Question

Suppose that p and q are rational numbers and r is an irrational number. Which expression represents a rational number?

A. p + r

B. p + pr

C. p + q

D. p + qr

Answer 1

To determine which expression represents a rational number, let's analyze each option step by step:

A. \( p + r \)
- \( p \) is a rational number and \( r \) is an irrational number. The sum of a rational number and an irrational number is always irrational. Therefore, A does not represent a rational number.

B. \( p + pr \)
- Here, \( p \) is rational, and \( pr \) (the product of a rational and an irrational number) is irrational. The sum of a rational number and an irrational number is also irrational. Thus, B does not represent a rational number.

C. \( p + q \)
- Both \( p \) and \( q \) are rational numbers. The sum of two rational numbers is rational. Therefore, C represents a rational number.

D. \( p + qr \)
- \( qr \) (the product of a rational number \( q \) and an irrational number \( r \)) is irrational. The sum of a rational number and an irrational number is irrational. Thus, D does not represent a rational number.

Based on the analysis, the expression that represents a rational number is:

**C. \( p + q \)**.