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Multiplication · level 2

Reference multiples of ten

Any multiple of ten can be the reference number. Pick the nearest one to both numbers and the circles stay tiny — this covers all of the two-digit multiplications the 100-reference handles badly.

Worked example: 42 × 48

reference number 40
42+2
48+8
cross-add: 42 +8 = 50
× reference: 2,000
circles: +2 × +8 = 16
= 2,016

Step by step

  1. 1

    Choose the reference number: 40

    42 is + 2 · 48 is + 8

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

  2. 2

    Cross-subtract (or cross-add) diagonally

    42 + 8 = 50

    The other diagonal gives the same answer: 48 + 2 = 50.

  3. 3

    Multiply that result by the reference number

    50 × 40 = 2,000

  4. 4

    Multiply the two circled numbers

    (+2) × (+8) = 16

  5. 5

    Add it to the running total

    2,000 + 16 = 2,016

42 × 48 = 2,016

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.