Answer :
We begin by simplifying the target fraction:
[tex]$$
\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}.
$$[/tex]
Now, we compare each option to [tex]$\frac{4}{5}$[/tex]:
1. For option A,
[tex]$$
\frac{14}{20} = \frac{14 \div 2}{20 \div 2} = \frac{7}{10},
$$[/tex]
which is not equal to [tex]$\frac{4}{5}$[/tex].
2. For option B,
[tex]$$
\frac{7}{10},
$$[/tex]
which, as seen above, is not equal to [tex]$\frac{4}{5}$[/tex].
3. For option C,
[tex]$$
\frac{3}{5},
$$[/tex]
is different from [tex]$\frac{4}{5}$[/tex].
4. For option D,
[tex]$$
\frac{3}{4},
$$[/tex]
is also different from [tex]$\frac{4}{5}$[/tex].
5. For option E,
[tex]$$
\frac{4}{5},
$$[/tex]
which is the same as the simplified target fraction.
6. For option F,
[tex]$$
\frac{8}{10} = \frac{8 \div 2}{10 \div 2} = \frac{4}{5},
$$[/tex]
which matches the target fraction.
Thus, the fractions equivalent to [tex]$\frac{24}{30}$[/tex] are in options E and F.
[tex]$$
\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}.
$$[/tex]
Now, we compare each option to [tex]$\frac{4}{5}$[/tex]:
1. For option A,
[tex]$$
\frac{14}{20} = \frac{14 \div 2}{20 \div 2} = \frac{7}{10},
$$[/tex]
which is not equal to [tex]$\frac{4}{5}$[/tex].
2. For option B,
[tex]$$
\frac{7}{10},
$$[/tex]
which, as seen above, is not equal to [tex]$\frac{4}{5}$[/tex].
3. For option C,
[tex]$$
\frac{3}{5},
$$[/tex]
is different from [tex]$\frac{4}{5}$[/tex].
4. For option D,
[tex]$$
\frac{3}{4},
$$[/tex]
is also different from [tex]$\frac{4}{5}$[/tex].
5. For option E,
[tex]$$
\frac{4}{5},
$$[/tex]
which is the same as the simplified target fraction.
6. For option F,
[tex]$$
\frac{8}{10} = \frac{8 \div 2}{10 \div 2} = \frac{4}{5},
$$[/tex]
which matches the target fraction.
Thus, the fractions equivalent to [tex]$\frac{24}{30}$[/tex] are in options E and F.
