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Suppose A and B are two rational numbers.
So A = p/q where p and q are integers and q > 0
and B = r/s where r and s are integers and s > 0.
Then A - B = p/q - r/s = ps/qs - qr/qs = (ps - qr)/qs
Now,
p,q,r,s are integers so ps and qr are integers and so x = ps-qr is an integer
and
y = qs is an integer which is > 0
Thus A-B can be written as a ratio of two integers, x/y where y>0. Therefore, A-B is rational.
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Is the difference between two rational numbers always a rational numbers?
no
Is the difference between two rational numbers be a rational numbers?
Yes.
Is the difference of two rational numbers a rational number?
Yes.
Is the difference between two rational numbers always rational?
Yes, it is.
What is the difference between two rational numbers and one rational numbers?
Their count. Two in the first case, one in the second.
Must the difference between two rational numbers be a rational number?
Yes.
Is it true that The difference of two rational numbers always a rational number?
Yes. The rational numbers are a closed set with respect to subtraction.
How the difference of two rational numbers can be rational and irrational?
There is no number which can be rational and irrational so there is no point in asking "how".
The difference of two rational numbers is always a rational number?
Yes, that's true.
Is the difference between two rational Numbers always negative?
No.
How is the distance between two rational numbers related to their difference?
Directly. Their difference IS the difference between them.
Is the difference of two rational numbers always rational?
Yes. This is the same as asking for one rational number to be subtracted from another; to do this each rational number is made into an equivalent rational number so that the two rational numbers have the same denominator, and then the numerators are subtracted which gives a rational number which may possibly be simplified.
