I had some questions and small discoveries.

 I thought the trick is properly for any mod that among 1 through 9.
?? Is that right  When the number is smaller than the mod number, the remainder also can be negative numbers too.
 I thought the trick is properly for any mod that among 1 through 9.

@sincereseagull This is a great observation! There definitely exist negative remainders, and they are incredibly useful when we want to find the remainder of a product of numbers that are multiplied together. Prof. Loh covers negative remainders in Day 1 Challenge Part 7, Day 1 Your Turn Part 2, Day 3 Your Turn Part 3, and Day 4 Challenge Part 4.