Final answer:
The statement that the ratio a/b of two rational numbers is always rational is true, because by definition rational numbers can be represented as fractions of integers, and the division of two fractions results in another rational number as long as the denominator is not zero. Option A is the correct answer.
Step-by-step explanation:
The student has asked whether it is true that if a and b are rational numbers, then a/b is also rational. A rational number is defined as a number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not being zero. If both a and b are rational, then they can be written as fractions where a = m/n and b = p/q, with m, n, p, q being integers and n, q not being zero.
To find a/b, we divide the two fractions, which is the same as multiplying a by the reciprocal of b, thus a/b = (m/n)/(p/q) = (m/n)×(q/p). Simplifying this, we get (mq)/(np), which is still a ratio of two integers as long as p is not zero, meaning a/b is a rational number. Therefore, the correct answer is (a) True, because the ratio of two rational numbers is always rational.