BODMAS Notes and Practice Questions for Competitive Exams (Civil Services, SSC CGL, Banking)

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1. What is BODMAS?

BODMAS is an acronym that guides the order in which operations should be performed in a mathematical expression to get the correct answer.

• B - Brackets (Parentheses, Curly braces, Square brackets)

• O - Orders (Exponents and Roots, i.e., powers and square roots)

• D - Division

• M - Multiplication

• A - Addition

• S - Subtraction

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2. Why is BODMAS Important?

Without following BODMAS, the same expression can give different answers. It ensures consistency and accuracy in solving expressions.

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3. The BODMAS Rule Explained

• Step 1: Solve anything inside brackets first.
  Brackets can be of various types: ( ), { }, [ ]. Start from the innermost bracket.

• Step 2: Calculate orders
  Powers (like $2^3$) and roots (like $\sqrt{9}$).

• Step 3: Perform Division and Multiplication
  These two are of equal priority; solve from left to right.

• Step 4: Perform Addition and Subtraction
  These two are also of equal priority; solve from left to right.

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4. Important Points to Remember

• Division and multiplication are on the same level; solve in the order they appear from left to right.

• Addition and subtraction are on the same level; solve in the order they appear from left to right.

• Always simplify inside brackets first, even if it contains multiple operations.

• Exponents and roots come after brackets but before division/multiplication.

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5. Examples to Illustrate BODMAS

Example 1

Evaluate: $8+2\times 5$
Solution:
Multiply first: $2\times 5=10$
Add: $8+10=18$

Example 2

Evaluate: $(3+6)\times 2$
Solution:
Brackets first: $3+6=9$
Multiply: $9\times 2=18$

Example 3

Evaluate: $18÷3\times (5+4)$
Solution:
Brackets: $5+4=9$
Division and multiplication left to right:
$18÷3=6$
$6\times 9=54$

Example 4

Evaluate: $5+2^3\times 3$
Solution:
Orders: $2^3=8$
Multiply: $8\times 3=24$
Add: $5+24=29$

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6. Common Mistakes to Avoid

• Ignoring the order and solving from left to right without following BODMAS.

• Treating multiplication as always before division or addition before subtraction.

• Forgetting to simplify inside brackets first.

• Miscalculating powers or roots.

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7. Tips to Solve BODMAS Questions Quickly

• Identify and solve brackets first.

• Calculate powers and roots next.

• Scan the expression from left to right for division and multiplication.

• Finally, do addition and subtraction from left to right.

• Practice mental math and shortcuts for powers and roots.

• Use approximation if allowed and when numbers are complex.

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100 BODMAS Practice Questions

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Questions 1 to 20 (with solutions)

1. $8+2\times 5$
   Answer: 18
   Explanation: $2\times 5=10$; $8+10=18$

2. $16÷4\times 2$
   Answer: 8
   Explanation: $16÷4=4$; $4\times 2=8$

3. $3+6\times (5+4)÷3$
   Answer: 21
   Explanation: $5+4=9$; $6\times 9=54$; $54÷3=18$; $3+18=21$

4. $2\times \{17-2\times (9-6)\}$
   Answer: 22
   Explanation: $9-6=3$; $2\times 3=6$; $17-6=11$; $2\times 11=22$

5. $5^2+3\times 4-6$
   Answer: 31
   Explanation: $5^2=25$; $3\times 4=12$; $25+12=37$; $37-6=31$

6. $8÷4\times (6+2\times 4)+32-2$
   Answer: 58
   Explanation: $2\times 4=8$; $6+8=14$; $8÷4=2$; $2\times 14=28$; $28+32=60$; $60-2=58$

7. $(18-[6-\{4-(8-9)\}])$
   Answer: 17
   Explanation: $8-9=-1$; $4-(-1)=5$; $6-5=1$; $18-1=17$

8. $45+34÷2\times 8^2÷16\times (-3)$
   Answer: -159
   Explanation: $34÷2=17$; $8^2=64$; $17\times 64=1088$; $1088÷16=68$; $68\times (-3)=-204$; $45+(-204)=-159$

9. $30+5\times 2$
   Answer: 40
   Explanation: $5\times 2=10$; $30+10=40$

10. $20+20\times 20÷20+20$
    Answer: 60
    Explanation: $20\times 20=400$; $400÷20=20$; $20+20=40$; $40+20=60$

11. $3+2^4\times (15÷3)$
    Answer: 83
    Explanation: $2^4=16$; $15÷3=5$; $16\times 5=80$; $3+80=83$

12. $8+8\times 8÷8-34÷5$
    Answer: 9.2
    Explanation: $8\times 8=64$; $64÷8=8$; $8+8=16$; $34÷5=6.8$; $16-6.8=9.2$

13. $25-[20-\{10-(8-3)\}]$
    Answer: 10
    Explanation: $8-3=5$; $10-5=5$; $20-5=15$; $25-15=10$

14. $9+6÷(3\times 5)-10$
    Answer: -0.6
    Explanation: $3\times 5=15$; $6÷15=0.4$; $9+0.4=9.4$; $9.4-10=-0.6$

15. $2\times [4+3\times (6-2)]$
    Answer: 32
    Explanation: $6-2=4$; $3\times 4=12$; $4+12=16$; $2\times 16=32$

16. $8÷8\times 8+8$
    Answer: 16
    Explanation: $8÷8=1$; $1\times 8=8$; $8+8=16$

17. $\{[(12-4)\times 3]÷2\}+5$
    Answer: 17
    Explanation: $12-4=8$; $8\times 3=24$; $24÷2=12$; $12+5=17$

18. $100÷(5\times 4)+6$
    Answer: 11
    Explanation: $5\times 4=20$; $100÷20=5$; $5+6=11$

19. $15-3\times [2+(4-1)]$
    Answer: 0
    Explanation: $4-1=3$; $2+3=5$; $3\times 5=15$; $15-15=0$

20. $7\times (3+2)-4^2$
    Answer: 19
    Explanation: $3+2=5$; $7\times 5=35$; $4^2=16$; $35-16=19$

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Questions 21 to 100 (Practice Only)

21. $12+18÷3\times 2$

22. $(20-5)\times 3+4$

23. $100-[25\times (2+2)]$

24. $8\times 2+6÷3$

25. $50÷5\times 4+6$

26. $(15+5)\times 2-10$

27. $9\times (4+2)-8$

28. $36÷(6\times 2)+5$

29. $10+6\times 2-4$

30. $(8+2)\times (5-3)$

31. $18-3\times 2+4$

32. $24÷(3+1)\times 2$

33. $16-[4\times (2+2)]$

34. $40÷4\times 3+2$

35. $6\times (3+2)-5$

36. $25-5\times 2+8$

37. $30÷(5+1)\times 3$

38. $14+6\times 2-8$

39. $(12-2)\times (4+1)$

40. $45÷5\times 2+3$

41. $20+8\times 2-6$

42. $(10+5)\times 3-7$

43. $28÷(7\times 2)+9$

44. $18+4\times 2-3$

45. $(9+3)\times (6-2)$

46. $36-6\times 2+8$

47. $24÷(4+2)\times 3$

48. $32-[8\times (2+2)]$

49. $60÷5\times 4+7$

50. $7\times (5+3)-6$

51. $21-3\times 2+5$

52. $27÷(3+6)\times 4$

53. $18-[3\times (2+4)]$

54. $50÷5\times 3+8$

55. $8\times (6+2)-9$

56. $35-5\times 3+6$

57. $40÷(8+2)\times 5$

58. $16+4\times 3-7$

59. $(15-5)\times (6+2)$

60. $54÷6\times 2+3$

61. $22+7\times 2-9$

62. $(14+6)\times 3-8$

63. $36÷(9\times 2)+7$

64. $20+5\times 3-4$

65. $(10+8)\times (5-2)$

66. $30-6\times 2+9$

67. $28÷(4+3)\times 2$

68. $24-[6\times (2+2)]$

69. $70÷7\times 5+6$

70. $8\times (7+1)-4$

71. $16-2\times 3+5$

72. $18÷(3+3)\times 4$

73. $12-[2\times (3+3)]$

74. $40÷4\times 5+2$

75. $9\times (2+4)-7$

76. $27-3\times 4+8$

77. $30÷(5+5)\times 6$

78. $14+3\times 2-5$

79. $(8+4)\times (5-1)$

80. $48÷6\times 3+2$

81. $20+4\times 3-10$

82. $(11+9)\times 2-6$

83. $32÷(8\times 2)+5$

84. $18+5\times 2-4$

85. $(7+5)\times (6-3)$

86. $27-6\times 2+8$

87. $36÷(12+6)\times 4$

88. $24-[3\times (4+2)]$

89. $60÷6\times 5+3$

90. $8\times (4+2)-7$

91. $22-2\times 5+6$

92. $18÷(6+3)\times 5$

93. $20-[2\times (3+5)]$

94. $35÷5\times 4+2$

95. $(6+2)\times (5-1)$

96. $32-4\times 2+7$

97. $28÷(7+7)\times 3$

98. $16-[2\times (5+3)]$

99. $40÷8\times 5+4$

100. $9\times (3+2)-8$

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Final Words

Mastering BODMAS is essential for solving quantitative aptitude questions efficiently and accurately in competitive exams. Practice these questions regularly, follow the rules strictly, and improve your speed and accuracy.

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Good luck with your preparation!