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Multiplication · level 1

Just below 100

The same circles work with a reference of 100. Because the circles are small, the whole product falls out in two chunks: hundreds from the cross-subtraction, and the last two digits from the circles.

Worked example: 96 × 97

reference number 100
96−4
97−3
cross-add: 96 −3 = 93
× reference: 9,300
circles: −4 × −3 = 12
= 9,312

Step by step

  1. 1

    Choose the reference number: 100

    96 is − 4 · 97 is − 3

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

  2. 2

    Cross-subtract (or cross-add) diagonally

    96 − 3 = 93

    The other diagonal gives the same answer: 97 − 4 = 93.

  3. 3

    Multiply that result by the reference number

    93 × 100 = 9,300

  4. 4

    Multiply the two circled numbers

    (−4) × (−3) = 12

  5. 5

    Add it to the running total

    9,300 + 12 = 9,312

96 × 97 = 9,312

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.