The basic pattern
For a two-digit number AB, multiplying by 11 usually means writing A, then A+B, then B. Example: 52 x 11 becomes 5, 7, 2, so the answer is 572.
When the middle digit is 10 or more
If A+B is 10 or more, write the ones digit in the middle and carry 1 to the first digit. Example: 67 x 11. Since 6+7=13, write 3 in the middle and carry 1 to 6. Answer: 737.
Use it backward to check
A product of a two-digit number times 11 often has a middle digit related to the outer digits. For 638, the outer digits are 6 and 8. Since 6+8=14, carrying explains the middle 3. That matches 58 x 11 = 638.
Practice problems
- 43 x 11
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Add 4 + 3 = 7, then place 7 between 4 and 3. Answer: 473.
- 72 x 11
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Add 7 + 2 = 9, then place 9 between 7 and 2. Answer: 792.
- 78 x 11
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Add 7 + 8 = 15, put 5 in the middle and carry 1 to the 7. Answer: 858.
References
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