47 × 53 in Two Seconds

Question

Compute 47 times 53 mentally, in under three seconds. Then explain the technique that makes it instant.

Accepted Answer

Both factors straddle 50 by 3: 47 times 53 = (50-3)(50+3) = 50^2 - 3^2 = 2500 - 9 = mathbf2491. Difference of squares is the highest-value trick in the mental-math arsenal because near-symmetric products appear constantly: 98 times 102 = 9996, 61 times 59 = 3599, 45 times 55 = 2475. Asymmetric products reduce to it too: anchor at a round number and adjust, 47 times 56 = 47 times 53 + 47 times 3 = 2491 + 141 = 2632. For the Optiver/Flow-style arithmetic screens, drill until "two numbers near a round center" automatically triggers a^2 - b^2, recognizing the pattern is the speed; the arithmetic is trivial.

47 × 53 in Two Seconds

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