Technique explanation
Teaching Explanation
Subtracting from numbers like 1,000 or 10,000 often requires tedious borrowing across multiple zeros. The All from 9, Last from 10 rule simplifies this by transforming the operation into a series of independent digit-level complements. To find the result, subtract every digit of the number from 9, moving from left to right, except for the final non-zero digit, which is subtracted from 10. This method naturally accounts for the "carries" inherent in the base-10 system.
Method Conditions
Specifically for subtractions where the minuend is a power of 10 ($10^k$).
Standard Fallback
Standard column subtraction with regrouping (borrowing) across zeros.
Misconception & Correction
Misconception: Subtracting the last digit from 9 instead of 10 (e.g., $100 - 64 = 35$).
Correction: The last digit must complete the 10 to trigger the carry that justifies subtracting the other digits from 9.
Module
Worked examples
Worked Examples
- Calculate $1000 - 472$. Step 1: Subtract hundreds digit from 9: $9 - 4 = 5$. Step 2: Subtract tens digit from 9: $9 - 7 = 2$. Step 3: Subtract units digit from 10: $10 - 2 = 8$. Result: 528. Verification: $472 + 528 = 1000$.
- Calculate $100 - 64$. Step 1: Subtract tens digit from 9: $9 - 6 = 3$. Step 2: Subtract units digit from 10: $10 - 4 = 6$. Result: 36. Verification: $64 + 36 = 100$.
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