Multiply two teens: 14 × 17

Question

Products of two teen numbers have a tidy shortcut worth memorising. Solve in your head. What is 14 	imes 17? Aim: under 8 seconds.

Accepted Answer

Add the first number to the second's units digit, times 10, then add the product of the units digits: (14 + 7)	imes 10 + 4 	imes 7 = 210 + 28 = 238. So 14 	imes 17 = \mathbf{238}. Check by distributing: 14 	imes 17 = 14 	imes 10 + 14 	imes 7 = 140 + 98 = 238. Matches. The rule is just (10+a)(10+b) = 100 + 10(a+b) + ab; the "add across" step folds the 100 and 10(a+b) together. Takeaway. Teen times teen: "one number plus the other's ones digit, times ten, plus the ones-digit product." It's the base-10 version of the near-100 method.

Multiply two teens: 14 × 17

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