The five-digit number $246\underline{\hspace{5pt}}8$ is divisible by 9. What is the missing digit?
I know that a number is divisible by 9 if and only if the sum of its digits is divisible by 9. So I need to find a digit that makes the sum of 2, 4, 6, the missing digit, and 8 divisible by 9. The sum of 2, 4, 6, and 8 is 20, so I need to add a digit that makes 20 plus that digit a multiple of 9. The only digit that works is 7, because 20 + 7 = 27, which is divisible by 9. So the missing digit is 7. 