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A rational number is one that can be expressed as a/b

The sum of two rational numbers is:

a/b + c/d

=ad/bd + bc/bd

=(ad+bc)/bd

=e/f

which is rational

The difference of two rational numbers is:

a/b - c/d

=ab/bd - bc/bd

=(ab-bc)/bd

=e/f

which is rational

The product of two rational numbers is:

(a/b)(c/d)

=ac/bd

=e/f

which is rational

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Q: Why the sum difference and product of 2 rational numbers rational?
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