Question

Is the difference of two rational numbers always a rational​ number? Explain.

Answer 1

Answer:

Yes

Step-by-step explanation:

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.