Multiplying Fractions

Multiply the numerators: $3\times 2=6$. Then, multiply the denominators: $5\times 7=35$. The result is $\frac{6}{35}$, which cannot be simplified further.

Multiply $\frac{7}{5}\times 15$ by rewriting 15 as $\frac{15}{1}$. Cross-cancel 5 and 15 to get 1 and 3. Multiply 7 by 3 to get 21.

Simplify $\frac{15}{35}$ to $\frac{3}{7}$ and $\frac{5}{10}$ to $\frac{1}{2}$. Multiply the numerators: $3\times 1=3$. Multiply the denominators: $7\times 2=14$. The result is $\frac{3}{14}$.

Simplify: 16 and 24 divide by 8, becoming 2 and 3, and 18 and 27 divide by 9, becoming 2 and 3. Multiply: $2\times 2=4$ and $3\times 3=9$, giving $\frac{4}{9}$.

Simplify: 25 and 50 divide by 25, becoming 1 and 2, and 40 and 32 divide by 8, becoming 5 and 4. Multiply: $1\times 4=4$ and $5\times 2=10$, giving $\frac{4}{10}$, which simplifies to $\frac{2}{5}$.

Convert $2\frac{1}{3}$ into an improper fraction: $2\frac{1}{3}=\frac{7}{3}$. Cross-cancel: 9 and 3 divide by 3, becoming 3 and 1. Multiply: $7\times 3=21$ and $1\times 4=4$, giving $\frac{21}{4}$.