9 3/5 • 10//21

To multiply the mixed number \(9 \frac{3}{5}\) by the fraction \(\frac{10}{21}\), you first need to convert the mixed number into an improper fraction.

1. Convert \(9 \frac{3}{5}\) into an improper fraction: \[ 9 \frac{3}{5} = \frac{9 \times 5 + 3}{5} = \frac{45 + 3}{5} = \frac{48}{5} \]

2. Now, multiply \(\frac{48}{5}\) by \(\frac{10}{21}\): \[ \frac{48}{5} \times \frac{10}{21} = \frac{48 \times 10}{5 \times 21} = \frac{480}{105} \]

3. Now simplify \(\frac{480}{105}\):

   • The greatest common divisor (GCD) of 480 and 105 is 15.
   • Divide both the numerator and the denominator by their GCD: \[ \frac{480 \div 15}{105 \div 15} = \frac{32}{7} \]

4. Therefore, the final result in improper fraction form is: \[ \frac{32}{7} \]

5. If you need it to be in mixed number form:

   • Divide 32 by 7, which gives 4 with a remainder of 4: \[ \frac{32}{7} = 4 \frac{4}{7} \]

Thus, the result of \(9 \frac{3}{5} \times \frac{10}{21}\) is: \[ \frac{32}{7} \text{ or } 4 \frac{4}{7} \]