Trick 8 divided by 9. The same idea works for any divisor just below 10, 100 or 1000: use its complement (8 → 2, 88 → 12, 897 → 103) and you only multiply by small numbers and add.
✓ You passed this trick’s test.
The trick
Nikhilam Navatashcaramam Dashatah — “all from 9 and the last from 10”
Write the complement of the divisor (8 → 2, 97 → 03, 88 → 12, 997 → 003, 897 → 103).
Split off as many last digits as the base has zeros (1 for 8, 2 for 88, 3 for 997) — that is the remainder part.
Bring down each column total, multiply it by the complement, and add the result under the next column(s).
If the remainder is not smaller than the divisor, divide it again and add to the quotient.
Use it for: Dividing by 8, 98, 97, 96, 89, 88, 997, 998, 989, 988, 897 — numbers a little below 10, 100 or 1000. Just above? See trick 28.
Worked example: 1234 ÷ 88 = 14 remainder 2
88 is 12 less than 100: complement 12. Split 12 | 34.
Total 1: add 1 × 12 → 1 and 2 under the next two columns; next total 2 + 1 = 3.
Total 3: add 3 × 12 → 3 and 6 under the next two columns.
Quotient 13; remainder columns 8 and 10 → 90. 90 is more than 88 → 14 remainder 2.
Check: 88 × 14 + 2 = 1232 + 2 = 1234 ✓
✏️ Practice
Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.
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🏁 Trick 18 test
20 sums. Check each answer, then go to the next one. Get 16 or more right to pass.
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