n × 11
The trick, step by step
Write the two digits with a gap between them.
Add the two digits and put the sum in the gap: 3 + 6 = 9.
That is the answer: 36 × 11 = 396.
If the sum is 10 or more, write only its last digit in the gap and add 1 to the left digit: 78 × 11 → 7, 15, 8 → 858.
Longer numbers: keep the last digit, then add each digit to the one on its right: 347 × 11 → 3, 3 + 4, 4 + 7, 7 → 3, 7 + 1 carried, 1, 7 → 3817.
given working answer taken away
Why it works
A two digit number is 10a + b. Times 11 it is 110a + 11b = 100a + 10(a + b) + b: the first digit a stays in the hundreds, the sum a + b lands in the tens, and b stays in the ones. A sum of 10 or more carries 1 into the hundreds. Longer numbers work the same way, because n × 11 = n × 10 + n adds every digit to its neighbour.
Practise this trick