Technique explanation
Teaching Explanation
Every number has a "secret code" called a digit sum. To find it, add all the digits. If you get a 2-digit number, add those digits too, until you have just one digit (1–9). (Note: In this method, a sum of 9 is treated like 0).
If you add two numbers, their digit sums added together should match the digit sum of the answer. If they don't, your answer is definitely wrong! But be careful: sometimes the digit sum matches even if the answer is wrong (like if you swapped two digits).
Method Condition
Works for addition, subtraction, and multiplication.
Standard Fallback
Estimation (checking if the answer is in the right ballpark) or re-calculating using the standard algorithm.
Misconception & Correction
- Misconception: Thinking that a matching digit sum proves the answer is 100% correct.
- Correction: Digit sums catch most errors, but they cannot catch swapped digits or errors that are multiples of 9. It is a "check," not a "proof."
Module
Worked examples
Worked Examples
Example: 45 + 37 = 82
- Digit Sum of 45: 4 + 5 = 9 (or 0).
- Digit Sum of 37: 3 + 7 = 10 → 1 + 0 = 1.
- Expected Sum: 9 + 1 = 10 → 1.
- Digit Sum of Answer (82): 8 + 2 = 10 → 1.
- Check: 1 = 1. (The answer is likely correct).
Example: 23 × 12 = 276
- Digit Sum of 23: 2 + 3 = 5.
- Digit Sum of 12: 1 + 2 = 3.
- Expected Product: 5 × 3 = 15 → 1 + 5 = 6.
- Digit Sum of Answer (276): 2 + 7 + 6 = 15 → 1 + 5 = 6.
- Check: 6 = 6. (The answer is likely correct).
Academy Course
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