As a learner, one of the earliest lessons in mathematics was learning how to solve expressions using the BODMAS rule. At that time, it felt like just another formula to memorise, but over the years its importance becomes much clearer. Every calculation, whether simple or complex, depends on the correct order of operations, and one small mistake can change the entire answer.
BODMAS is not just a school-level concept but a lifelong mathematical principle. It gives structure, removes confusion, and ensures that everyone solving the same problem arrives at the same solution.
In this blog, you will discover the most common BODMAS mistakes learners make and how to avoid them, along with practical tips to build accuracy and confidence in problem solving.
What are the Common BODMAS Mistakes?
Mastering BODMAS is essential for solving mathematical expressions correctly, yet many learners still fall into common traps that change the entire outcome of a problem. From overlooking brackets to rushing through calculations, these mistakes can easily be avoided with the right approach. Below are seven frequent BODMAS errors and practical tips to overcome them.
Ignoring Brackets
A common mistake students make is ignoring brackets when solving expressions. Brackets are used to group numbers or operations and must always be prioritised. Treating them as optional often leads to completely different results.
For example, consider this expression:
- Correct: 2 + (3 × 4) = 2 + 12 = 14
- Incorrect: (2 + 3) × 4 = 5 × 4 = 20
The mistake occurs when someone solves the addition first instead of focusing on the brackets. Always remember to calculate what is inside the brackets before moving forward.
Tip: Always solve expressions inside brackets first, regardless of other operations.
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Misinterpreting the Order of Operations
Another common error happens when people confuse the priority of operations. Multiplication and division must come before addition and subtraction. When this rule is ignored, answers go wrong.
Example:
- Correct: 6 + 2 × 3 = 6 + 6 = 12
- Incorrect: (6 + 2) × 3 = 8 × 3 = 24
Many learners assume that addition comes before multiplication because it appears first in the expression. The rule is simple: division and multiplication have equal priority, and both must be done before addition and subtraction.
Tip: Follow the left-to-right rule within the same level of operations.
Forgetting Exponents/Orders
Exponents or orders are often overlooked. Squaring, cubing, and roots are powerful operations that need to be solved immediately after brackets but before multiplication or addition. Ignoring this sequence leads to major errors.
Example:
- Correct: 2 + 3² = 2 + 9 = 11
- Incorrect: (2 + 3)² = 25
Mistakes often occur because exponents are either skipped or misplaced in the calculation.
Tip: Always solve exponents right after handling brackets.
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Ignoring Left-to-Right Rule
Operations of the same rank must follow the left-to-right rule. When division and multiplication or addition and subtraction appear together, the operation written first should be solved first.
Example:
- Correct: 12 ÷ 3 × 2 = 4 × 2 = 8
- Incorrect: 12 ÷ (3 × 2) = 12 ÷ 6 = 2
Skipping the left-to-right sequence results in completely different outcomes.
Tip: Perform multiplication and division sequentially from left to right.
Nested Brackets Confusion
Nested brackets can look intimidating, but the key is to start with the innermost bracket and move outward. Many errors occur when people try to skip steps or misplace operations.
Example:
- Correct: 2 × (3 + (4 × 5)) = 2 × (3 + 20) = 2 × 23 = 46
- Incorrect: 2 × (3 + 4) × 5 = 2 × 7 × 5 = 70
The difference is huge, showing how crucial it is to handle each layer of brackets carefully.
Tip: Always start from the innermost brackets and proceed step by step.
Using Negative Numbers Incorrectly
Negative numbers and subtraction can be tricky. Misinterpreting signs often leads to mistakes, especially when brackets are involved.
Example:
- Correct: 5 - (2 - 7) = 5 - (-5) = 10
- Incorrect: 5 - (2 - 7) = 5 - 5 = 0
The main issue is forgetting that subtracting a negative number changes the sign.
Tip: Pay close attention to signs and rewrite subtraction involving negatives carefully.
Rushing Through Calculations
Speed often leads to mistakes. Students sometimes skip writing steps or misread an operator because they want to finish quickly. Even if they know the rules, rushing can ruin accuracy.
Tip: Write out each step clearly and underline or highlight brackets and exponents. Regular practice with a focus on accuracy will reduce careless errors and build confidence.
Why Understanding BODMAS is Crucial in Mathematics
BODMAS is more than a school-level rule; it is a fundamental principle of mathematics. Following the correct order makes sure that calculations are accurate and consistent across all learners.
Ensures Consistency in Solutions
A clear sequence ensures that everyone solving the same expression reaches the same result. Without this rule, answers could vary from person to person. Whether you are solving a simple arithmetic problem or a complex algebraic expression, consistency is key to reliability in mathematics.
Prevents Miscalculations in Advanced Math
BODMAS forms the foundation of advanced topics like algebra, calculus, and applied mathematics. Incorrect use of BODMAS in basic arithmetic can create bigger errors in complex formulas. Consistency in applying the rule ensures that future learning in mathematics is accurate and dependable.
Tips and Strategies to Avoid BODMAS Mistakes
A few simple strategies can help avoid the most common mistakes.
Highlight or Underline Key Operations
Highlighting brackets or underlining exponents can serve as visual reminders. This technique ensures that no step is skipped. Students who use this strategy often catch mistakes early because their attention is drawn to the operations that matter most.
Practice Step-by-Step Problem Solving
Working slowly and methodically is the best way to avoid errors. Each step should be written down clearly instead of trying to solve problems mentally. Step-by-step problem solving not only improves accuracy but also helps build long-term confidence in mathematical reasoning.
Use Worksheets and Online Tools
Regular practice builds mastery. Worksheets provide structured repetition, while online BODMAS calculators allow students to check their work instantly. These tools help reinforce the order of operations and provide the feedback needed to improve.
Conclusion
Mastering BODMAS is not just about passing exams, it is about developing a solid foundation in mathematics. Errors often arise from ignoring brackets, misinterpreting orders, or skipping steps. Practising carefully and following the rules will make problem solving accurate and reliable. Visual cues like underlining, step-by-step solutions, and consistent practice with worksheets can greatly reduce mistakes.
When students understand the importance of BODMAS, they not only avoid careless errors but also build the confidence needed to handle more advanced mathematical challenges.
Frequently Asked Questions
BODMAS is a rule that shows the order of operations in mathematics: Brackets, Orders, Division/Multiplication, Addition, and Subtraction.
BODMAS is a rule that shows the order of operations in mathematics: Brackets, Orders, Division/Multiplication, Addition, and Subtraction.
Yes. Even one mistake in order of operations can change the entire answer, leading to a loss of marks.
Think of the acronym BODMAS itself. Brackets first, then Orders, followed by Division/Multiplication, and finally Addition/Subtraction.
Ignoring brackets or misplacing exponents are the most common errors.
May, 10, 2026 
