Question

Question 1: Suppose f, g, and are all rational numbers. Is n a rational number? Explain your answer. VA No; the denominator could be 0, so the result may not be rational. There is not enough information to answer the question. No, a quotient of rational numbers is not always rational. O Yes, the square and square roots cancel out, leaving a non-zero rational denominator.

Answer 1

If f, g, and h are all rational numbers and none of them is zero, then n, represented by the expression f / (g / h), is indeed a rational number as long as we are not dividing by zero.

Step-by-step explanation:

The student's question seems to be asking whether a number n, derived as a quotient of two rational numbers, is also a rational number. By definition, a rational number is one that can be expressed as the quotient of two integers, where the denominator is not zero. When dividing two rational numbers, if the denominator of the divisor is not zero, the result is also a rational number, because the division of integers (except by zero) results in another integer or a rational number.

If f, g, and h are all rational numbers, and we are dealing with the expression f / (g / h), where neither g nor h is zero, then n would be a rational number since you are essentially multiplying f by h over g (because division by a fraction is the same as multiplication by its reciprocal), and this would result in a rational number as long as g and h are not zero.