Mathematics Operations - Hierarchy ( BODMAS )

 Points to be understood clearly        Practice Test

1)  ×  and  ÷  are of equal ranks 

2) + and    –.  are of equal ranks

3) The operations ×  and  ÷    are always  higher rank than  + and    –.   So if all the four or three operations are there,  then first  we have to do   ×  and  ÷  and then we have to do  + and    –. 

4(i)Within the operations  ×  and  ÷ (that is  if these two operations occur simultaneously) we have to do the operations from left to right.

 4(ii)Within the operations  + and    –  (that is  if these two operations occur simultaneously) we have to do the operations from left to right.

Case-1  If there are   only two operations  (+ & –   or  × &  ÷ )  occurs in an expression

Example.   1888÷32÷8 =?    [Bank P.O.2008 ]

Steps

1888÷32÷8

Thought process

Activity

Step-1

59 ÷8

Left to right

1888÷32=59

Step-2

7.375

 

59 ÷8  = 7.375

Example.     Simplify  20 – 11 + 100 

Here,  –  and  +  are two operations of equal rank. So we have to do from left to right. (Doing from right to left is not allowed) 

Step-1 we have to do  20 – 11  which is equal to 9

 20 – 10 + 100 

9+100

Step-2  We have to do 9+100

     9+ 100 

   109

Answer = 109. 

Case-2  If there are 2 operations one from (+,  –) and one from  (×,  ÷) occurs  in an expression

Example 1) Simplify 100 – 40 ÷ 2 

Here there are two operations only.  Clearly  ÷  is of higher operation than  –. So first we have to do division then do subtraction.

Solution:

100 – 40 ÷ 2

Step-1   100 – 20

Step-2   80 

100 – 40 ÷ 2 = 80

Example-2)  Simplify 10 + 2 × 20  

Here, similar to example-1,  there are two operations only.  Clearly  ×  is of higher operation than  + . So first we have to do multiplication  then do addition.

Solution: 10 + 2 × 20  

Step-1  10+40

Step-2  50 

 Practice  Questions

  1.  Simplify : 6 ÷ 6 + 6 x 6 – 6   [AISSEE 2018 ] 
    1. 1
    2. 7   
    3. 31
    4. 36


  2.  Value of (700÷10) – {(12x8) ÷ (34-10)}  is   [AISSEE 2018 ]
    1. 69
    2. 68               
    3. 67
    4. 66 

  3. Simplify 165 ÷15+5x10 =  
    1. 51
    2. 52
    3. 61
    4. 71
  4. (27-25)(12+1)  =   
    1. 21 
    2. 23  
    3. 24  
    4. 26

  4900÷ 28 x 444÷ 12 =?    [SBI Clerk-2014 ]

 Practice

1)   4+ 5 × 32 – 2

2)   6x3+4x(93)

3)   2+6x(4+5) 3-5

4)   4+(5x9+2)

5)   [(324)+3]x2

6)   4-5(8-3)x2+5

7)   9-24  8x2+3

8)   (3x255)-(16-10)

9)   4 × (5 + 3)

10)       5 × 22

11)       2 + 5 × 3

12)       30 ÷ 5 × 3

13)       3 + 6 × 2 

14)       (3 + 6) × 2

15)       12 ÷  6 × 3 ÷  2 

16)       7 + (6 × 52 + 3)

17)       6 ÷ 3 + 4 × 2

18)       6 × 4 - 12 ÷ 3 – 8

19)        4 × 4 - 3 × 3 - 16 ÷ 4

20)        20 - (3 × 23 - 5)

21)       (5 + 2)2 - 9 × 3 + 23

22)       (12 ÷ 3 + 4) - (42 - 6 × 2)

23)        (52 - 5) ÷ (42 + 8 - 7 × 2)

24)        (33 - 9 ÷ 3) + (4 × 3 - 32)

Answers

1.      162

2.      30

3.      15

4.      51

5.      22

6.      7

7.      6

8.      9

9.      32(23)

10.  20(100)

11.  17(21)

12.  18(2)

13.  15

14.  18

15.  3

16.  160

17.  10

18.  12

19.  3

20.  1

21.  30

22.  4

23.  2

24.  27

II. Coding Type Questions

  1. If '+' means "minus",  '+' means "minus", '-' means "multiply", 'x' means 'add" then what is the value of  10x5+3-2? AISSEE2021   1.242.523.94.10
  2. If '+' means '÷ ', '×' means '–', '÷' means '×' and '–' means '+', what will be the value of the following expression?  9 + 3 ÷ 4 – 8 × 2 = ? [SSC-Sub. Ins.-2014]
  3. In the question below, if the given mathematical symbols are changed from '+'to '÷',   '-'to 'x',  '÷'to '-' and from 'x' to '÷' then  67x119+17-27÷259=     [DMRC-CRA 2016]  1.-13 2.-3 3.4   4.7
  4. If P means ‘÷’, Q means ‘+’ , R means ‘-‘ and S means ‘×’, then what will be the value of 10R192P48S48P96Q1?  [NTSE Bihar 2020-21 ] (1) 10 (2) 9 (3) 8 (4) 7 
  5. If ‘+’ means ‘×’, ‘-‘ means ‘÷’, ‘×’ means ‘+’ and ‘÷’ means ‘-‘ then compute the value of following expression 45 – 9 + 4 × 5    [NTSE Bihar 2020-21 ]  (1) 21 (2) 25 (3) 26 (4) 23 

III. Signs Change Type Questions

  1. Which signs should be interchanged to correct the equation given below? 4 −13÷ 7+ 6 ÷7 ×1 =5  (1) × and + (2) – and ×  (3) + and - (4) + and ×     [NTSE Bihar 2020-21 ]



Simplifications based on Distributive Property

Evaluate 123x999 =123   [ESIC UDC 2016]

  1. 246999  
  2. 123000  
  3. 246000 
  4. 123999

 


 


Comments

  1. SUNIL NAGABATHULANov 23, 2023, 6:59:00 AM

    23-29+56x36/4 in the above case which operation have to done first sir.

    ReplyDelete

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