Multiplication of Fractions
The multiplication of two fractions involves multiplying the numerators (top numbers) together and the denominators (bottom numbers) together.
So for the fractions \( \frac{3}{5} \) and \( \frac{7}{6} \), you multiply the numerators 3 and 7 to get 21, and you multiply the denominators 5 and 6 to get 30.
The resulting fraction is:
\[ \frac{3}{5} \times \frac{7}{6} = \frac{3 \times 7}{5 \times 6} = \frac{21}{30} \]
To simplify the fraction further, find the greatest common divisor (GCD) of 21 and 30. The GCD of 21 and 30 is 3.
So we divide both numerator and denominator by 3:
\[ \frac{21 \div 3}{30 \div 3} = \frac{7}{10} \]
Hence, \( \frac{3}{5} \times \frac{7}{6} = \frac{7}{10} \) after simplification.
