To determine why the number \(-\frac{2}{11}\) is a rational number, we need to recall that a rational number is defined as a number that can be expressed as the quotient of two integers (where the denominator is not zero).
In the case of \(-\frac{2}{11}\), it is expressed as the quotient of \(-2\) (the numerator, which is an integer) and \(11\) (the denominator, which is also an integer and not zero).
Now let's analyze the options:
A. It is the quotient of -2 divided by -11.
- This is incorrect because \(-\frac{2}{11}\) is not equal to \(-2/-11\).
B. It is the quotient of -11 divided by 2.
- This is incorrect because \(-\frac{2}{11}\) does not equal \(-11/2\).
C. It is the quotient of 2 divided by -11.
- This is correct because \(-\frac{2}{11}\) can be expressed as \(2/-11\).
D. It is the quotient of -11 divided by -2.
- This is incorrect because \(-\frac{2}{11}\) does not equal \(-11/-2\).
The correct reasoning is found in option C. However, it is also important to note that \(-\frac{2}{11}\) itself directly satisfies the definition of a rational number as the quotient of two integers, specifically \(-2\) and \(11\).
Thus, the best choice from the options provided is C. It is the quotient of 2 divided by -11.
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