“Why is six afraid of seven?”

– Old math joke

I recently picked up a cool little math trick called “Casting Out 9’s.” It’s a useful method for checking answers that I’d never heard of before. How it works is as follows:

“When any number is divided by 9, the remainder will equal the sum of the number’s digits, or the sum of the number’s digits after “casting out” 9’s.”

For example, dividing 16 by 9 would leave you with the answer of 1 with a remainder of 7. The digit sum of 16 is 1+6 or 7, the exact same as the remainder after dividing by 9.

Any number whose digit sum is greater than 9, gets its digit sum divided by 9. Leaving the results equal to the remainder. 38 divided by 9 equals 4 with a remainder of 2. The digit sum of 38 is 3+8, or 11. 11 divided by 9 equals 1 with a remainder of 2, the same as the original equations remainder.

As far as math related tricks go, I thought that the process of “Casting Out 9’s” was pretty cool.