⚡️ The Near-100 Multiplication Trick ⚡️

Ever wished you could multiply big numbers like $97 \times 98$ in your head in seconds? Stop reaching for the calculator! This trick will make you a mental math wizard!

Subject: mental-calculation • Classes: 6–12 • Difficulty: intermediate (9-10)

The Trick

To multiply two numbers just below 100: 1. Find how much each number is *less* than 100. Let's call these 'deficits'. 2. Multiply these two deficits. This product gives you the *last two digits* of your answer. If it's a single digit, add a leading zero (e.g., $3 \times 2 = 6$, write $06$). 3. Subtract one number's deficit from the *other* number. This gives you the *first part* of your answer. 4. Combine the results from step 3 and step 2. **Why it works:** Let the numbers be $(100-a)$ and $(100-b)$. Their product is $(100-a)(100-b) = 10000 - 100a - 100b + ab = 100(100 - a - b) + ab$. The term $(100-a-b)$ is our 'cross-subtraction', and $ab$ is the product of deficits.

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