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Multiplication · level 2

Three digits near 1000

The circles method scales. With a reference of 1000 you multiply three-digit numbers faster than you can write them down.

Worked example: 994 × 1013

reference number 1,000
994−6
1,013+13
cross-add: 994 +13 = 1,007
× reference: 1,007,000
circles: −6 × +13 = −78
= 1,006,922

Step by step

  1. 1

    Choose the reference number: 1,000

    994 is − 6 · 1013 is + 13

    Write each number with its difference from the reference in a circle.

  2. 2

    Cross-subtract (or cross-add) diagonally

    994 + 13 = 1,007

    The other diagonal gives the same answer: 1013 − 6 = 1,007.

  3. 3

    Multiply that result by the reference number

    1,007 × 1,000 = 1,007,000

  4. 4

    Multiply the two circled numbers

    (−6) × (+13) = −78

  5. 5

    Subtract it from the running total

    1,007,000 − 78 = 1,006,922

994 × 1013 = 1,006,922

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.