Multiplying by 11

Mental Math · Axiom Academy

Spread the two digits apart, drop their sum into the gap that opens between them — and know exactly what to do when that sum passes 9. 1. Open a Gap, Drop the Sum In Take 32 × 11 . Pull the two digits apart so an empty place opens between them: a 3 , a gap, then a 2 . Now add the two digits you just separated — 3 + 2 = 5 — and drop that 5 straight into the gap. Reading left to right you get 3, 5, 2 , so the answer is 352 . The outer digits never changed; the only new digit is the one that filled the space. Separate the two digits, leaving an empty place between them. Add the two digits you just separated. Drop that sum into the empty place, then read the three digits left to right. The digits step aside; their sum takes the place between them The first digit of 32 stays the first digit of 352, and the last stays the last. You only ever work out the middle. It is 3 + 2, never 3 × 2. Nothing in this method multiplies two digits together. 50 × 11 has 5 + 0 = 5 in the gap, giving 550. Likewise 30 × 11 = 330 — the digit simply repeats. 44 × 11 puts 4 + 4 = 8 in the gap for 484. Any repeated digit below 5 behaves this cleanly. A digit, a gap, a digit — with their sum dropped in between. Nothing is carried in any of these, because every pair adds to 9 or less. 2. When the Sum Passes 9, the Carry Moves Left

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