The simple way: multiply the numerators to get the numerator, multiply the denominators to get the denominator.
To get the preferred answer cancel common factors in the new numerator and denominator. But this can be tricky.
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Yes. Since 0.555 and 0.5 are both rational numbers, their product will be rational.
0.75 and 1 is one possible pair.
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.
Yes.
All rational numbers are real numbers.