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
C. P + q
To determine which expression represents a rational number, we need to recall that the sum of a rational number and an irrational number is always irrational. However, the sum of two rational numbers is always rational.
Considering this, we can eliminate options A (P + r) and B (P + pr) since they involve adding an irrational number to the rational number P. This leaves us with options C (P + q) and D (P + qr).
Option C (P + q) represents the sum of two rational numbers, P and q. Since the sum of two rational numbers is always rational, option C represents a rational number.
Therefore, the expression that represents a rational number in this scenario is C. P + q.
The expression that represents a rational number is option C, P + q.
A rational number is defined as the quotient of two integers, where the denominator is not equal to zero. Since both p and q are rational numbers, their sum in the expression P + q would also be a rational number.