Multiplication · level 2
No close reference number
Numbers like 23 and 79 sit nowhere near a shared reference. Give each one its own reference instead: leave one factor alone, round the other to the nearest ten, multiply, then correct by the small amount you moved.
Worked example: 23 × 79
Step by step
- 1
Neither number has a close reference
23 × 79
Give each number its own reference: 23 keeps its value, 79 borrows 80.
- 2
Round 79 to 80
79 = 80 − 1
- 3
Multiply by the easy reference
23 × 80 = 23 × 8 × 10 = 1,840
- 4
Compensate: you added too much
23 × 1 = 23
- 5
Subtract the correction
1,840 − 23 = 1,817
- 6
Check with digit sums
5 × 7 → 8 = 8
23 × 79 = 1,817
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.