Mental Math
Fast Multiplication & Squaring
Overview
Mental math speed in trading interviews is non-negotiable. The goal isn't calculator accuracy — it's 'fast enough to participate in live markets.' The key techniques: (1) decompose numbers into round numbers ± small corrections, (2) use algebraic identities like (a+b)(a−b), (3) percentage swapping. Practice the same 10 patterns until they're automatic. Zetamac is the best free tool — aim for 40+ correct per minute.
How to Recognize
- →Any quick arithmetic under interview pressure
- →Pricing derivatives: 'What's 47² ≈?'
- →Speed is the key differentiator vs. other candidates
Step-by-Step Approach
- 1.(a+b)² = a²+2ab+b²: decompose into round numbers
- 2.Near-squares: (a+b)(a−b) = a²−b² — fastest for numbers close to a round number
- 3.Multiply by 9: multiply by 10 then subtract the original
- 4.FOIL with friendly splits: 47×83 = (50−3)(80+3) = 4000+150−240−9 = 3901
Key Formulas
Worked Examples
Problem
Compute 97² and 103² mentally.
Solution
97² = (100−3)² = 10000 − 600 + 9 = 9409.
103² = (100+3)² = 10000 + 600 + 9 = 10609.
Pattern: (100±n)² = 10000 ± 200n + n². Fast for n ≤ 10.
Answer
, . The (100±n)² pattern gives answers in 3 seconds.
Common Mistakes
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Using the long multiplication algorithm under pressure — much slower than decomposition tricks.
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Not practicing daily. Mental math is a physical skill (like a sport) that requires repetition, not just understanding.
Practice Problems
Click "Show Answer" to revealCompute 64² mentally.
Compute 43 × 57 mentally.
What is 17% of 300?