How to Multiply by 9 in Your Head
Level 1 Mental multiplication · Reviewed by The NumThink editorial team · Last reviewed
Short version: To multiply by 9, multiply by 10 and subtract the number once. 47 × 9 = 470 − 47 = 423.
Because 9 is "ten minus one", every ×9 problem becomes a free ×10 plus one subtraction — with a beautiful built-in check at the end.
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No signup · instant feedbackWhy it works
9 is 10 minus 1, so n × 9 = n × 10 − n. Multiplying by 10 costs nothing mentally, and subtracting the number from itself shifted by one place avoids every carry.
This generalizes: ×99 = ×100 then subtract once (34 × 99 = 3,400 − 34 = 3,366), and ×999 works the same way.
The steps
- Multiply by 10. Shift the number: 47 becomes 470.
- Subtract the original number. 470 − 47 = 423.
Worked examples
easy 7 × 9
Show the thinking
7 × 10 = 70
70 − 7 = 63
So 7 × 9 = 63.
Answer: 63
medium 47 × 9
Show the thinking
47 × 10 = 470
470 − 47 = 423
So 47 × 9 = 423.
Answer: 423
hard 312 × 9
Show the thinking
312 × 10 = 3,120
3,120 − 312 = 2,808
So 312 × 9 = 2,808.
Answer: 2,808
When to use it
- Any multiplication by 9 — especially 2- and 3-digit numbers where the times table stops helping.
- ×99 and ×999: same pattern with 100 and 1,000 (63 × 99 = 6,300 − 63 = 6,237).
When not to use it
- When the other factor is 1-digit — 6 × 9 is faster from memory.
- When the number ends in a pattern that makes ×9 direct, e.g. 25 × 9 = 225 (a quarter of 900) may be quicker via the ×25 family.
Common mistakes
Subtracting the wrong amount. Subtracting 9 or the shifted number. Fix: Subtract the original number exactly once — not 9, not 90.
Losing a borrow. Mentally borrowing across zeros and losing track. Fix: Say the subtraction out loud in chunks: 3,120 − 312 = 3,120 − 300 − 12 = 2,808.
Check yourself: Any multiple of 9 has a digit sum that is also a multiple of 9: 4+2+3 = 9 ✓.