How many positive multiples of nine are two-digit numbers?
I need to find the smallest and largest two-digit multiples of nine, and then count how many there are in between. The smallest two-digit multiple of nine is 9 times 2, which is 18. The largest two-digit multiple of nine is 9 times 11, which is 99. I can use a formula to find the number of multiples of nine between 18 and 99, inclusive. If I divide each number by nine, I get a sequence of integers from 2 to 11, inclusive. The number of integers in this sequence is the same as the number of multiples of nine in the original sequence. To find the number of integers in a sequence, I can subtract the first term from the last term and add one. So the number of multiples of nine between 18 and 99 is 11 minus 2 plus 1, which is 10. 