BODMAS Full Form, Rule and Questions with Solutions

B — Brackets: ( ), { }, [ ] Solve innermost bracket first, then outward. Order: ( ) → { } → [ ]

O — Orders: powers and roots Solve squares, cubes, square roots, cube roots. Example: 2³ = 8, √16 = 4

D — Division: ÷ M — Multiplication: × Division and Multiplication: same priority — solve left to right.

A — Addition: + S — Subtraction: − Addition and Subtraction: same priority — solve left to right.

Rule: When two operations have the same priority (D & M, or A & S), solve LEFT TO RIGHT.

Example 1: 18 ÷ 6 × 3 + 2 − 1 Step 1: Division: 18÷6 = 3 → 3 × 3 + 2 − 1 Step 2: Multiplication: 3×3 = 9 → 9 + 2 − 1 Step 3: Addition: 9+2 = 11 → 11 − 1 Step 4: Subtraction: 11−1 = 10 Answer: 10

Example 2: 5 + [3 × {8 − (2 + 3)}] Step 1: Innermost bracket ( ): 2+3=5 → 5 + [3 × {8−5}] Step 2: Curly bracket { }: 8−5=3 → 5 + [3 × 3] Step 3: Square bracket [ ]: 3×3=9 → 5 + 9 Step 4: Addition: 5+9 = 14 Answer: 14

Example 3: 2³ + 4 × 3 − 6 ÷ 2 Step 1: Orders: 2³=8 → 8 + 4×3 − 6÷2 Step 2: Division: 6÷2=3 → 8 + 4×3 − 3 Step 3: Multiplication: 4×3=12 → 8 + 12 − 3 Step 4: Addition: 8+12=20 → 20−3 Step 5: Subtraction: 17 Answer: 17

Example 4: 100 ÷ [5 × {2 + (4 − 1)}] Inner: 4−1=3 → 100÷[5×{2+3}] Curly: 2+3=5 → 100÷[5×5] Square: 5×5=25 → 100÷25 Division: 100÷25=4 Answer: 4

Mistake 1: Left-to-right for same-priority operations. Wrong: 12÷4×3 = 12÷12 = 1 Right: 12÷4=3, then 3×3=9. Answer: 9 Reason: Division and multiplication are equal priority — go left to right.

Mistake 2: Ignoring bracket hierarchy. Always solve ( ) first, then { }, then [ ].

Mistake 3: Adding before multiplying. Wrong: 3+4×2 = 7×2 = 14 Right: 3+(4×2) = 3+8 = 11 Multiplication before addition — BODMAS!

US vs Indian terminology: • BODMAS (India/UK): B-O-D-M-A-S • PEMDAS (USA): P(Parentheses), E(Exponents), M, D, A, S • BIDMAS (UK variant): I = Indices (same as Orders) • All give the same result — just different acronyms