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
The expression that represents a rational number is option C, p + q.
To determine which expression represents a rational number, we need to understand the properties of rational and irrational numbers.
Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. These numbers can be written as a/b, where a and b are integers and b is not zero.
Irrational numbers, on the other hand, cannot be expressed as a simple fraction or quotient of two integers. They can be non-repeating and non-terminating decimals, like √2 or π.
Let's analyze each expression:
A. p + r
If p is rational and r is irrational, the sum of a rational number and an irrational number is always irrational. Thus, expression A represents an irrational number.
B. p + pr
If p is rational and r is irrational, then the product of a rational number and an irrational number is always irrational. Thus, expression B represents an irrational number.
C. p + q
If both p and q are rational numbers, the sum of two rational numbers is always rational. Thus, expression C represents a rational number.
D. p + qr
If p is rational and q is rational, the product of two rational numbers is always rational. Thus, expression D represents a rational number.
Therefore, the expression that represents a rational number is C. p + q.