The sum and product of two rational numbers are rational.

Let \(a=\frac{m}{n}\) and \(b=\frac{p}{q}\) for some integers \(m,n,p,q\) (\(n,q\neq 0\))

(i) 

\[a+b=\frac{m}{n}+\frac{p}{q}=\frac{mq+pn}{nq}\]

Since \(m,n,p,q\) are all integers, \(a+b\) is rational.

(ii)

\[ab=\frac{m}{n}\times \frac{p}{q}=\frac{mp}{nq}\]

Since \(m,n,p,q\) are all integers, \(ab\) is also rational.