Question

Let a and b be rational numbers. Then by definition

Answer 1

Answer:

the product of two rational numbers is a rational number!

Step-by-step explanation:

Answer 2

Answer:

The product of two rational numbers is a rational number

Step-by-step explanation:

I'll quickly recap the proof: a rational number is, by definition, the ratio between two integers. So, there exists four integers m,n,p,q such that

$a=\dfrac{m}{n},\quad b=\dfrac{p}{q}$

If we multiply the fractions, we have

$ab = \dfrac{mp}{nq}$

Now, mp and nq are multiplication of integers, and thus they are integers themselves. So, ab is also a ratio between integer, and thus rational.