Given the equality [tex]\( -\frac{8}{2} = \frac{17}{3} \)[/tex], let's convert and compare the fraction and each of the given choices.
First, simplify [tex]\( -\frac{8}{2} \)[/tex]:
[tex]\[ -\frac{8}{2} = -4 \][/tex]
Next, we need to evaluate the right-hand side [tex]\(\frac{17}{3}\)[/tex] and see if any of the provided options are equivalent to [tex]\( \frac{17}{3} \)[/tex]:
1. Option A: [tex]\(\frac{58}{6}\)[/tex]
[tex]\[
\frac{58}{6} \approx 9.666666666666666
\][/tex]
2. Option B: [tex]\(\frac{31}{4}\)[/tex]
[tex]\[
\frac{31}{4} = 7.75
\][/tex]
3. Option C: [tex]\(\frac{7}{3}\)[/tex]
[tex]\[
\frac{7}{3} \approx 2.3333333333333335
\][/tex]
4. Option D: [tex]\(\frac{16}{2}\)[/tex]
[tex]\[
\frac{16}{2} = 8.0
\][/tex]
Comparing each option to [tex]\( \frac{17}{3} \approx 9.666666666666666 \)[/tex]:
- Option A is [tex]\( 9.666666666666666 \)[/tex], which is equivalent to [tex]\( \frac{17}{3} \)[/tex].
- Option B is [tex]\( 7.75 \)[/tex], which is not equivalent.
- Option C is [tex]\( 2.3333333333333335 \)[/tex], which is not equivalent.
- Option D is [tex]\( 8.0 \)[/tex], which is not equivalent.
Thus, the correct number to complete the equality is in Option A, which is [tex]\( \frac{58}{6} \)[/tex].
