How many positive multiples of $9$ are less than $1000$?
To find the positive multiples of $9$, I can start by listing them in increasing order: $9, 18, 27, \dots$. I can also notice that they are all of the form $9k$, where $k$ is a positive integer. To find the largest multiple of $9$ that is less than $1000$, I can divide $1000$ by $9$ and round down to the nearest integer. This gives me $\lfloor 1000/9 \rfloor = 111$. This means that $9 \cdot 111 = 999$ is the largest multiple of $9$ that is less than $1000$. Therefore, there are $111$ positive multiples of $9$ that are less than $1000$. 