Question

amy simplified this complex fraction problem.
\\(\frac{-2\frac{1}{2}}{\frac{5}{4}}\\)
\\(\frac{-\frac{5}{2}}{\frac{5}{4}}\\)
\\(-\frac{5}{2}\left(\frac{5}{4}\
ight) = -\frac{10}{8}\\)
the quotient is \\(-\frac{5}{4}\\).
what errors did amy make? select all that apply.
\\(\square\\) she converted the mixed number to the wrong improper fraction.
\\(\square\\) she did not use the reciprocal of the divisor.
\\(\square\\) she added the numerators.
\\(\square\\) she added the denominators.
\\(\square\\) she did not simplify.

Explanation:

1. Converting Mixed Number: The mixed number \(-2\frac{1}{2}\) should convert to \(-\frac{5}{2}\) (since \(2\times2 + 1=5\), and the sign is negative), which Amy did correctly. So the first option is incorrect.
2. Reciprocal of Divisor: When dividing by a fraction \(\frac{a}{b}\), we multiply by its reciprocal \(\frac{b}{a}\). Here, the divisor is \(\frac{5}{4}\), so we should multiply by \(\frac{4}{5}\), but Amy multiplied by \(\frac{5}{4}\) (did not use the reciprocal). This is an error.
3. Adding Numerators/Denominators: Amy multiplied the fractions, not added, so these options are incorrect.
4. Simplifying: Amy’s final answer \(-\frac{5}{4}\) is simplified from \(-\frac{10}{8}\) (dividing numerator and denominator by 2), so she did simplify.

Answer:

She did not use the reciprocal of the divisor.