Multiply. Use the distributive property. $$ \begin{array}{ll} ext { 9. } \frac{3}{5} imes 3 \frac{1}{2}= \ ext { 11. } \frac{3}{7} imes 4 \frac{3}{3}= \ ext { 11. } & ext { 10. } \ 5\end{array} $$

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Multiply. Use the distributive property. $$ \begin{array}{ll}	ext { 9. } \frac{3}{5} 	imes 3 \frac{1}{2}= \ 	ext { 11. } \frac{3}{7} 	imes 4 \frac{3}{3}= \ 	ext { 11. } & 	ext { 10. } \ 5\end{array} $$

UpStudy AI · Accepted Answer

To solve the multiplication problems using the distributive property, we first need to convert the mixed numbers into improper fractions. Then we can multiply the fractions.

### Problem 9: $$ \frac{3}{5} \times 3 \frac{1}{2} $$

1. Convert $$ 3 \frac{1}{2} $$ to an improper fraction:
   $$
   3 \frac{1}{2} = 3 \times 2 + 1 = 6 + 1 = 7 \quad \Rightarrow \quad \frac{7}{2}
   $$

2. Now multiply $$ \frac{3}{5} $$ by $$ \frac{7}{2} $$:
   $$
   \frac{3}{5} \times \frac{7}{2} = \frac{3 \times 7}{5 \times 2} = \frac{21}{10}
   $$

### Problem 10: $$ \frac{3}{7} \times 4 \frac{3}{3} $$

1. Convert $$ 4 \frac{3}{3} $$ to an improper fraction:
   $$
   4 \frac{3}{3} = 4 \times 3 + 3 = 12 + 3 = 15 \quad \Rightarrow \quad \frac{15}{3} = 5
   $$

2. Now multiply $$ \frac{3}{7} $$ by $$ 5 $$:
   $$
   \frac{3}{7} \times 5 = \frac{3}{7} \times \frac{5}{1} = \frac{3 \times 5}{7 \times 1} = \frac{15}{7}
   $$

### Summary of Results:
- For Problem 9: $$ \frac{3}{5} \times 3 \frac{1}{2} = \frac{21}{10} $$
- For Problem 10: $$ \frac{3}{7} \times 4 \frac{3}{3} = \frac{15}{7} $$
- $$ \frac{3}{5} \times 3 \frac{1}{2} = \frac{21}{10} $$ - $$ \frac{3}{7} \times 4 \frac{3}{3} = \frac{15}{7} $$

Multiply. Use the distributive property.

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