Construct an argument that shows that the set of rational numbers is closed under division. that is, if x and y are
rational numbers (with y nonzero) and = x / y' prove that must also be a rational number.

can also be expressed as a ratio of two integers.

Step-by-step explanation:

Assume x and y are rational number, then x and y can be written as:

, where a and b are integers and b≠0

, where c and d are integers and d≠0

Then,

=

=  

Since the set of integers are closed under multiplication, a*d is also an integer. Similarly b*c is also an integer.

can be expressed as a proportion of two integers, provided that y≠0. From this we can conclude that  is a rational number, which concludes that the set of rational numbers are closed under division.

5050

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