Multiply. Use the distributive property. \( \begin{array}{ll}\text { 9. } \frac{3}{5} \times 3 \frac{1}{2}= \\ \text { 11. } \frac{3}{7} \times 4 \frac{3}{3}= \\ \text { 11. } & \text { 10. } \\ 5\end{array} \)
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The Deep Dive
To find the product using the distributive property, we need to express the mixed numbers as improper fractions first. For \( \frac{3}{5} \times 3 \frac{1}{2} \): 1. Convert \( 3 \frac{1}{2} \) to an improper fraction: \( 3 \times 2 + 1 = 7 \), so \( 3 \frac{1}{2} = \frac{7}{2} \). 2. Now you can multiply: \( \frac{3}{5} \times \frac{7}{2} = \frac{3 \times 7}{5 \times 2} = \frac{21}{10} = 2 \frac{1}{10} \). For \( \frac{3}{7} \times 4 \frac{3}{5} \): 1. Convert \( 4 \frac{3}{5} \) to an improper fraction: \( 4 \times 5 + 3 = 23 \), so \( 4 \frac{3}{5} = \frac{23}{5} \). 2. Then multiply: \( \frac{3}{7} \times \frac{23}{5} = \frac{3 \times 23}{7 \times 5} = \frac{69}{35} \). There you go! You've got your products. Keep practicing, and soon this will feel like a walk in the park! Don't forget the beauty of improper fractions – they're just mixed numbers dressed up for a party!
