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Multiplication · level 2

One above, one below

When one number is above the reference and the other below, the circle product is negative — so the last move is a subtraction. This is the only place beginners slip.

Worked example: 98 × 134

reference number 100
98−2
134+34
cross-add: 98 +34 = 132
× reference: 13,200
circles: −2 × +34 = −68
= 13,132

Step by step

  1. 1

    Choose the reference number: 100

    98 is − 2 · 134 is + 34

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

  2. 2

    Cross-subtract (or cross-add) diagonally

    98 + 34 = 132

    The other diagonal gives the same answer: 134 − 2 = 132.

  3. 3

    Multiply that result by the reference number

    132 × 100 = 13,200

  4. 4

    Multiply the two circled numbers

    (−2) × (+34) = −68

  5. 5

    Subtract it from the running total

    13,200 − 68 = 13,132

98 × 134 = 13,132

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.