Suppose that p and q are rational numbers and r is an irrational number. Which expression represents a rational number?
p+r
p+pr
p+q
p+qr
The expression that represents a rational number is p + q.
The expression that represents a rational number is p+q.
To determine which expression represents a rational number, we need to understand the properties of rational and irrational numbers.
A rational number is any number that can be expressed as the ratio of two integers, where the denominator is not zero. In other words, a rational number can be written in the form a/b, where a and b are integers and b is not equal to zero.
On the other hand, an irrational number is any number that cannot be expressed as the ratio of two integers. Irrational numbers include numbers such as √2, π, or e.
Let's evaluate each expression to determine whether it represents a rational number:
1. p+r: If we add a rational number (p) to an irrational number (r), the result will always be an irrational number. So, this expression does **not** represent a rational number.
2. p+pr: If we factor out p and rewrite the expression as p(1+r), it is the product of a rational number (p) and an irrational number (1+r). Therefore, the result of this expression will always be an irrational number as well. This expression does **not** represent a rational number.
3. p+q: Since both p and q are rational numbers and you can add rational numbers together, the result of this expression will always be a rational number. This expression **does** represent a rational number.
4. p+qr: If we factor out q and rewrite the expression as p+(q*r), it is the sum of a rational number (p) and the product of a rational number (q) and an irrational number (r). The result of this expression will always be an irrational number. Therefore, this expression does **not** represent a rational number.
In summary, out of the given options, the expression that represents a rational number is p+q.