Answer :
Let's analyze each option step by step.
1. For option (A), we have
[tex]$$
\frac{1}{4} \times \frac{1}{10} = \frac{1}{40}.
$$[/tex]
Since [tex]$\frac{1}{40}$[/tex] is not equal to [tex]$\frac{1}{20}$[/tex], option (A) is false.
2. For option (B), we have
[tex]$$
\frac{1}{8} \times \frac{16}{5} = \frac{16}{40} = \frac{2}{5}.
$$[/tex]
This matches the given value, so option (B) is true.
3. For option (C), we have
[tex]$$
\frac{2}{3} \times \frac{4}{9} = \frac{8}{27}.
$$[/tex]
Since [tex]$\frac{8}{27}$[/tex] is different from [tex]$\frac{8}{9}$[/tex], option (C) is false.
4. For option (D), we have
[tex]$$
\frac{10}{7} \times \frac{14}{5} = \frac{140}{35} = 4.
$$[/tex]
This equals the stated value, so option (D) is true.
5. For option (E), we have
[tex]$$
\frac{6}{5} \times \frac{3}{4} = \frac{18}{20} = \frac{9}{10}.
$$[/tex]
This is equivalent to the given value [tex]$\frac{18}{20}$[/tex], so option (E) is true.
Thus, the true statements are options (B), (D), and (E).
1. For option (A), we have
[tex]$$
\frac{1}{4} \times \frac{1}{10} = \frac{1}{40}.
$$[/tex]
Since [tex]$\frac{1}{40}$[/tex] is not equal to [tex]$\frac{1}{20}$[/tex], option (A) is false.
2. For option (B), we have
[tex]$$
\frac{1}{8} \times \frac{16}{5} = \frac{16}{40} = \frac{2}{5}.
$$[/tex]
This matches the given value, so option (B) is true.
3. For option (C), we have
[tex]$$
\frac{2}{3} \times \frac{4}{9} = \frac{8}{27}.
$$[/tex]
Since [tex]$\frac{8}{27}$[/tex] is different from [tex]$\frac{8}{9}$[/tex], option (C) is false.
4. For option (D), we have
[tex]$$
\frac{10}{7} \times \frac{14}{5} = \frac{140}{35} = 4.
$$[/tex]
This equals the stated value, so option (D) is true.
5. For option (E), we have
[tex]$$
\frac{6}{5} \times \frac{3}{4} = \frac{18}{20} = \frac{9}{10}.
$$[/tex]
This is equivalent to the given value [tex]$\frac{18}{20}$[/tex], so option (E) is true.
Thus, the true statements are options (B), (D), and (E).
