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It follows from the closure of integers under addition and multiplication.
Any rational number can be expressed as a ratio of two integers, where the second is not zero. So two rational numbers may be expressed as p/q and r/s.
A common multiple of their denominators is qs. So the numbers could also have been expressed as ps/qs and qr/qs.
Both these have the same denominator so their sum is (ps + qr)/qs.
Now, because the set of integers is closed under multiplication, ps, qr and qs are integers and because the set of integers is closed under addition, ps + qr is an integer.
Thus the sum has been expressed as a ratio of two integers, ps + qr, and qs and so it is a rational number.
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Is the product of two rational numbers irrational?
The product of two rational numbers is always a rational number.
Is multiplication of a whole number associative?
Yes. Multiplication of integers, of rational numbers, of real numbers, and even of complex numbers, is both commutative and associative.
What s happens when rational numbers are multplied?
The product of two rational numbers is always a rational number.
Why does a rational number plus a rational number or a rational number multiplied by a rational number equal to rational number?
The way in which the binary functions, addition and multiplication, are defined on the set of rational numbers ensures that the set is closed under these two operations.
How are multiplying and dividing rational numbers related?
Dividing by a rational number (other than zero) is simply multiplication by its reciprocal.
