Why multiplying by 11 works

The split-and-add shortcut works because of place value, not a memorized rule.

2 min read

Spread digits

For 63 x 11, keep 6 and 3 outside. Put their sum between them.

63 \times 11 = 6(6+3)3 = 693

11 means 10 + 1. One copy shifts left; the overlap becomes the digit sum.

63 \times 11 = 630 + 63

For 87, the middle sum is 15. Place 5 and carry 1 left.

87 \times 11 = 957

For 111, overlapping copies create a longer addition window.

63 \times 111 = 6300 + 630 + 63