A check that misses some mistakes
A vegetable seller checks a bill in one line. How can that catch most wrong totals?
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- 47 × 6 is written down as 282.
- Mark of 47 is 2. Mark of 6 is 6. 2 × 6 = 12, and 12 has mark 3.
- Mark of 282 is 3. The two marks agree. The check passes.
- 372 also has mark 3, and 372 is wrong.
The rule
A wrong total usually leaves a different remainder after dividing by 9.
Divide a number by 9 and keep the remainder. The remainder is what is left over. That remainder is the number's mark. Add the digits, and add again if needed. You end on the mark, except that a 9 means mark 0. The digital root is the single digit you end on.
To check a product, take the marks of both numbers. Multiply the marks. Compare with the mark of the written answer.
Rule: If the marks disagree, the answer is wrong. If they agree, it might be right.
The table checks the product 47 × 6, whose wanted mark is 3.
| Written answer | Mark | Mark wanted | Passes? | Actually right? |
|---|---|---|---|---|
| 282 | 3 | 3 | yes | yes |
| 372 | 3 | 3 | yes | no |
| 228 | 3 | 3 | yes | no |
| 285 | 6 | 3 | no | no |
372 and 228 each differ from 282 by a multiple of 9. So they have mark 3 too, and the check passes them.