UP Police Constable · Bite-size lessons
Simplification
About 6 min · Numerical & Mental Ability · English
Time worked out from the lesson's 310 words at 150 words a minute, plus a minute for each question.
Simplification is the foundation of quantitative aptitude in UP Police Constable exams. Every numerical problem—whether profit-loss, time-work, or data interpretation—requires you to simplify expressions correctly and quickly. Questions in this section test your ability to apply BODMAS rules, handle fractions and decimals, and compute squares, cubes, and their roots accurately.
Key ideas
- BODMAS/BODMAS Rule: Operations must follow the strict order — Brackets first, then Orders (powers/roots), then Division and Multiplication (left to right), finally Addition and Subtraction (left to right). Violating this order is the most common error.
- Fraction Operations: For addition/subtraction, convert to common denominator; for multiplication, multiply numerators and denominators directly; for division, multiply by the reciprocal. Mixed fractions must be converted to improper fractions before operations.
- Decimal Handling: Align decimal points for addition/subtraction. For multiplication, count total decimal places in factors and place that many in the product. For division, shift decimal points to make divisor a whole number.
- Square and Cube Roots: Perfect squares (1, 4, 9, 16, 25...144, 169, 196, 225, 256, 289, 324, 361, 400) and perfect cubes (1, 8, 27, 64, 125, 216, 343, 512, 729, 1000) must be memorized. Use factorization or digit methods for non-perfect roots.
- Reciprocal and Negative Signs: Division by a fraction equals multiplication by its reciprocal. Double negatives make positive; a negative times positive stays negative. Track sign changes carefully through multi-step problems.
Quick reference
- BODMAS = Brackets → Orders → Division/Multiplication (L to R) → Addition/Subtraction (L to R)
- Fraction division: flip the second fraction and multiply
- Decimal multiplication: ignore decimals, multiply, then count total decimal places
- Memorize squares 1–20 and cubes 1–10 cold
- √(perfect square) via factorization: pair prime factors
Check yourself: 3 questions
1. Simplify: 36 ÷ 6 × 3 + 12 - 8
2. What is the value of (2/5 + 3/10) × (5/6 - 1/3)?
3. Simplify: √1296 + ∛512 - 20
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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