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Yes.

Since they are rational numbers, let's call the first one a/b and the second one c/d where a,b,c, and d are integers.

Now we can subtract by finding a common denominator. Let's use bd.

So we have ad/bd-cb/bc= (ad-bc)/CD which is rational since we know ad and bc are integers being the product of integers and CD is also an integers.

Call ad-bd=P and call CD=Q where P and Q are integers. We now see the difference is of two rationals is rational.

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โˆ™ 2011-09-13 05:21:55
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Q: Is the difference of two rational numbers always a rational number?
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