Gunakasamuccayah Sutra

How can you be sure your multiplication is correct without re-doing the whole problem? The "Gunakasamuccayah" sutra provides an elegant method for checking your answers, also known as "casting out nines" or using "digit sums."

The "Product of the Sums" Rule ✔️

The digit sum of the product of two numbers is equal to the digit sum of the product of their individual digit sums.

Let's Check if 23 × 14 = 322

1. Digit Sum of Factors: Digit sum of 23 is 5. Digit sum of 14 is 5.
2. Multiply Digit Sums: 5 × 5 = 25.
3. Digit Sum of that Product: Digit sum of 25 is 7. This is our "check number."
4. Digit Sum of the Answer: Digit sum of 322 is 7.
5. Compare: The check number (7) matches the answer's digit sum (7). Correct!