Why multiplying by 11 feels like magic
The "split-and-add" trick is older than your grandparents - and it works because of how we write numbers.
The party trick
Quick: 11 × 63. Most people grab a calculator. The trick: split the digits (6 _ 3), add them (6 + 3 = 9), drop the sum in the gap → 693. Done.
Why it works
Multiplying any 2-digit number AB by 11 is the same as adding (10 × AB) + AB. The tens digit shifts left, the original digit stays - and where they overlap, you add. That overlap is the middle digit.
The carry case
For 11 × 87: 8 + 7 = 15. You write the 5 in the gap and carry the 1 → 957. Same rule, just with a carry. This is also why kids who learn it as "magic" are often confused by 11 × 99.
Generalising
It generalises: 111 × AB has its own pattern (try it). The deeper truth is that any "rep-unit" multiplier (11, 111, 1111…) interacts with positional notation in a way that lets you skip the long-multiplication grid.