Simplification BODMAS Fast Calculation Questions for BIHAR POLICE CONSTABLE

BODMAS Rule: The Golden Sequence

BODMAS is your roadmap for solving any expression with mixed operations. It stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction — in that exact order. The key insight: you MUST follow this sequence strictly. Many aspirants make mistakes by doing addition before division, or multiplication before brackets. Think of BODMAS like traffic rules — if you ignore the order, you crash. In Bihar Police exams, expressions often have nested brackets and multiple operations to test whether you know the sequence.

• B = Brackets (solve innermost first, then work outward)
• O = Orders (powers, square roots, cube roots)
• DM = Division and Multiplication (left to right, whichever comes first)
• AS = Addition and Subtraction (left to right, whichever comes first)
• Common error: treating Division before Multiplication always — wrong! Go left to right
• Brackets include (), {}, [] — solve from innermost outward

Step-by-Step Approach for Complex Expressions

Break down any expression into layers. Start with the innermost bracket, solve it completely, then move outward. Once all brackets are gone, handle powers/roots. Then scan left to right for division and multiplication in order of appearance. Finally, addition and subtraction left to right. This methodical approach prevents skipping steps and catching errors early. Bihar Police papers often include expressions with 3-4 nested brackets to test patience and accuracy.

• Identify all brackets and number them (innermost = 1, next = 2, etc.)
• Solve innermost bracket first, replace with result
• Repeat until no brackets remain
• Apply powers and roots next
• Scan left to right for ÷ and × — do whichever appears first
• Finally scan left to right for + and − — do whichever appears first

Fast Mental Shortcuts & Tricks

In a timed exam, you can't afford to write every step. Learn to spot patterns and simplify mentally. Fractions that cancel, numbers that form neat products, expressions that telescope — these are your speed weapons. For instance, if you see 48 ÷ 12, don't compute; recognize 48 = 12 × 4. If you see 99 × 101, use (100-1)(100+1) = 10000 - 1 = 9999. Bihar Police papers reward quick mental math — the faster you solve, the more time for harder sections.

• Spot cancellable fractions early: 24/36 = 2/3 before multiplying
• Use difference of squares: (a-b)(a+b) = a² - b²
• Recognize common products: 12×25=300, 15×20=300, 16×25=400
• Break large numbers into factors: 144 = 12² = 144, easier to divide
• Negative signs: count them. Odd count = negative result, even = positive
• Simplify before multiplying, not after — saves mental load

Handling Negative Numbers & Signs

Sign errors are the #1 silly mistake in simplification. Remember: negative × negative = positive, negative × positive = negative. When you have a string of operations with negatives, count the total negative signs. If odd, final answer is negative; if even, positive. This is faster than tracking signs step-by-step. Also, subtraction is not commutative — 5 - 3 is not the same as 3 - 5. Be careful with bracket negatives: -(3 + 2) = -5, not -3 + 2.

• Negative × Negative = Positive (two wrongs make a right)
• Negative × Positive = Negative
• Count total negatives in expression: odd = negative answer, even = positive
• Subtraction order matters: a - b ≠ b - a
• When bracket has minus outside: -(a + b) = -a - b (distribute the negative)
• Double negatives cancel: --5 = +5

Common Expression Types in Bihar Police Papers

Examiners use a few standard templates. Type 1: nested brackets with all four operations. Type 2: fractions with mixed operations. Type 3: expressions with powers/roots mixed in. Type 4: long chains of additions and subtractions (test your left-to-right discipline). Recognizing the type helps you choose the fastest approach. For instance, if you see fractions, simplify them first before touching the rest. If you see powers, compute those early.

• Type 1 (Nested Brackets): Solve innermost first, work outward systematically
• Type 2 (Fractions): Find LCM of denominators, convert, then simplify
• Type 3 (Powers/Roots): Compute 2², √16, etc. before other operations
• Type 4 (Long Chains): Mark each operation, go strictly left to right
• Mixed Type: Always prioritize Brackets > Orders > DM > AS

• Ignoring bracket priority: Solving 2 + 3 × 4 as (2 + 3) × 4 = 20 instead of 2 + (3 × 4) = 14. Brackets must be solved first, but only if they exist.
• Wrong order for division and multiplication: Treating ÷ as always before ×. Actually, go left to right. In 12 ÷ 3 × 2, the answer is (12 ÷ 3) × 2 = 8, not 12 ÷ (3 × 2) = 2.
• Sign errors with negatives: Forgetting to distribute negative signs in brackets. -(5 + 3) = -8, not -5 + 3 = -2. Count negatives: odd = negative answer.
• Skipping steps mentally: Writing down intermediate results saves time and prevents errors. Don't try to do everything in your head under pressure.
• Misreading the expression: In a hurry, aspirants misread 48 ÷ 12 as 48 × 12. Double-check operators before starting.

• BODMAS = 'Bracket Officer Divides, Multiplies, Adds, Subtracts' — think of a strict officer enforcing rules in order.
• DM and AS are pairs: Division-Multiplication are siblings (same priority, left to right). Addition-Subtraction are siblings (same priority, left to right).
• Negative sign rule: 'Odd negatives go negative, even negatives go positive' — like flipping a light switch odd times leaves it on, even times leaves it off.
• Brackets are walls: Solve everything inside the wall before breaking the wall down. Innermost wall first.

• Bihar Police papers typically have 2-3 simplification questions in the Numerical Ability section. They range from easy (single bracket, 4 operations) to medium (nested brackets, mixed fractions). Rarely hard, but tricky if you rush.
• Time pressure is real: You have ~90 seconds per question. Practice mental shortcuts so you don't write every step. Examiners reward speed without sacrificing accuracy.
• Negative numbers appear in almost every paper: Expect at least one expression with multiple negatives. Practice the 'count negatives' trick until it's automatic.
• Fractions mixed with BODMAS: If you see 1/2 + 3/4 × 2, remember multiplication comes before addition. Compute 3/4 × 2 = 3/2 first, then add 1/2 + 3/2 = 2.
• Recent trend: Examiners are including expressions with powers and roots (e.g., 2³ + √16 - 5). Solve powers/roots early (step 2 in BODMAS), then proceed normally.