1. What is Simplification?
Simplification means reducing a mathematical expression to its correct and simplest value by performing the given operations in the proper order. An expression may contain addition, subtraction, multiplication, division, brackets, powers, roots and sometimes the word “of”.
The individual calculations may be easy, but a wrong order of operations can completely change the answer. For this reason, BODMAS is one of the most fundamental rules used in competitive-exam arithmetic.
Example:
Simplify: 18 + 24 ÷ 6 × 3
24 ÷ 6 = 4
4 × 3 = 12
18 + 12 = 30.
Common Mistake:
Do not solve an expression simply from whichever operation looks easiest. The prescribed order of operations must be followed.
2. Meaning of BODMAS
The standard BODMAS sequence is:
| Letter |
Meaning |
Examples |
| B | Brackets | ( ), [ ], { } |
| O | Orders | Powers, indices, roots |
| D | Division | ÷ |
| M | Multiplication | × |
| A | Addition | + |
| S | Subtraction | − |
Key Rule:
Brackets → Orders → Division/Multiplication → Addition/Subtraction.
Note:
In many Indian competitive-exam books, the letter O is also used while discussing the word “of”. Strictly, “Orders” refers to powers and roots, while “of” represents multiplication. Exam questions that explicitly contain “of” are discussed separately below.
3. Brackets are Solved First
If an expression contains brackets, simplify the operation inside the bracket before dealing with the operations outside it.
Example:
Simplify: 7 + 3 × (12 − 8)
First solve the bracket:
12 − 8 = 4
Now:
7 + 3 × 4
= 7 + 12
= 19.
Exam Tip:
Before beginning a calculation, scan the complete expression for brackets. Missing a bracket is one of the most common causes of an otherwise avoidable wrong answer.
Scope Note:
Detailed treatment of multiple nested brackets and vinculum is covered separately in Topic 2.2. Here we concentrate on the basic BODMAS principle.
4. Orders: Powers and Roots
After brackets, powers, indices and roots are evaluated before ordinary multiplication, division, addition or subtraction.
Example:
Simplify: 5 + 32 × 2
First evaluate the power:
32 = 9
Then:
5 + 9 × 2
= 5 + 18
= 23.
Example:
Simplify: 30 − √64 ÷ 2
√64 = 8
8 ÷ 2 = 4
30 − 4 = 26.
Exam Trap:
In 4 + 52, do not add 4+5 before squaring. The power belongs to 5 only, so the value is 4+25=29.
5. Division and Multiplication Have Equal Priority
This is one of the most important facts about BODMAS. The letters D and M do not mean that every division must always be completed before every multiplication.
When division and multiplication occur at the same level, perform them from left to right.
Key Rule:
Division and multiplication have equal priority. When both are present at the same level, work from left to right.
Example:
Simplify: 48 ÷ 6 × 4
Proceed from left to right:
48 ÷ 6 = 8
8 × 4 = 32.
Common Mistake:
Doing 6×4 first would give 48÷24=2, which is incorrect for the expression as written.
6. Addition and Subtraction Have Equal Priority
Addition and subtraction also have equal priority. If both appear at the same level, calculate them from left to right.
Example:
Simplify: 30 − 12 + 5
30 − 12 = 18
18 + 5 = 23.
Exam Trap:
Do not add 12+5 first merely because A appears before S in the word BODMAS. Addition and subtraction are equal-priority operations.
7. Correct Left-to-Right Rule
A useful practical way to remember BODMAS is to think in levels rather than six completely separate priorities:
Priority Levels:
Level 1: Brackets
Level 2: Powers and roots
Level 3: Multiplication and division — left to right
Level 4: Addition and subtraction — left to right
Shortcut:
Instead of memorising “D before M” and “A before S”, remember the pairs DM and AS. Operations inside each pair have equal priority and are processed from left to right.
Example:
Simplify: 36 ÷ 3 × 2 − 5 + 7
36 ÷ 3 = 12
12 × 2 = 24
Now addition/subtraction from left to right:
24 − 5 + 7
= 19 + 7
= 26.
8. How to Treat “of” in Competitive-Exam Questions
The word “of” mathematically represents multiplication. For example:
Key Rule:
3/4 of 20 = 3/4 × 20 = 15.
Many Indian competitive-exam simplification questions explicitly use the word “of”. In such convention-based questions, published answer keys commonly evaluate the “of” part first before continuing with the remaining division/multiplication.
Exam Tip:
When an exam expression explicitly contains the word “of”, follow the convention expected by that examination and first convert the “of” portion into multiplication as one grouped quantity. This avoids ambiguity in expressions involving fractions.
Important Observation:
In ordinary modern mathematical notation, multiplication and division share the same precedence. Expressions should ideally be written with brackets if there is any possibility of ambiguity. Competitive-exam questions, however, sometimes follow the conventional “of first” treatment.
Example:
3/5 of 25 + 7
3/5 × 25 = 15
15 + 7 = 22.
9. Handling a Minus Sign Before a Bracket
A minus sign outside a bracket affects the complete value of the bracket. First evaluate the bracket and then apply the sign.
Example:
Simplify: 40 − (15 − 7)
15 − 7 = 8
40 − 8 = 32.
If a bracket is opened algebraically, every sign inside changes when the bracket is preceded by a minus sign:
Sign Rule:
−(a+b) = −a−b
−(a−b) = −a+b
Common Mistake:
Do not change only the first sign when removing a minus bracket. The negative sign applies to every term inside the bracket.
10. A Reliable Step-by-Step Method for Exams
For a long expression, use the following systematic method rather than trying to calculate everything mentally at once.
Exam Method:
1. Look for brackets.
2. Evaluate powers and roots.
3. Simplify any clearly defined “of” portion where the examination convention requires it.
4. Complete multiplication and division from left to right.
5. Complete addition and subtraction from left to right.
6. Recheck signs before marking the answer.
Example:
Simplify: 84 ÷ 7 + 5 × 6 − 8
Division and multiplication:
84 ÷ 7 = 12
5 × 6 = 30
Now:
12 + 30 − 8
= 42 − 8
= 34.
11. Calculation Shortcuts Without Breaking BODMAS
Shortcuts are useful only after the order of operations has been established correctly.
Shortcut:
After completing brackets, powers, multiplication and division, positive terms and negative terms may sometimes be grouped separately to reduce arithmetic effort.
Example:
94 + 61 − 38 + 96 − 91
Positive terms = 94+61+96 = 251
Negative terms = 38+91 = 129
251−129 = 122.
Exam Tip:
Grouping is safe only after higher-priority operations have been completed. Never regroup across an unresolved multiplication, division, power or bracket.
12. Common BODMAS Traps
Trap 1 — Treating multiplication as higher than division:
They have equal priority. Use left-to-right order.
Trap 2 — Treating addition as higher than subtraction:
They also have equal priority. Use left-to-right order.
Trap 3 — Ignoring brackets:
A bracket can change the entire value of an expression.
Trap 4 — Ignoring a power:
Powers and roots are evaluated before ordinary multiplication and addition.
Trap 5 — Losing a negative sign:
Whenever a bracket or negative number is involved, check the sign again before proceeding.
Trap 6 — Using a shortcut before applying BODMAS:
A shortcut must simplify the calculation, not change the mathematical order.
13. Quick Revision
Remember:
• Solve brackets first.
• Evaluate powers and roots next.
• Multiplication and division are equal-priority operations.
• Addition and subtraction are equal-priority operations.
• Equal-priority operations are performed from left to right.
• “Of” means multiplication; in conventional aptitude questions, treat its intended grouping carefully.
• Never sacrifice the correct order merely to use a faster shortcut.
14. Verified Previous-Year Questions
SSC CGL PYQ
BODMAS
24 September 2024 · Tier-I · Shift II
Q1. Simplify: 133 ÷ 19 × 3 − 48 × 2 ÷ 24 + 841 ÷ (45 − 16)
A. 46
B. 21
C. 12
D. 42
Correct Answer: A. 46
First solve the bracket:
45−16 = 29.
Now:
133÷19×3 − 48×2÷24 + 841÷29
= 7×3 − 96÷24 + 29
= 21−4+29
= 46.
SSC CGL PYQ
BODMAS with Powers
14 July 2023 · Tier-I · Shift IV
Q2. Simplify: (2×7 − 5 + 9÷3) ÷ (4+2)2 × 2
A. 2
B. 3/2
C. 2/3
D. 3
Correct Answer: C. 2/3
First bracket:
2×7−5+9÷3 = 14−5+3 = 12.
Second bracket and power:
(4+2)2 = 62 = 36.
Therefore:
12÷36×2
= 1/3×2
= 2/3.
RRB NTPC PYQ
Brackets & BODMAS
18 June 2026 · CBT-I · Shift III
Q3. Simplify: 156 ÷ [12 + {7 × (15−9) − 28}]
A. 8
B. 10
C. 6
D. 12
Correct Answer: C. 6
15−9 = 6.
7×6−28 = 42−28 = 14.
12+14 = 26.
Therefore:
156÷26 = 6.
SSC MTS PYQ
Order of Operations
11 February 2026 · Shift II
Q4. Simplify: 94 + 61 − 38 + (27+21) × 2 − 91
A. 145
B. 147
C. 149
D. 122
Correct Answer: D. 122
Bracket first:
27+21 = 48.
Then multiplication:
48×2 = 96.
Expression becomes:
94+61−38+96−91
= 122.
15. Practice MCQs
Practice MCQ
Q1. Simplify: 18 + 24 ÷ 6 × 3
A. 24
B. 26
C. 30
D. 42
Correct Answer: C. 30
24÷6×3 = 4×3 = 12. Therefore 18+12=30. Practice MCQ
Q2. Simplify: 64 ÷ 8 × 2 + 5
A. 13
B. 16
C. 21
D. 25
Correct Answer: C. 21
64÷8=8, then 8×2=16 and 16+5=21. Practice MCQ
Q3. Simplify: 72 − 18 ÷ 3 × 4
A. 24
B. 48
C. 54
D. 60
Correct Answer: B. 48
18÷3×4 = 6×4=24. Therefore 72−24=48. Practice MCQ
Q4. Simplify: 7 + 3 × (12−8)
A. 19
B. 28
C. 40
D. 12
Correct Answer: A. 19
12−8=4, then 3×4=12 and 7+12=19. Practice MCQ
Q5. Simplify: 96 ÷ (8+4) × 3
A. 8
B. 16
C. 24
D. 32
Correct Answer: C. 24
8+4=12. Then 96÷12×3 = 8×3=24. Practice MCQ
Q6. Simplify: 23 + 18 ÷ 3 × 2
A. 16
B. 18
C. 20
D. 24
Correct Answer: C. 20
23=8. Also 18÷3×2=6×2=12. Therefore 8+12=20. Practice MCQ
Q7. Simplify: 50 − 6 × 4 + 8 ÷ 2
A. 26
B. 28
C. 30
D. 34
Correct Answer: C. 30
6×4=24 and 8÷2=4. Therefore 50−24+4=30. Practice MCQ
Q8. Simplify: 36 ÷ 3 × 2 − 5 + 7
A. 22
B. 24
C. 26
D. 28
Correct Answer: C. 26
36÷3×2=12×2=24. Then 24−5+7=19+7=26. Practice MCQ
Q9. Simplify: 84 ÷ 7 + 5 × 6 − 8
A. 30
B. 32
C. 34
D. 36
Correct Answer: C. 34
84÷7=12 and 5×6=30. Thus 12+30−8=34. Practice MCQ
Q10. Simplify: (18+6) ÷ 3 + 42
A. 20
B. 22
C. 24
D. 26
Correct Answer: C. 24
(18+6)=24; 24÷3=8; 42=16. Therefore 8+16=24.
1. Simplification क्या है?
Simplification अर्थात किसी mathematical expression में दी गई संक्रियाओं को सही क्रम में करके उसका सही और सरलतम मान निकालना। किसी expression में addition, subtraction, multiplication, division, brackets, powers, roots तथा कभी-कभी “of” भी दिया हो सकता है।
अलग-अलग calculations सरल होने के बावजूद operations का क्रम गलत होने पर पूरा answer बदल सकता है। इसी कारण BODMAS competitive mathematics की सबसे बुनियादी और महत्वपूर्ण rules में से एक है।
उदाहरण:
सरल कीजिए: 18 + 24 ÷ 6 × 3
24 ÷ 6 = 4
4 × 3 = 12
18 + 12 = 30।
सामान्य गलती:
जिस operation की calculation आसान दिखाई दे, उसे पहले करना सही तरीका नहीं है। हमेशा prescribed order of operations का पालन करें।
2. BODMAS का अर्थ
| Letter |
अर्थ |
उदाहरण |
| B | Brackets / कोष्ठक | ( ), [ ], { } |
| O | Orders / घात एवं मूल | Powers, indices, roots |
| D | Division / भाग | ÷ |
| M | Multiplication / गुणा | × |
| A | Addition / जोड़ | + |
| S | Subtraction / घटाव | − |
मुख्य नियम:
Brackets → Orders → Division/Multiplication → Addition/Subtraction.
नोट:
कई Indian competitive-exam books में O को “of” से भी जोड़ा जाता है। Standard mathematical meaning में O का अर्थ Orders अर्थात powers और roots है, जबकि “of” multiplication को दर्शाता है।
3. Brackets को पहले Solve करें
यदि expression में bracket दिया हो, तो सबसे पहले bracket के अंदर की calculation की जाती है।
उदाहरण:
सरल कीजिए: 7 + 3 × (12 − 8)
पहले bracket:
12 − 8 = 4
अब:
7 + 3 × 4
= 7 + 12
= 19।
Exam Tip:
Calculation शुरू करने से पहले पूरे expression को एक बार देखें और सभी brackets पहचान लें।
Scope Note:
Multiple nested brackets और vinculum का विस्तृत अध्ययन Topic 2.2 में किया जाएगा।
4. Orders: Powers एवं Roots
Brackets के बाद powers, indices और roots solve किए जाते हैं।
उदाहरण:
सरल कीजिए: 5 + 32 × 2
32 = 9
5 + 9×2
= 5+18
= 23।
उदाहरण:
सरल कीजिए: 30 − √64 ÷ 2
√64 = 8
8÷2 = 4
30−4 = 26।
Exam Trap:
4 + 52 में पहले 4+5 नहीं करेंगे। 52=25, इसलिए answer 4+25=29 होगा।
5. Division और Multiplication की Priority समान है
BODMAS में D पहले और M बाद में लिखा होने का अर्थ यह नहीं है कि प्रत्येक division को हर multiplication से पहले किया जाएगा।
यदि multiplication और division एक ही level पर हों, तो उन्हें left to right solve किया जाता है।
मुख्य नियम:
Division और multiplication की priority समान है। दोनों साथ हों तो बाएँ से दाएँ calculation करें।
उदाहरण:
48 ÷ 6 × 4
48÷6 = 8
8×4 = 32।
सामान्य गलती:
6×4 को पहले करके 48÷24=2 निकालना गलत होगा।
6. Addition और Subtraction की Priority समान है
Addition और subtraction भी equal-priority operations हैं। दोनों एक ही level पर हों तो left to right solve करें।
उदाहरण:
30 − 12 + 5
30−12 = 18
18+5 = 23।
Exam Trap:
BODMAS में A, S से पहले लिखा है इसलिए 12+5 पहले करना सही नहीं है। Addition और subtraction की priority समान है।
7. सही Left-to-Right Rule
Priority Levels:
Level 1: Brackets
Level 2: Powers एवं roots
Level 3: Multiplication एवं division — left to right
Level 4: Addition एवं subtraction — left to right
Shortcut:
D और M को अलग-अलग priority मानने के बजाय DM pair तथा A और S को AS pair समझें। प्रत्येक pair में calculation left to right होती है।
उदाहरण:
36 ÷ 3 × 2 − 5 + 7
36÷3 = 12
12×2 = 24
24−5+7
= 19+7
= 26।
8. Competitive Exams में “of” का प्रयोग
“Of” mathematically multiplication को दर्शाता है।
मुख्य नियम:
3/4 of 20 = 3/4 × 20 = 15.
Indian competitive examinations के कई traditional simplification questions में “of” explicitly लिखा होता है। ऐसे questions की conventional answer-key method में “of” वाले grouped part को पहले simplify किया जाता है और उसके बाद शेष division/multiplication किया जाता है।
Exam Tip:
यदि expression में explicitly “of” दिया हो, तो examination द्वारा अपनाए गए conventional interpretation को ध्यान में रखते हुए उस portion को एक grouped multiplication की तरह simplify करें।
महत्वपूर्ण Observation:
Standard modern mathematical notation में multiplication और division समान precedence रखते हैं। Ambiguity से बचने के लिए brackets का प्रयोग बेहतर होता है। Competitive aptitude questions में कभी-कभी traditional “of first” convention प्रयुक्त होता है।
उदाहरण:
3/5 of 25 + 7
3/5×25 = 15
15+7 = 22।
9. Bracket के पहले Minus Sign
Bracket के पहले minus sign होने पर वह पूरे bracket के value को affect करता है।
उदाहरण:
40 − (15 − 7)
15−7 = 8
40−8 = 32।
Sign Rule:
−(a+b) = −a−b
−(a−b) = −a+b
सामान्य गलती:
Minus bracket खोलते समय केवल पहले term का sign न बदलें। Bracket के सभी terms पर outside negative sign लागू होता है।
10. Exam में अपनाने योग्य Step-by-Step Method
Exam Method:
1. Brackets पहचानें और solve करें।
2. Powers एवं roots निकालें।
3. यदि conventional question में clearly “of” दिया हो तो उसका grouped value निकालें।
4. Multiplication और division को left to right करें।
5. Addition और subtraction को left to right करें।
6. Final answer mark करने से पहले signs दोबारा check करें।
उदाहरण:
84 ÷ 7 + 5 × 6 − 8
84÷7 = 12
5×6 = 30
12+30−8
= 42−8
= 34।
11. BODMAS को तोड़े बिना Calculation Shortcuts
Shortcut का प्रयोग तभी करें जब higher-priority operations पहले ही complete हो चुके हों।
Shortcut:
Brackets, powers, multiplication और division solve करने के बाद आवश्यकता पड़ने पर positive तथा negative terms को अलग-अलग group किया जा सकता है।
उदाहरण:
94 + 61 − 38 + 96 − 91
Positive terms = 94+61+96 = 251
Negative terms = 38+91 = 129
251−129 = 122।
Exam Tip:
Unresolved multiplication, division, power या bracket के across terms को group न करें।
12. BODMAS के Common Traps
Trap 1:
Multiplication को division से higher priority मानना गलत है। दोनों equal priority हैं।
Trap 2:
Addition को subtraction से higher priority मानना गलत है। दोनों equal priority हैं।
Trap 3:
Bracket ignore करना पूरे answer को बदल सकता है।
Trap 4:
Power या root को ordinary multiplication/addition से पहले solve करना आवश्यक है।
Trap 5:
Negative sign खो देना simplification questions में बहुत common error है।
Trap 6:
Shortcut के लिए mathematical order बदलना कभी सही नहीं है।
13. Quick Revision
एक नज़र में:
• Brackets सबसे पहले।
• उसके बाद powers एवं roots।
• Multiplication और division equal priority — left to right।
• Addition और subtraction equal priority — left to right।
• “Of” multiplication दर्शाता है; exam convention को ध्यान से समझें।
• Minus sign और brackets पर विशेष ध्यान दें।
• Shortcut का प्रयोग सही BODMAS order के बाद ही करें।
14. Verified Previous-Year Questions
SSC CGL PYQ
BODMAS
24 सितंबर 2024 · Tier-I · Shift II
प्रश्न 1. सरल कीजिए: 133 ÷ 19 × 3 − 48 × 2 ÷ 24 + 841 ÷ (45 − 16)
A. 46
B. 21
C. 12
D. 42
सही उत्तर: A. 46
पहले bracket:
45−16 = 29।
अब:
133÷19×3 − 48×2÷24 + 841÷29
= 7×3 − 96÷24 + 29
= 21−4+29
= 46।
SSC CGL PYQ
BODMAS with Powers
14 जुलाई 2023 · Tier-I · Shift IV
प्रश्न 2. सरल कीजिए: (2×7 − 5 + 9÷3) ÷ (4+2)2 × 2
A. 2
B. 3/2
C. 2/3
D. 3
सही उत्तर: C. 2/3
पहला bracket:
2×7−5+9÷3 = 14−5+3 = 12।
दूसरा bracket:
(4+2)2 = 62 = 36।
अब:
12÷36×2
= 1/3×2
= 2/3।
RRB NTPC PYQ
Brackets & BODMAS
18 जून 2026 · CBT-I · Shift III
प्रश्न 3. सरल कीजिए: 156 ÷ [12 + {7 × (15−9) − 28}]
A. 8
B. 10
C. 6
D. 12
सही उत्तर: C. 6
15−9=6।
7×6−28=42−28=14।
12+14=26।
156÷26=6।
SSC MTS PYQ
Order of Operations
11 फरवरी 2026 · Shift II
प्रश्न 4. सरल कीजिए: 94 + 61 − 38 + (27+21) × 2 − 91
A. 145
B. 147
C. 149
D. 122
सही उत्तर: D. 122
27+21=48।
48×2=96।
अब:
94+61−38+96−91
= 122।
15. Practice MCQs
Practice MCQ
प्रश्न 1. 18 + 24 ÷ 6 × 3 का मान क्या है?
A. 24
B. 26
C. 30
D. 42
सही उत्तर: C. 30
24÷6×3=4×3=12। इसलिए 18+12=30। Practice MCQ
प्रश्न 2. 64 ÷ 8 × 2 + 5 का मान क्या है?
A. 13
B. 16
C. 21
D. 25
सही उत्तर: C. 21
64÷8=8, 8×2=16 और 16+5=21। Practice MCQ
प्रश्न 3. 72 − 18 ÷ 3 × 4 का मान क्या है?
A. 24
B. 48
C. 54
D. 60
सही उत्तर: B. 48
18÷3×4=6×4=24। इसलिए 72−24=48। Practice MCQ
प्रश्न 4. 7 + 3 × (12−8) का मान क्या है?
A. 19
B. 28
C. 40
D. 12
सही उत्तर: A. 19
12−8=4, 3×4=12 तथा 7+12=19। Practice MCQ
प्रश्न 5. 96 ÷ (8+4) × 3 का मान क्या है?
A. 8
B. 16
C. 24
D. 32
सही उत्तर: C. 24
8+4=12। फिर 96÷12×3=8×3=24। Practice MCQ
प्रश्न 6. 23 + 18 ÷ 3 × 2 का मान क्या है?
A. 16
B. 18
C. 20
D. 24
सही उत्तर: C. 20
23=8 तथा 18÷3×2=12। इसलिए 8+12=20। Practice MCQ
प्रश्न 7. 50 − 6 × 4 + 8 ÷ 2 का मान क्या है?
A. 26
B. 28
C. 30
D. 34
सही उत्तर: C. 30
6×4=24 और 8÷2=4। इसलिए 50−24+4=30। Practice MCQ
प्रश्न 8. 36 ÷ 3 × 2 − 5 + 7 का मान क्या है?
A. 22
B. 24
C. 26
D. 28
सही उत्तर: C. 26
36÷3×2=24। फिर 24−5+7=19+7=26। Practice MCQ
प्रश्न 9. 84 ÷ 7 + 5 × 6 − 8 का मान क्या है?
A. 30
B. 32
C. 34
D. 36
सही उत्तर: C. 34
84÷7=12 और 5×6=30। इसलिए 12+30−8=34। Practice MCQ
प्रश्न 10. (18+6) ÷ 3 + 42 का मान क्या है?
A. 20
B. 22
C. 24
D. 26
सही उत्तर: C. 24
(18+6)=24, 24÷3=8 तथा 42=16। इसलिए 8+16=24।