Bodmas Questions

Article Summary

• BODMAS dictates the order in which you solve mathematical operations: Brackets, Orders, Division, Multiplication, Addition, Subtraction, with equal-precedence pairs solved left to right.
• This guide walks you through 28 worked problems across three difficulty levels, a visual mnemonic chart, and a dedicated troubleshooting section for the seven most common mistakes.
• Class 6 students will find exam-level questions aligned to NCERT Chapter 1 and RS Aggarwal Chapter 6, complete with board-exam trap warnings and step-by-step solutions.

One small mistake in the order of operations can completely change your answer in maths. For example, solving 25 – 5 × 2 + (10 ÷ 2) without following the correct order of operations may give you the wrong result. This is where the BODMAS rule becomes important. BODMAS helps students solve mathematical expressions accurately by following a fixed order: Brackets, Orders, Division, Multiplication, Addition, and Subtraction. It is one of the most essential concepts taught in CBSE Class 6 Maths and forms the foundation for algebra, simplification, and preparation for competitive exams.

In this guide, you will learn the BODMAS rule in a simple, structured way through clear explanations, step-by-step methods, solved examples, practice questions, and exam-level worksheets. Whether you are preparing for school exams, improving your calculation speed, or strengthening your maths basics, these BODMAS questions will help you build confidence and accuracy. You will also discover common mistakes students make and practical tips to avoid them while solving expressions.

If you are looking for structured support with your maths fundamentals or exam strategy, Leverage Edu offers free one-on-one counselling sessions to help you build confidence and clarity.

What Is the BODMAS Rule?

Definition of BODMAS

BODMAS is a rule that tells the order in which mathematical operations must be carried out: Brackets, Orders, Division, Multiplication, Addition, and Subtraction. In the Indian NCERT context, the “O” can also stand for “of” (meaning fraction multiplication), not only exponents. You will encounter three types of brackets: parentheses ( ), square brackets [ ], and curly braces { }. Always solve the innermost bracket first, then work outward. The bracket hierarchy follows this sequence: vinculum/bar, then ( ), then { }, then [ ]. After solving brackets, continue with the remaining operations according to the BODMAS sequence.

Order of Operations Explained

When both division and multiplication appear in the same expression, solve them from left to right as they appear, because they hold equal priority. The same rule applies to addition and subtraction. A key misconception is that students incorrectly believe division must always come before multiplication and addition before subtraction based purely on the acronym’s letter order; research confirms these pairs hold equal precedence and must be worked left to right. For example, 18 ÷ 9 × 2 equals 4 (not 1), because you divide 18 by 9 to get 2, then multiply by 2. Similarly, 12 ÷ 4 × 3 equals 9.

Why BODMAS Matters

BODMAS questions form the base of arithmetic and simplification in the CBSE syllabus. They appear in Class 6 exams as MCQs and short-answer questions based on simplification. Beyond school, BODMAS is tested in competitive exams. In RRB NTPC CBT 1, simplification and BODMAS typically account for 4–5 of the 30 total maths questions. Knowledge of order of operations has been called a “cornerstone” for advanced mathematics because it helps you interpret algebraic structure. Mastering BODMAS now pays dividends in algebra, calculus, and every quantitative exam you will face.

Quick BODMAS Order Chart & Mnemonic

Here is your six-step operation hierarchy at a glance:

Step	Letter	Operation	Example
1	B	Brackets (innermost first: vinculum → ( ) → { } → [ ])	(4 + 3) = 7
2	O	Orders / Of (powers, roots, and “of” as multiplication)	2³ = 8; √9 = 3
3	D	Division (left to right)	12 ÷ 4 = 3
4	M	Multiplication (left to right, equal priority to D)	3 × 5 = 15
5	A	Addition (left to right)	6 + 4 = 10
6	S	Subtraction (left to right, equal priority to A)	10 – 3 = 7

To remember the sequence, use the mnemonic “Brave Officers Do March And Sing”. Print this chart and pin it above your study desk. When you are stuck mid-problem during homework, a quick glance at this hierarchy will remind you which operation to tackle next. Worksheets aligned to national curriculum goals are available for Year 6 students, designed for differentiated use as starters, extension tasks, or homework.

How to Apply BODMAS: Step-by-Step Method

4-Step Checklist

Follow this sequence every time you face a BODMAS expression:

Step 1: Identify and solve all brackets, starting from the innermost and working outward.

Step 2: Solve orders/exponents, which include powers (e.g., 2³) and roots (e.g., √9), and treat “of” as multiplication.

Step 3: Scan left to right for division and multiplication; perform whichever appears first.

Step 4: Finish with addition and subtraction, scanning left to right and performing whichever appears first.

The last four operations must be solved from left to right in the order they appear; otherwise, you will get the wrong answer. Do not skip the left-to-right scan, no matter how confident you feel.

Worked Example Walkthrough

Let’s apply the checklist to three expressions:

Problem: 7 + (8 – 5) × 3

• Brackets: 8 – 5 = 3
• Multiplication: 3 × 3 = 9
• Addition: 7 + 9 = 16

Problem: 8 + (4 × 3)

• Brackets: 4 × 3 = 12
• Expression becomes: 8 + 12 = 20

Problem: 2 + 3 × 4

• Multiplication first (no brackets): 3 × 4 = 12
• Addition: 2 + 12 = 14
• Incorrect approach (left to right without BODMAS): 2 + 3 = 5, then 5 × 4 = 20

Notice how skipping the order of operations turns 14 into 20. Write out every step clearly, and underline brackets before you begin.

10 Worked BODMAS Questions (Easy)

These integer-only expressions build your foundation. Try solving each on your own before checking the solution.

Problem	Step-by-Step Solution	Answer
8 + (4 × 3)	Brackets: 4 × 3 = 12; Add: 8 + 12	20
9 × 2 + 6 ÷ 3	Division: 6 ÷ 3 = 2; Multiply: 9 × 2 = 18; Add: 18 + 2	20
12 – 3 × (2 + 4)	Brackets: 2 + 4 = 6; Multiply: 3 × 6 = 18; Subtract: 12 – 18	–6
7 + (8 – 5) × 3	Brackets: 8 – 5 = 3; Multiply: 3 × 3 = 9; Add: 7 + 9	16
6 + (15 – 9) ÷ 3	Brackets: 15 – 9 = 6; Divide: 6 ÷ 3 = 2; Add: 6 + 2	8
4 × (18 ÷ (9 – 3)) + 1	Innermost: 9 – 3 = 6; Divide: 18 ÷ 6 = 3; Multiply: 4 × 3 = 12; Add: 12 + 1	13
5 × (6 + 4) ÷ (3 – 1)	Round brackets: 6 + 4 = 10 and 3 – 1 = 2; Multiply: 5 × 10 = 50; Divide: 50 ÷ 2	25
12 – (6 – 2) × 4	Brackets: 6 – 2 = 4; Multiply: 4 × 4 = 16; Subtract: 12 – 16	–4
3 × (2 + 3) × 5	Brackets: 2 + 3 = 5; Left to right: 3 × 5 = 15; 15 × 5	75
(20 ÷ 5) × 2 + 1	Brackets: 20 ÷ 5 = 4; Multiply: 4 × 2 = 8; Add: 8 + 1	9

If you got all ten correct, move to the medium set. If not, revisit the 4-step checklist and try again.

10 Worked BODMAS Questions (Medium)

These problems introduce decimals, nested brackets, and exponents.

Problem	Solution	Exam Context	Answer
(6 + 4) × (3 – 1)	Round brackets: 6 + 4 = 10 and 3 – 1 = 2; Multiply: 10 × 2	Tests simultaneous bracket resolution	20
8 × (2 + 3) + 8	Brackets: 2 + 3 = 5; Multiply: 8 × 5 = 40; Add: 40 + 8	Mixing brackets with two operations	48
4 × [15 – (9 + 2)]	Round: 9 + 2 = 11; Square: 15 – 11 = 4; Multiply: 4 × 4	Nested square and round brackets	16
5 × [20 – (9 + 2)]	Round: 9 + 2 = 11; Square: 20 – 11 = 9; Multiply: 5 × 9	Multi-bracket simplification	45
6 + {8 ÷ (2 + 1)}	Innermost: 2 + 1 = 3; Curly: 8 ÷ 3 ≈ 2.67; Add: 6 + 2.67	Introduction to curly brackets	8.67
3 + {12 ÷ (6 ÷ 3)}	Innermost: 6 ÷ 3 = 2; Curly: 12 ÷ 2 = 6; Add: 3 + 6	Division nested inside curly brackets	9
4 + 3 × (5 – 2)²	Brackets: 5 – 2 = 3; Orders: 3² = 9; Multiply: 3 × 9 = 27; Add: 4 + 27	Combines the Orders step with brackets	31
3 + {(12 – 4) × 2 ÷ 4}	Brackets: 12 – 4 = 8; Multiply: 8 × 2 = 16; Divide: 16 ÷ 4 = 4; Add: 3 + 4	All operations inside curly brackets	7
6 + {(4 × 2) ÷ 2 + 1}	Brackets: 4 × 2 = 8; Divide: 8 ÷ 2 = 4; Add inside: 4 + 1 = 5; Add: 6 + 5	All-operations sequence	11
30 ÷ 2 × 3 – 4 + 1	Left to right: 30 ÷ 2 = 15; 15 × 3 = 45; A/S: 45 – 4 + 1	No brackets—pure left-to-right rule	42

Medium-level problems simulate the complexity you will face in mid-term exams and competitive test preliminaries. If you need extra practice with nested brackets or exponents, Leverage Edu’s free resource library includes topic-specific worksheets and video walkthroughs tailored to your grade level.

BODMAS Questions for Class 6 (Exam-Level)

BODMAS is included in the CBSE Class 6 Maths syllabus and forms the base of arithmetic and simplification. Ganita Prakash is the official NCERT textbook for Class 6 Maths, and all school exam questions are framed directly from this book as per CBSE guidelines.

BODMAS features in NCERT Chapter 1 (Knowing Our Numbers), and RS Aggarwal Class 6 Chapter 6 (“Simplification”) focuses entirely on this rule. The eight questions below mirror board-exam patterns and carry time pressure: aim to solve each in under 90 seconds.

Problem	Full Solution	Board Exam Trap	Answer
210 + [24 – {4 of 3 + (7 – 4)}]	Innermost ( ): 7 – 4 = 3; “of”: 4 × 3 = 12; { }: 12 + 3 = 15; [ ]: 24 – 15 = 9; Final: 210 + 9	“of” is treated as addition instead of multiplication	219
25 – [25 – {25 – (25 – 25 – 25)}]	Innermost: 25 – 25 – 25 = –25; { }: 25 – (–25) = 50; [ ]: 25 – 50 = –25; Final: 25 – (–25)	Negative sign confusion in nested brackets	50
37 – [5 + {28 – (19 – 7)}]	Innermost: 19 – 7 = 12; { }: 28 – 12 = 16; [ ]: 5 + 16 = 21; Final: 37 – 21	Rushing past innermost brackets	16
(60 – 32) ÷ 14 + 12 of 3 – 7 × 5	Brackets: 60 – 32 = 28; “of”: 12 × 3 = 36; Division: 28 ÷ 14 = 2; Multiply: 7 × 5 = 35; Final: 2 + 36 – 35	Ignoring the “of” operator, treating the bar as subtraction	3
18 ÷ (9 – 3) × 2 + 4	Brackets: 9 – 3 = 6; Division: 18 ÷ 6 = 3; Multiply: 3 × 2 = 6; Add: 6 + 4	Doing multiplication before division (left to right ignored)	10
5 × [20 – (9 + 2)]	Round: 9 + 2 = 11; Square: 20 – 11 = 9; Multiply: 5 × 9	Misidentifying which bracket type to solve first	45
3 + {(12 – 4) × 2} ÷ 4	Brackets: 12 – 4 = 8; Multiply: 8 × 2 = 16; Divide: 16 ÷ 4 = 4; Add: 3 + 4	Performing division before multiplication in the wrong sequence	7
39 – [23 – {29 – (17 – 9 – 3)}]	Innermost: 17 – 9 – 3 = 5; { }: 29 – 5 = 24; [ ]: 23 – 24 = –1; Final: 39 – (–1)	A negative result inside the square bracket produces a wrong subtraction	40

Time yourself on these eight questions. If you consistently finish under 12 minutes total, your speed and accuracy are exam-ready.

Interested in maths, explore more such questions.

Common Mistakes & How to Avoid Them

Even confident students trip over these seven errors. Recognise them now, and your accuracy will jump.

Error Type	Example	Quick Fix
Ignoring the left-to-right rule for equal-precedence operations	10 ÷ 5 × 2 calculated as 10 ÷ 10 = 1 instead of 2 × 2 = 4	Always scan left to right when division and multiplication (or addition and subtraction) appear together
Wrong order in nested brackets	Solving the outermost bracket before the innermost	Always work from the innermost outward
Treating “of” as addition instead of multiplication	“4 of 3” calculated as 4 + 3 = 7 instead of 4 × 3 = 12	Remember, “of” means multiply in the Indian curriculum
Applying multiplication before division by default	Students give priority to M over D based on acronym order	Both have equal priority; solve left to right
Performing addition before multiplication	2 + 3 × 4 = 20 (wrong) instead of 14	Multiplication always comes before addition unless brackets dictate otherwise
Parentheses confusion in simplification	2(3 + 4) calculated as 2 × 3 + 4 = 10 rather than 2 × 7 = 14	Treat implicit multiplication by brackets as part of the bracket step; “parentheses confusion accounts for nearly 40%” of calculation errors at key stage 3
Rushing through steps/skipping written steps	Speed leads to misreading operators	Write out each step clearly; underline brackets and exponents before starting

Education research confirms that misconceptions of the order of operations have been documented among children (aged 6–11), adolescents (aged 12–18), and even trainee teachers. The difference between those who master BODMAS and those who struggle is not intelligence; it is deliberate, structured practice. Return to the mnemonic chart whenever you feel uncertain, and cross-check your work against the 4-step checklist.

Wanted to explore other types of maths problems, try this out.

Conclusion & Next Steps

BODMAS is not a magic trick or a shortcut; it is a universal mathematical rule that helps students solve expressions accurately and systematically. By following the correct order of operations- brackets, orders, Division, Multiplication, Addition, and Subtraction- you can avoid confusion and reduce calculation errors. In this guide, you explored 28 BODMAS questions ranging from easy and medium-level problems to exam-oriented practice questions. Along the way, you also learned the importance of solving equal-precedence operations, such as multiplication and division, from left to right, which is one of the most common areas where students make mistakes.

You also discovered several common errors students make, such as ignoring brackets, performing operations in the wrong order, or rushing through calculations without writing out the proper steps. Understanding these mistakes is important because it helps you become more careful and confident while solving maths problems. The more you practise, the more naturally the BODMAS sequence will come to you.

To strengthen your skills, dedicate 10–15 minutes each day to solving mixed-difficulty BODMAS questions. Try timing yourself when working through exam-level problems to improve both speed and accuracy. You can also use the mnemonic chart regularly to memorise the sequence of operations more effectively. Consistent practice will help you build a strong foundation not only for Class 6 Maths but also for algebra, higher-level mathematics, and competitive exams in the future.

If you are preparing for competitive exams or need personalised guidance to strengthen your maths foundation, reach out to Leverage Edu for a free counselling session. We will help you build a study plan that fits your goals and timeline.

FAQs