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

sagnuhh 2020-11-27 Answered
prove that for all rational numbers r and s, rs is rational
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curwyrm
Answered 2020-11-28 Author has 87 answers

Given that r and s are rational numbers. That is r and s can be written in the form r=ab and s=cd,b,d is not zero.
Obtain the value of r×s as shown below.
r×s=ab×cd
r×s=acbd
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.

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