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Multiplication · level 1

Small numbers, reference 10

Every number from 5 to 9 sits just below 10. Write how far below in a circle, cross-subtract, then multiply the circles. This single move replaces the upper half of the times tables.

Worked example: 7 × 8

reference number 10
7−3
8−2
cross-add: 7 −2 = 5
× reference: 50
circles: −3 × −2 = 6
= 56

Step by step

  1. 1

    Choose the reference number: 10

    7 is − 3 · 8 is − 2

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

  2. 2

    Cross-subtract (or cross-add) diagonally

    7 − 2 = 5

    The other diagonal gives the same answer: 8 − 3 = 5.

  3. 3

    Multiply that result by the reference number

    5 × 10 = 50

  4. 4

    Multiply the two circled numbers

    (−3) × (−2) = 6

  5. 5

    Add it to the running total

    50 + 6 = 56

7 × 8 = 56

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.