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Both factors just under a round number

Mental mathEasy

$2$ prices are quoted just below a round level, at $98$ and $97$ . Multiply them together in your head.

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Hint

Measure how far each factor sits below $100$ .

Solution

Write $98 = 100 - 2$ and $97 = 100 - 3$ .
Cross-subtract: $98 - 3 = 95$ (or $97 - 2 = 95$ ), which gives the hundreds part $9500$ .
Multiply the shortfalls: $2 \times 3 = 6$ .
Add the parts: $9500 + 6 = 9506$ , so the product is $9506$ .

Answer: $9506$