×QvantCase
← All techniques

Multiplication · level 1

Multiplying by 11

Write the number with a zero in front and behind, then replace every digit by itself plus its right-hand neighbour. Carry when a pair exceeds nine.

Worked example: 362 × 11

position 40 + 3 = 3
position 33 + 6 = 9
position 26 + 2 = 8
position 12 + 0 = 2

Step by step

  1. 1

    Pad with zeros

    0 3 6 2 0

  2. 2

    Add each digit to its right neighbour

    0 + 3 = 3 · 3 + 6 = 9 · 6 + 2 = 8 · 2 + 0 = 2

  3. 3

    Carry where a pair passed 9

    = 3,982

    Work right to left when carrying.

362 × 11 = 3,982

The theory behind it

Intuition

Multiplication is easiest near a round number. You multiply the friendly number, then repair the difference — the repair term is always (how far off) × (the other factor).

Common pitfalls

  • ×Losing the sign of the correction: rounding up means you subtract, rounding down means you add.
  • ×Correcting against the wrong factor — the repair multiplies the factor you did not round.

In the interview

Every case round is a multiplication: users × price, volume × margin, market × share. Speed here buys you thinking time for the so-what.