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Multiplication · level 3

General 4-digit multiplication

When no reference number is close, split the smaller number into pieces you can multiply on sight, work left to right, and add as you go. You only ever hold one running total.

Worked example: 3,826 × 47

3,826 × 40153,040
3,826 × 726,782
total179,822

Step by step

  1. 1

    Split the short number

    47 = 40 + 7

  2. 2

    Multiply by the tens part

    3,826 × 40 = 153,040

  3. 3

    Multiply by the units part

    3,826 × 7 = 26,782

  4. 4

    Add the partial products

    153,040 + 26,782 = 179,822

  5. 5

    Check with digit sums

    1 × 2 → 2 = 2

3,826 × 47 = 179,822

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.