Oh my. The state of US education is even worse than I thought. I hope you don't work in a technical field.
Argue with the high school teacher.
The integers are closed under multiplication (if you multiply two integers, you get another integer), but they are _not_ closed under division, since you can divide two integers to get a rational number that isn't an integer.
The rationals, however, are closed under addition, subtraction, multiplication, and division.