Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Select all the true statements.

A. [tex]\frac{1}{4} \times \frac{1}{10} = \frac{1}{40}[/tex]
B. [tex]\frac{1}{8} \times \frac{16}{5} = \frac{2}{5}[/tex]
C. [tex]\frac{2}{3} \times \frac{4}{9} = \frac{8}{27}[/tex]
D. [tex]\frac{10}{7} \times \frac{14}{5} = 4[/tex]
E. [tex]\frac{6}{5} \times \frac{3}{4} = \frac{18}{20}[/tex]

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).