### Instruction: What is the remainder when (99)(101) is divided by 9?### Response: This problem involves finding a remainder, which means I might want to use modular arithmetic to simplify the calculations.
In modular arithmetic, I can use the notation a mod n to mean the remainder when a is divided by n.
For example, 17 mod 5 = 2, since 17 divided by 5 gives a quotient of 3 and a remainder of 2.
One useful property of modular arithmetic is that if a mod n = b mod n, then a + c mod n = b + c mod n, and a * c mod n = b * c mod n, for any integer c.
This means I can add or multiply any integer to both sides of a modular equation, and the remainders will still be equal.
I can also use the fact that a mod n = a - kn mod n, for any integer k. This means I can subtract any multiple of n from a, and the remainder will stay the same.
So, to find the remainder when (99)(101) is divided by 9, I can first notice that 99 mod 9 = 0, since 99 is a multiple of 9.
This means that 99 * 101 mod 9 = 0 * 101 mod 9 = 0 mod 9.