Rational numbers are closed under

A:If $a,b\in Q$ then $a-b\in Q$ , then $a,b$ are closed under subtraction

Ex: $\frac{2}{3},\frac{5}{9}\in Q$ , then $\frac{2}{3}-\frac{5}{9}=\frac{6-5}{9}=\frac{1}{9}\in Q$

B: If $a,b\in Q$ then $a,b$ are closed under division

Ex: $\frac{2}{3},\frac{3}{2}\in Q$ then $\frac{2}{3}÷\frac{3}{2}=\frac{\left(\frac{2}{3}\right)}{\left(\frac{3}{2}\right)}=\frac{2}{3}\times \frac{3}{2}=\frac{4}{9}\in Q$

But, $\frac{2}{3},0\in Q$ then$\frac{2}{3}÷0=\frac{\left(\frac{2}{3}\right)}{\left(0\right)}=\frac{2}{0}$ (Not defined)

So, rational numbers are not closed under division

C: If $a,b\in Q$ then $a+b\in Q$ then$a,b$ are closed under addition

Ex: $\frac{2}{3},\frac{3}{5}\in Q$ ,then $\frac{2}{3}+\frac{3}{2}=\frac{10+9}{15}=\frac{19}{15}\in Q$

D: If $a,b\in Q\text{}$ , then $a,b$ are closed under multiplication

Ex: $\frac{2}{3},\frac{5}{9}\in Q$ , then $\frac{2}{3}\times \frac{5}{9}=\frac{10}{27}\in Q$

and also $\frac{2}{3},0\in Q$ ,then $\frac{2}{3}\times 0=0\in Q$

Hence, rational numbers are closed under multiplication.