How to Simplify Expressions Using BODMAS
Master BODMAS order of operations with the correct left-to-right rules, a worked example, and aptitude practice questions with answers.
Expected Interview Answer
BODMAS fixes a strict evaluation order — Brackets, Of, Division, Multiplication, Addition, Subtraction — so any expression with mixed operators simplifies to exactly one correct value.
Work brackets from the innermost outward first, resolve “of” (which means multiply) next, then scan left to right resolving division and multiplication at equal precedence, and finally resolve addition and subtraction left to right at equal precedence. The most common trap is treating multiplication as always outranking division, or addition as always outranking subtraction — within each pair the rule is left-to-right, not a fixed hierarchy. A second trap is applying a minus sign outside a bracket to only the first term inside instead of distributing it across every term. Rewriting the expression step by step, replacing one resolved operation at a time, prevents both errors.
- One fixed order removes all ambiguity from mixed-operator expressions
- Left-to-right tie-breaking prevents the division/multiplication trap
- Careful bracket distribution avoids sign errors
AI Mentor Explanation
A match referee applies rules in a strict order: first check the field restrictions (brackets), then powerplay overs (of), then no-ball reviews (division/multiplication), then runs and penalties (addition/subtraction). Skipping straight to totaling runs before resolving a no-ball review gives the wrong final score, just as skipping brackets before multiplying gives the wrong value. BODMAS enforces exactly this fixed checking order so every umpire, like every calculator, reaches the same result.
Worked example
Bracket
- (6 - 2) = 4
Of, Division, Multiplication
- 8 of 2 = 16
- 4 / 2 = 2
- 2 x 3 = 6
Left to right
- 12 + 16 - 6 = 22
Step-by-Step Explanation
Step 1
Resolve brackets innermost-out
Simplify the deepest nested brackets first, then work outward.
Step 2
Resolve “of”
"Of" means multiply — resolve it right after brackets.
Step 3
Division and multiplication, left to right
Equal precedence — whichever appears first, left to right, resolves first.
Step 4
Addition and subtraction, left to right
Equal precedence — resolve left to right for the final value.
What Interviewer Expects
- Correct order: Brackets, Of, Division/Multiplication, Addition/Subtraction
- Left-to-right tie-breaking within Division/Multiplication and Addition/Subtraction
- Correct sign distribution when a bracket is preceded by a minus
- A step-by-step rewrite rather than mental shortcuts prone to error
Common Mistakes
- Always doing multiplication before division regardless of left-to-right order
- Always doing addition before subtraction regardless of left-to-right order
- Distributing a leading minus sign to only the first term inside a bracket
- Resolving brackets outside-in instead of innermost-out
Best Answer (HR Friendly)
“I follow BODMAS strictly: brackets first, then “of” as multiplication, then division and multiplication left to right since they are equal priority, and finally addition and subtraction left to right. I rewrite the expression one step at a time rather than trying to do it all mentally, which avoids the classic trap of assuming multiplication always beats division.”
Follow-up Questions
- How does BODMAS differ from PEMDAS used in some countries?
- How do you simplify an expression with nested brackets three levels deep?
- Why is left-to-right order needed for division and multiplication specifically?
- How would a misplaced bracket change the final answer in a given expression?
MCQ Practice
1. Simplify: 18 / 3 x 2 - 4
18/3=6 (division first, left to right), 6x2=12, 12-4=8.
2. Simplify: 5 + 3 of 4 - (2 + 1)
Bracket: (2+1)=3. Of: 3 of 4=12. Then 5+12-3=14.
3. In BODMAS, when division and multiplication both appear, which resolves first?
Division and multiplication share equal precedence, resolved strictly left to right.
Flash Cards
What does BODMAS stand for? — Brackets, Of, Division, Multiplication, Addition, Subtraction.
What does "Of" mean in BODMAS? — Multiply — e.g. "8 of 2" means 8 x 2.
How are Division/Multiplication resolved when both appear? — Equal precedence, resolved left to right.
Common sign-distribution trap? — A minus before a bracket must be applied to every term inside, not just the first.