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Multiplication · level 2

No close reference number

Numbers like 23 and 79 sit nowhere near a shared reference. Give each one its own reference instead: leave one factor alone, round the other to the nearest ten, multiply, then correct by the small amount you moved.

Worked example: 23 × 79

23 × 801,840
23 × 1− 23
total1,817

Step by step

  1. 1

    Neither number has a close reference

    23 × 79

    Give each number its own reference: 23 keeps its value, 79 borrows 80.

  2. 2

    Round 79 to 80

    79 = 80 − 1

  3. 3

    Multiply by the easy reference

    23 × 80 = 23 × 8 × 10 = 1,840

  4. 4

    Compensate: you added too much

    23 × 1 = 23

  5. 5

    Subtract the correction

    1,840 − 23 = 1,817

  6. 6

    Check with digit sums

    5 × 7 → 8 = 8

23 × 79 = 1,817

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.