Compute 47 × 53 in your head

Question

Solve in your head, no paper, no long multiplication. What is 47 	imes 53? Aim: under 5 seconds.

Accepted Answer

Both numbers sit symmetrically around 50: they are 50 - 3 and 50 + 3. 47 	imes 53 = (50 - 3)(50 + 3) = 50^2 - 3^2 = 2500 - 9 = 2491. The plodding route, 47 	imes 53 = 47 	imes 50 + 47 	imes 3 = 2350 + 141, lands on the same 2491, but spotting the midpoint turns the whole thing into one square minus a tiny square. Takeaway. When two factors share an easy midpoint m and sit d on either side, the product is m^2 - d^2. Scan every two-digit multiplication for that symmetry first.

Compute 47 × 53 in your head

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