BODMAS Rules: Every Type of Question Solved (With Worked Examples)

BODMAS is the rule that determines the order in which mathematical operations must be performed in any expression. Without it, the same expression can produce completely different answers depending on which operation you do first — and only one answer is correct.

The full form of BODMAS is: Brackets → Orders (powers and roots) → Division → Multiplication → Addition → Subtraction. In some countries and textbooks, the same rule is called PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) or BIDMAS — but the mathematical logic is identical.

BODMAS questions appear in every competitive exam in India — SSC CGL, SSC CHSL, IBPS, RRB, NTSE, Class 6 to 10 boards, and even entrance exams like CAT and GMAT. This guide covers every type of BODMAS question with full worked solutions, common mistakes, and exam-specific shortcuts.

Part 1: BODMAS — Complete Order Reference

The Full Hierarchy

Bracket Hierarchy — Which Opens First

When multiple bracket types appear together, solve innermost first:

Order of bracket types (inner to outer):
Round brackets ( ) → Curly brackets { } → Square brackets []

Example structure: [ { ( ) }]
Solve ( ) first → then { } → then []

Division and Multiplication — Same Priority

When D and M appear together with no other priority difference, solve left to right.

12 ÷ 4 × 3 = 3 × 3 = 9 (NOT 12 ÷ 12 = 1)

Addition and Subtraction — Same Priority

When A and S appear together, solve left to right.

10 − 3 + 2 = 7 + 2 = 9 (NOT 10 − 5 = 5)

Part 2: Basic BODMAS — Step by Step

Level 1 — Simple Expressions

Worked Example 1:
Solve: 3 + 4 × 2

Step 1: No brackets or orders
Step 2: Multiplication first → 4 × 2 = 8
Step 3: Addition → 3 + 8 = 11

❌ Common mistake: 3 + 4 = 7, then 7 × 2 = 14 → Wrong!

Worked Example 2:
Solve: 20 − 4 ÷ 2 + 3

Step 1: Division → 4 ÷ 2 = 2
Step 2: Left to right → 20 − 2 + 3 = 18 + 3 = 21

Worked Example 3:
Solve: 5 × 3 + 8 ÷ 4 − 2

Step 1: Multiplication → 5 × 3 = 15
Step 2: Division → 8 ÷ 4 = 2
Step 3: Left to right → 15 + 2 − 2 = 15

Worked Example 4:
Solve: 18 ÷ 6 × 3 ÷ 9

D and M same priority → left to right:
18 ÷ 6 = 3 → 3 × 3 = 9 → 9 ÷ 9 = 1

Part 3: BODMAS with Brackets

Single Bracket

Worked Example 5:
Solve: (3 + 5) × 4 − 6

Step 1: Bracket → 3 + 5 = 8
Step 2: Multiply → 8 × 4 = 32
Step 3: Subtract → 32 − 6 = 26

Worked Example 6:
Solve: 50 ÷ (2 + 3) × 4

Step 1: Bracket → 2 + 3 = 5
Step 2: Left to right → 50 ÷ 5 = 10 → 10 × 4 = 40

Nested Brackets

Worked Example 7:
Solve: [3 + {4 × (2 + 1)} − 5]

Step 1: Innermost ( ) → 2 + 1 = 3
Step 2: { } → 4 × 3 = 12
Step 3: [] → 3 + 12 − 5 = 10

Worked Example 8:
Solve: 100 − [40 + {20 − (10 + 5)}]

Step 1: ( ) → 10 + 5 = 15
Step 2: { } → 20 − 15 = 5
Step 3: [] → 40 + 5 = 45
Step 4: Final → 100 − 45 = 55

Worked Example 9:
Solve: 3 × [4 + {6 − (2 × 1 + 1)}]

Step 1: ( ) → 2 × 1 = 2, then 2 + 1 = 3
Step 2: { } → 6 − 3 = 3
Step 3: [] → 4 + 3 = 7
Step 4: Final → 3 × 7 = 21

Part 4: BODMAS with Powers and Roots (Orders)

Powers and roots are solved immediately after brackets — before division, multiplication, addition, subtraction.

Worked Example 10:
Solve: 2 + 3² × 4

Step 1: Order → 3² = 9
Step 2: Multiply → 9 × 4 = 36
Step 3: Add → 2 + 36 = 38

❌ Common mistake: (2 + 3)² × 4 = 25 × 4 = 100 → only valid if brackets present

Worked Example 11:
Solve: √64 + 4² ÷ 8 − 3

Step 1: Orders → √64 = 8, 4² = 16
Step 2: Division → 16 ÷ 8 = 2
Step 3: Left to right → 8 + 2 − 3 = 7

Worked Example 12:
Solve: (2 + 3)² − 4 × 3 + √9

Step 1: Bracket → 2 + 3 = 5
Step 2: Orders → 5² = 25, √9 = 3
Step 3: Multiply → 4 × 3 = 12
Step 4: Left to right → 25 − 12 + 3 = 16

Worked Example 13:
Solve: 2³ + √(9 + 16) − 4²÷8

Step 1: Orders inside root → 9 + 16 = 25, √25 = 5
Step 2: Other orders → 2³ = 8, 4² = 16
Step 3: Division → 16 ÷ 8 = 2
Step 4: Left to right → 8 + 5 − 2 = 11

Part 5: BODMAS with Fractions

Fractions are treated as division — numerator ÷ denominator. The fraction bar also acts as a grouping symbol (bracket).

Rule: Fraction Bar = Invisible Bracket

(3 + 5) / (2 + 2) means (3+5) ÷ (2+2) — solve numerator and denominator separately first.

Worked Example 14:
Solve: (8 + 4) / (9 − 3)

Numerator = 12, Denominator = 6
Answer = 12/6 = 2

Worked Example 15:
Solve: 3 + 12/(2 × 3) − 1

Step 1: Fraction denominator → 2 × 3 = 6
Step 2: Fraction → 12/6 = 2
Step 3: Left to right → 3 + 2 − 1 = 4

Worked Example 16:
Solve: (5² − 3²) / (5 + 3) × 4

Step 1: Orders → 5² = 25, 3² = 9
Step 2: Numerator → 25 − 9 = 16
Step 3: Denominator → 5 + 3 = 8
Step 4: Fraction → 16/8 = 2
Step 5: Multiply → 2 × 4 = 8

Shortcut — Difference of squares: (5² − 3²) / (5 + 3) = (5−3)(5+3)/(5+3) = (5−3) = 2 → saves a step!

Worked Example 17 — Complex Fraction:
Solve: [3 × 4 + 2²] / [5² − (3 + 2²)]

Numerator: 3 × 4 = 12, 2² = 4 → 12 + 4 = 16
Denominator: 5² = 25, 2² = 4 → 3 + 4 = 7 → 25 − 7 = 18
Answer = 16/18 = 8/9

Part 6: BODMAS with Decimals

Decimals follow the exact same BODMAS order. The key is to keep decimal points aligned correctly.

Worked Example 18:
Solve: 3.5 + 2.5 × 4 − 1.2

Step 1: Multiply → 2.5 × 4 = 10
Step 2: Left to right → 3.5 + 10 − 1.2 = 12.3

Worked Example 19:
Solve: (4.8 + 1.2) ÷ 3 × 2.5

Step 1: Bracket → 4.8 + 1.2 = 6
Step 2: Left to right → 6 ÷ 3 = 2 → 2 × 2.5 = 5

Worked Example 20:
Solve: 0.5² × 8 + √0.64 − 1.2

Step 1: Orders → 0.5² = 0.25, √0.64 = 0.8
Step 2: Multiply → 0.25 × 8 = 2
Step 3: Left to right → 2 + 0.8 − 1.2 = 1.6

Part 7: BODMAS in Competitive Exam Questions

Competitive exams (SSC, IBPS, RRB) test BODMAS in three specific ways — direct simplification, missing number, and wrong number insertion.

Type 1 — Direct Simplification

Worked Example 21:
Simplify: 3/4 of 64 + 5/8 of 96 − 15% of 200

Step 1: "of" = multiplication → apply first
3/4 × 64 = 48
5/8 × 96 = 60
15/100 × 200 = 30
Step 2: Left to right → 48 + 60 − 30 = 78

Key rule: In competitive exams, "of" is treated as multiplication and solved at the Orders/Multiplication stage.

Worked Example 22:
Simplify: 25% of 400 + ⅓ of 270 − √225

Step 1: 25% of 400 = 100
Step 2: ⅓ of 270 = 90
Step 3: √225 = 15
Step 4: 100 + 90 − 15 = 175

Type 2 — Missing Number (? Questions)

Worked Example 23:
? + 3 × 4 = 50 − 2²

RHS: 2² = 4 → 50 − 4 = 46
LHS: 3 × 4 = 12 → ? + 12 = 46
? = 34

Worked Example 24:
144 ÷ ? × 3 = 36

144 ÷ ? = 12 (since 12 × 3 = 36)
? = 144 ÷ 12 = 12

Type 3 — Approximation (Competitive Exam Style)

Worked Example 25:
Approximate: 19.8% of 3995 + 4.9 × 79.8

≈ 20% of 4000 + 5 × 80
= 800 + 400 = 1200

Worked Example 26:
Approximate: √(399) × 5.02 + (14.97)²

≈ √400 × 5 + 15²
= 20 × 5 + 225
= 100 + 225 = 325

Part 8: Common BODMAS Mistakes — Avoid These

Mistake 1 — Ignoring Left-to-Right Rule

❌ Wrong: 12 ÷ 4 ÷ 3 = 12 ÷ 1 = 12
✅ Right: 12 ÷ 4 = 3, then 3 ÷ 3 = 1

Mistake 2 — Subtracting Before Adding

❌ Wrong: 10 + 5 − 8 = 10 + (5 − 8) = 10 − 3 = 7
✅ Right: 10 + 5 = 15, then 15 − 8 = 7 ← same here, but this fails when:

❌ Wrong: 10 − 5 + 8 = 10 − 13 = −3
✅ Right: 10 − 5 = 5, then 5 + 8 = 13

Mistake 3 — Forgetting "of" = Multiplication

❌ Wrong: ½ of 3 + 5 = ½ of 8 = 4
✅ Right: ½ × 3 = 1.5, then 1.5 + 5 = 6.5

Mistake 4 — Solving Power Inside vs Outside Bracket

❌ Wrong: 2 + 3² = 5² = 25
✅ Right: 3² = 9, then 2 + 9 = 11

Mistake 5 — Bar Fraction Not Treated as Bracket

❌ Wrong: 3 + 9/3 + 6 read as (3+9)/(3+6) = 12/9
✅ Right: 3 + (9/3) + 6 = 3 + 3 + 6 = 12 (slash is not a grouping bar)

Part 9: BODMAS Quick Reference — 20 Practice Questions