Since all counting numbers are rational numbers, arithmetic would never have started. There would have been no science nor technology.
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Fractions where both the numerator and divisor are rational numbers are always rational numbers.
Yes, irrational numbers are never rational numbers because irrational numbers can't be expressed, by definition, as a fraction of two integers.
The quotient of two nonzero integers is the definition of a rational number. There are nonzero numbers other than integers (imaginary, rational non-integers) that the quotient of would not be a rational number. If the two nonzero numbers are rational themselves, then the quotient will be rational. (For example, 4 divided by 2 is 2: all of those numbers are rational).
yes
False.