Let a and b be rational numbers is a•b rational or irrational

it is irrational

Step-by-step explanation:

A rational number is one that can be written as n/m, where n and m are both integers.

Let a be a rational number such that a=n/m

Let b be a rational number such that b=p/q.

Notice n, m, p, and q are all integers.

When we divide a by b, a/b = (n/m) / (p/q)

But we know that complex fractions can be simplified by multiplying the numerator by the denominator.

a/b = (n/m) * (q/p) = nq/mp.

One of the properties of integers is closure under multiplication: that is to say, the product of integers is always an integer. So nq and mp are both integers.

By the definition of rational numbers nq/mp is a rational number. Therefore, a/b is a rational number.