : Simplify 5 + 7 x 15 % 5
Solution : According to the BODMAS rule, we first perform multiplication followed by addition.
5 + 7 x 3

5 + 21 = 26

Example 4 : simplify 5 of 4 + 2 x 2 % 2
Solution : Here, the first operation to be performed is 'of'
20 + 2 x 2 % 2
20 + 2 x 1
20 + 2 = 22

Example 5 : 30 - (2 x 6 + 15 % 3) + 8 x 3 % 6
Solution : Here,
let us remove the brackets first,

so (2 x 6 + 15 % 3) becomes (12 + 5 ) = 17

Now, 30 - 17 + 8 x 3 % 6
= 30 - 17 + 8 x 1/2
= 30 - 17 + 4 = 17

Some important points to remember about BODMAS rule :

  1. If an expression contains brackets, you should solve the expression within brackets first.
  2. If the expression involves 'of' (as we have mentioned in one of the above examples), multiplication (or division), addition and subtraction, then 'of' should be performed first, followed by multiplication or division. Then proceeding from the left to the right, addition and subtraction are carried out in the order in which the sign of addition and subtraction are given. It should be noted that if the expression contains 'of' and 'division' always do 'of' first and then do 'division' in order to get the correct answer.
  3. Some problems may have certain numbers written in brackets or may contain more than one bracket. Such problems are solved with the help of following rule.
    • Let us look at the sequence of brackets to be removed
      • First bracket to be removed is the line "_______" bracket or the vinculum.
      • Second bracket to be removed is the simple ( ) bracket.
      • Third bracket to be removed is the curly { } bracket
      • Fourth bracket to be removed is the square [ ] bracket
Example 6 : 
   


Solution : '5+2' is the first operation here followed by other bracketed operations.
= [4 x {7 +(9-7)} + 3 ]
= [ 4 x {7+2} + 3]
= [ 4 x 9 + 3 ]
= 36 + 3 = 39 

Example 7 : 1 + {1 % [1+1 % (1+ (1%4))]}

Solution : 

= 1 + { 1 % [1 + 1 % (1 +  % 4) ] }
= 1 + {1 % [ 1 + 1 %  1 + 1/4)]}
= 1 + { 1 % [ 1 + 1 % (5/4) ] }
= 1 + { 1 % [ 1 + 4/5]}
= 1 + 1 % 9/5}
= 1 + { 5/9}
=  14/9

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20 comments:

  1. Shivani, example 4 is some mistake u think so chk it once

    ReplyDelete
    Replies
    1. Its a typing mistake Jyothi. I was intended to type "%". But instead of that I typed 5. Thank you so much for pointing out the mistake. Corrected it now :)

      Delete
  2. Thanks for sharing..

    ReplyDelete
  3. Ex 4: 5 of 4+2 * 252
    =>. 20 + 2 * 252
    =>20 + 504 =524 chk it shivani .

    ReplyDelete
  4. i think its a typing mistake

    ReplyDelete
    Replies
    1. Yes it is friend. Corrected it now. Sorry for the inconvenience.

      Delete
  5. Thanks. mam, we visually impaired using this site, pls avoid images very difficult to understand.. what does that venkulam does in that example? how does the question appears as it is an image.

    ReplyDelete
    Replies
    1. Vinculum is a horizontal line friend. We place it over a mathematical expression to indicate that it is to be considered grouped together (same as brackets). And that image consists of a mathematical problem of [4x{7+(9-5+2)}+3], here 5+2 has vinculum over it. Hope you got the question now.

      And thanks for the support. We will try to reduce images from now onwards. Good day :)

      Delete
  6. Ma'am please help me how to solve this using BODMAS 8/2(5-7+4)*2=?

    ReplyDelete
  7. Dear ma'am, in exp. 5 i think BODMAS is breaked ... if we go by it ans will be 9 instead of 17.... pls clear my doubt....

    ReplyDelete
  8. what if a zero is comes in b/w calculations i.e if the question is somethng like dis
    6-1*0+2/2=????
    1)we will divide first i.e 2/2=1
    2)we have multiply i.e 1*0=0
    3)it becomes 6-0+1=???? what should we do we have to consider 0 or neglect it?? kindly answer

    ReplyDelete
    Replies
    1. neglect with its sign then we left with 6+1 = 7
      thanks

      Delete
  9. Could anyone please solve this & tell me how to solve it..
    14+3(34-18-14)/3(6*2+17-2*7) & the answer of this ques. is 16.

    ReplyDelete
    Replies
    1. Starting with the last term i.e. 3(6*2+17-2*7).
      first multiply 2 with 7 i.e. 14 and then 6*2 i.e. 12, so the total comes out to be 3(15)
      then proceed to 3(34-18-14) which comes out to be 3(30). divide these two terms means 3(30)/3(15) which gives you 2 i.e. 14 + 2 = 16
      Then add it to 14 which would give you the desired answer.

      Or else you can start with second term also which is in bracket i.e. (34-18-14).
      Either way you will get the same answer, but first solve the terms in bracket then proceed.

      Thanks.

      Delete
    2. bhai tere jaise hi hote ho jo kahte hii 2+2= 5.

      by the way 34-32=30 ye kis maths ki book me hii pls tell me

      Delete
  10. 6-1*0+2/2 then what is the answer?

    ReplyDelete
  11. Here is the answer
    36/6×6
    6×6
    36

    ReplyDelete
  12. Hi Avela Bololotye... here you go

    (6-1×0)+2/2
    (6-0)+2/2
    6+2/2
    6+1
    7

    ReplyDelete

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