When $n$ is divided by 6, a remainder of 1 is given. What is the remainder when $n+2010$ is divided by 6?
I know that when a number is divided by 6, the possible remainders are 0, 1, 2, 3, 4, or 5. So I can write $n$ as $6k+1$, where $k$ is some integer. Then, $n+2010$ is $6k+1+2010$, which is $6k+2011$. To find the remainder of this when divided by 6, I can use the distributive property and write it as $6(k+335)+1$. Now I can see that the remainder is 1, regardless of the value of $k$. So the answer is 1. 