Question

which of the following fractions are equivalent to \\(\frac{8}{-c}\\)? select two correct answers. \\(\square -\frac{8}{-c}\\) \\(\square -\frac{8}{c}\\) \\(\square \frac{-8}{c}\\) \\(\square \frac{8}{c}\\) \\(\square \frac{-8}{-c}\\)

Explanation:

Step1: Recall the rule of signs in fractions

The rule for the sign of a fraction \(\frac{a}{b}\) is that \(\frac{a}{-b}=\frac{-a}{b}=-\frac{a}{b}\), and \(\frac{-a}{-b}=\frac{a}{b}\). Given the fraction \(\frac{8}{-c}\), we can analyze each option:

Step2: Analyze Option 1: \(-\frac{8}{-c}\)

Simplify \(-\frac{8}{-c}\). The two negative signs (in the numerator and denominator of the fraction part) will cancel out, so \(-\frac{8}{-c}=\frac{8}{c}\), which is not equal to \(\frac{8}{-c}\). So this option is incorrect.

Step3: Analyze Option 2: \(-\frac{8}{c}\)

Using the rule \(\frac{a}{-b}=-\frac{a}{b}\), here \(a = 8\) and \(b = c\), so \(\frac{8}{-c}=-\frac{8}{c}\). So this option is correct.

Step4: Analyze Option 3: \(\frac{-8}{c}\)

Using the rule \(\frac{a}{-b}=\frac{-a}{b}\), here \(a = 8\) and \(b = c\), so \(\frac{8}{-c}=\frac{-8}{c}\). So this option is correct.

Step5: Analyze Option 4: \(\frac{8}{c}\)

\(\frac{8}{c}\) has a positive denominator, while \(\frac{8}{-c}\) has a negative denominator. They are not equal (since \(\frac{8}{c}=-\frac{8}{-c}\) and \(\frac{8}{-c}=-\frac{8}{c}\)). So this option is incorrect.

Step6: Analyze Option 5: \(\frac{-8}{-c}\)

Simplify \(\frac{-8}{-c}\). The two negative signs cancel out, so \(\frac{-8}{-c}=\frac{8}{c}\), which is not equal to \(\frac{8}{-c}\). So this option is incorrect.

Answer:

B. \(-\frac{8}{c}\), C. \(\frac{-8}{c}\) (assuming the options are labeled as Option 2: \(-\frac{8}{c}\) and Option 3: \(\frac{-8}{c}\) in the order of the checkboxes)