To multiply the fractions \( \frac{3}{7} \) and \( \frac{9}{10} \), you simply multiply the numerators together and the denominators together:
\[ \frac{3}{7} \times \frac{9}{10} = \frac{3 \times 9}{7 \times 10} = \frac{27}{70} \]
Thus, the result of multiplying \( \frac{3}{7} \) by \( \frac{9}{10} \) is \( \frac{27}{70} \).
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