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Multiplication · level 1

Multiplying by factors

Awkward multipliers are friendly ones in disguise: × 5 is × 10 ÷ 2, × 25 is × 100 ÷ 4, × 15 is × 10 + half again.

Worked example: 384 × 25

Multiply by 100384 × 100 = 38,400
Halve twice19,200 → 9,600

Step by step

  1. 1

    Multiply by 100

    384 × 100 = 38,400

  2. 2

    Halve twice

    19,200 → 9,600

384 × 25 = 9,600

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.