To determine which of the given expressions are equivalent to [tex]\(-8\)[/tex], we need to evaluate each expression step by step.
Expression I: [tex]\(\frac{8}{-1}\)[/tex]
[tex]\[ \frac{8}{-1} = -8.0 \][/tex]
This expression is equivalent to [tex]\(-8\)[/tex].
Expression II: [tex]\(\frac{-40}{5}\)[/tex]
[tex]\[ \frac{-40}{5} = -8.0 \][/tex]
This expression is also equivalent to [tex]\(-8\)[/tex].
Expression III: [tex]\(\frac{-24}{-3}\)[/tex]
[tex]\[ \frac{-24}{-3} = 8.0 \][/tex]
This expression simplifies to [tex]\(8\)[/tex], which is not equivalent to [tex]\(-8\)[/tex].
Expression IV: [tex]\(\frac{16}{-2}\)[/tex]
[tex]\[ \frac{16}{-2} = -8.0 \][/tex]
This expression simplifies to [tex]\(-8\)[/tex] and is equivalent.
To summarize:
- [tex]\(\frac{8}{-1}\)[/tex] is equivalent to -8
- [tex]\(\frac{-40}{5}\)[/tex] is equivalent to -8
- [tex]\(\frac{-24}{-3}\)[/tex] is not equivalent to -8
- [tex]\(\frac{16}{-2}\)[/tex] is equivalent to -8
Thus, the correct answer is:
I, II, and IV
