Question
How do you multiply a two-digit number by 11 in your head?
Answer
Split the two digits apart and drop their sum in the middle — carrying if that sum reaches 10.
Because ×11 = ×10 + ×1, the middle digit becomes the sum of the outer two:
- 25 × 11 → 2 (2+5) 5 → 275.
- 72 × 11 → 7 (9) 2 → 792.
The carry pitfall (the most mis-stated trick online): if the digit sum is 10 or more, carry the ten leftward. 85 × 11 → 8 (13) 5 → the 13 gives 3 with 1 carried: (8+1) 3 5 → 935, not 8135.
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Question
How does the ×11 trick extend to longer numbers, e.g. 253 × 11?
Answer
Keep the first and last digits; between them, write the sum of each adjacent pair — carrying as needed.
253 × 11 → first digit 2, then (2+5)=7, then (5+3)=8, then last digit 3 → 2783.
Check: 253 × 11 = 2530 + 253 = 2783. ✓
With carries it still works, right to left: 758 × 11 → 7 | (7+5)=12 | (5+8)=13 | 8 → resolve carries → 8338. (Check: 7580 + 758 = 8338. ✓)
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