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Prove that if a and b are rational numbers then a multiplied by b is a rational number?
Wiki User
∙ 13y ago
If a is rational then there exist integers p and q such that a = p/q where q>0.
Similarly, b = r/s for some integers r and s (s>0)
Then a*b = p/q * r/s = (p*r)/(q*s)
Now, since p, q r and s are integers, p*r and q*s are integers. Also, q and s > 0 means that q*s > 0
Thus a*b can be expressed as x/y where
p and r are integers implies that x = p*r is an integer
q and s are positive integers implies that y = q*s is a positive integer.
That is, a*b is rational.
Wiki User
∙ 13y ago
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