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Explanation:
The proof of this is as follows
p, q, r and s are integers
q and s cannot be zero
A = some rational number = p/q
B = some other rational number = r/s
A*B = (p/q)*(r/s) = (p*q)/(r*s)
The result is of some form integer/integer, where the denominator is nonzero. This shows that A*B is rational.
Therefore,
rational*rational = rational
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A few examples:
Side note: any whole number is a rational number. For instance, the number 7 can be thought of as the fraction 7/1 or 14/2 or 21/3 and so on.
