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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).
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).
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