Question

Mary makes the claim that when p/q are both integers and n≠0, is multiplied by 7/3 the product will always be rational. Is Mary's claim correct? Justify your answer.

A) True, because multiplying two integers always results in a rational number.
B) True, because the product of any rational number and an integer is rational.
C) False, because the product of two integers can be irrational.
D) False, because the product of two rational numbers can be irrational.

Answer 1

Mary's claim is false, as the product of two integers can be irrational.

Step-by-step explanation:

Mary's claim is:

C) False, because the product of two integers can be irrational.

To prove this claim is false, we can provide a counterexample. Let's consider the values of p = 1, q = 2, and n = √2. When we multiply p/q by 7/3, we get (1/2) * (7/3) = 7/6, which is a rational number.

Therefore, Mary's claim is incorrect, and we have shown that multiplying p/q (where p and q are both integers and n ≠ 0) by 7/3 does not always result in an irrational number.