# Math Help - How to prove something is a subring

1. ## How to prove something is a subring

In the rational numbers, Q, let S be the collection of all fractions that can be written with odd denominator. Prove S is a subring of Q.

What properties of rings and subrings do I need to prove to show that S is a subring? I think I will have to prove addition, multiplication, existence of a "0", and existence of a "1", but what else must I prove?

2. I think you have to prove that if $a,b \in S$, $a+b\in S$ and $a\cdot b\in S$.