Final answer:
The quotient of two rational numbers is always a rational number because dividing one rational number by another is equivalent to multiplying by the reciprocal, resulting in a product that is also a rational number.
Step-by-step explanation:
Yes, the quotient of two rational numbers is always a rational number. A rational number is defined as a number that can be expressed as the fraction a/b, where 'a' is the numerator and 'b' is the denominator and both are integers, with 'b' not equal to zero. When dividing by another rational number, c/d, where 'c' and 'd' are also integers and 'd' is not zero, we multiply by the reciprocal of the second number, which gives us (a/b) × (d/c). Assuming both 'b' and 'd' is non-zero, the product of two rational numbers is again a rational number, with the numerator being 'a' × 'd' and the denominator being 'b' × 'c', both integers.
In the context of fraction multiplication, it is consistent with the rules of algebra that multiplying two fractions results in a new fraction where the numerator is the product of the numerators and the denominator is the product of the denominators. Therefore, since the quotient of two rational numbers results from such multiplication, the quotient itself is rational. This is similarly true when considering that any operation performed on both sides of the equals sign must maintain equality, further supporting the consistency of the resulting quotient being a rational number.