The difference of two rational numbers is rational. Let the two rational numbers be a/b and c/d, where a, b, c, and d are integers. Any rational number can be represented this way. Their difference is
a/b-c/d
= ad/bd-cb/bd
= (ad-cb)/bd.
Products and differences of integers are always integers. This means that ad-cb is an integer, and so is bd.
Thus, (ad-cb)/bd is a rational number (since it is the ratio of two integers). This is equivalent to the difference of the original two rational numbers.
Another rational number.
Yes.
The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c rational. Since b = c - a, it would have to be rational too. Thus you can't ever have a rational plus an irrational equalling a rational.
Yes.
Yes, it must.
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.
There is no number which can be rational and irrational so there is no point in asking "how".
An example of a whole number would be this >>> 2 1/3 Except a real number would be any rational Or irrational number :)
Yes, that's true.
Yes. 2+sqrt(3) and 5+sqrt(3). Their difference is 3, which is rational.
It is a rational number.
a rational number is different from a natural number because a rational number can be expressed as a fraction and natural numbers are just countinq numbers =D