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Justine is not given x or y, but she knows that the ratio x/y is defined as a rational number. Which can be possible values for x/y?

a. Irrational numbers
b. Imaginary numbers
c. Real numbers
d. Complex numbers

1 Answer

3 votes

Final answer:

The ratio x/y, being a rational number, can only be a real number. Rational numbers are expressed as fractions of integers and are always real, not irrational, imaginary, or complex.

Step-by-step explanation:

The question concerns the nature of the ratio x/y given that it is a rational number. A rational number is defined as a number that can be expressed as the quotient or fraction p/q of two integers, where p and q are integers and q is not equal to zero. Since x/y is defined as a rational number, this means that x and y must be integers, and y cannot be zero.

The possible values for x/y, considering it is a rational number, are:

c. Real numbers

A rational number is always a real number because it can be represented as a point on the number line. However, rational numbers cannot be irrational, imaginary, or complex numbers. Therefore, options a (irrational numbers), b (imaginary numbers), and d (complex numbers) are not correct in this context.

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