High School

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}{20}[/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]

Answer :

We will check each statement one by one.

1. For statement (A):

[tex]$$\frac{1}{4} \times \frac{1}{10} = \frac{1}{40}$$[/tex]

Since [tex]$\frac{1}{40} \neq \frac{1}{20}$[/tex], statement (A) is false.

2. For statement (B):

[tex]$$\frac{1}{8} \times \frac{16}{5} = \frac{16}{40} = \frac{2}{5}$$[/tex]

The result matches the given value [tex]$\frac{2}{5}$[/tex], so statement (B) is true.

3. For statement (C):

[tex]$$\frac{2}{3} \times \frac{4}{9} = \frac{8}{27}$$[/tex]

The expected value is [tex]$\frac{8}{9}$[/tex], but since [tex]$\frac{8}{27} \neq \frac{8}{9}$[/tex], statement (C) is false.

4. For statement (D):

[tex]$$\frac{10}{7} \times \frac{14}{5} = \frac{140}{35} = 4$$[/tex]

The computed result is 4, which is exactly what is given. Therefore, statement (D) is true.

5. For statement (E):

[tex]$$\frac{6}{5} \times \frac{3}{4} = \frac{18}{20}$$[/tex]

The result equals the provided value [tex]$\frac{18}{20}$[/tex], so statement (E) is true.

Thus, the true statements are (B), (D), and (E).