# prove that for all rational numbers r and s, rs is rational

prove that for all rational numbers r and s, rs is rational
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curwyrm

Given that r and s are rational numbers. That is r and s can be written in the form ,b,d is not zero.
Obtain the value of $r×s$ as shown below.
$r×s=\frac{a}{b}×\frac{c}{d}$
$r×s=\frac{ac}{bd}$
Note that, b, d is not equal to zero. Therefore, bd is not zero.
Further, note that as a, b, c and d are integers ac and bd are also integers.
Step 2
Therefore, note that the product $r×s$ is the ratio of two integers with denominator not equal to zero.
It is known that, the above is a definition of a rational number.
Thus, the product $r×s$ is rational.
Hence proved.