Since ad, bc, and bd space integers since integers are closed under the operation of multiplication and also ad-bc is an integer due to the fact that integers room closed under the procedure of subtraction, climate (ad-bc)/bd is a reasonable number because it is in the kind of 1 integer divided by another and also the denominator is not eqaul to 0 due to the fact that b and also d were no equal to 0. Hence a/b - c/d is a reasonable number.




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edited Sep 29 "15 at 1:44
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Tvisha GopiTvisha Gopi
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Another definitionof rational number isa real number $x$ together thatthere exists a non-zero essence $n$for which$nx$ is an integer.

Since$bd(a/b-c/d)=ad-bc$is one integer,$(a/b-c/d)$is rational.


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answered Sep 29 "15 in ~ 2:52
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marty cohenmarty cohen
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