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Question
What is casting out nines, and how do you use it to check a calculation?
Answer
Reduce each number to its digital root, do the same operation on the roots, and compare with the answer's root — a mismatch means an error.
The digital root is the digit sum reduced to one digit. To check 47 × 23 = 1081:
- root(47) = 4+7 = 11 → 2
- root(23) = 5
- 2 × 5 = 10 → 1
- root(1081) = 1+0+8+1 = 10 → 1 ✓ matches
Same for addition: 47 + 23 = 70; 2 + 5 = 7; root(70) = 7 ✓. If the two sides disagree, the answer is definitely wrong.
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