Multiplying Two-Digit Numbers by 11

Mental Math · Axiom Academy

EXAMPLE Multiplying Two-Digit Numbers by 11 Walk line by line, then handle the half of all two-digit numbers whose digits add past nine. Work out in your head: pull the 2 and the 3 apart so an empty place opens between them, add the two digits you separated, and drop that sum into the gap. Nicely done — four two-digit numbers multiplied by 11 , and not one written partial product. Worth holding on to: The outer digits are already the answer: the 2 and the 3 of 23 keep their places in 253 . The only digit you work out is the one that fills the gap between them. The gap holds a sum, never a product: it is 2 + 3 , not . Nothing in this method multiplies two digits together. A sum of 9 or less drops straight in: that is 45 of the 90 two-digit numbers, and is one of them. A sum of 10 or more sends 1 one place left: its ones digit stays in the gap and the front digit goes up by one — and . Writing the whole sum into the gap instead gives 5127 and 8124 , which are not those products. A front digit of 9 turns over: the carry lifts it to 10 , so the answer gains a place — , four digits, not three. Multiplying by 11 is multiplying by 10 and adding one more copy: 230 + 23 = 253 . The gap is the place where those two copies overlap, which is why a sum turns up there at all — and why it sometimes carries, exactly like any other addition.

This is the written version of the interactive lesson above. See the full Mental Math course.