To solve the expression \( \frac{7}{5} \times \frac{4}{21} \times 3 \times 25 \), we can break it down step-by-step:
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Multiply the fractions and whole numbers:
\[ \frac{7}{5} \times \frac{4}{21} = \frac{7 \times 4}{5 \times 21} = \frac{28}{105} \]
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Now multiply this result by 3:
\[ \frac{28}{105} \times 3 = \frac{28 \times 3}{105} = \frac{84}{105} \]
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Next, simplify \( \frac{84}{105} \):
Both 84 and 105 can be divided by their greatest common divisor (GCD), which is 21:
\[ \frac{84 \div 21}{105 \div 21} = \frac{4}{5} \]
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Finally, multiply by 25:
\[ \frac{4}{5} \times 25 = \frac{4 \times 25}{5} = \frac{100}{5} = 20 \]
Thus, the final result of the expression \( \frac{7}{5} \times \frac{4}{21} \times 3 \times 25 \) is:
\[ \boxed{20} \]