For rational numbers ab and pq, where a,b,p,q∈Q, ____ and ____ condition exists, then they are closed under division.

For rational numbers

\frac{a}{b}

and

\frac{p}{q}

, where

a, b, p, q \in Q

b \neq 0

and

q \neq 0

condition exists, then they are closed under division.
To find the condition, where for rational numbers

\frac{a}{b}

and

\frac{p}{q}

, where

a, b, p, q \in Q

exists, then they are closed under division.
The numbers

a \div 0

and

p \div 0

are not rational numbers.
So, for any rational numbers of the forms

\frac{a}{b}

and

\frac{p}{q}

where

b \neq 0

and

q \neq 0

and

a, b, p, q

are rational numbers, they are closed under division.
Therefore, the required condition is

b \neq 0

and

q \neq 0

, where for rational numbers

\frac{a}{b}

and

\frac{p}{q}

, where

a, b, p, q \in Q

exists, then they are closed under division.

For rational numbers $\frac{a}{b}$ and $\frac{p}{q}$ , where $a, b, p, q \in Q$ , and condition exists, then they are closed under division.