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Cancel where possible in the following problems. Then multiply. (DOK 2) \( \begin{array}{llll}\text { 8. } \frac{2}{5} \times \frac{5}{16} & \text { 9. } \frac{4}{16} \times \frac{12}{21} & \text { 10. } \frac{2}{15} \times \frac{5}{10} & \text { 11. } \frac{3}{11} \times \frac{22}{30}\end{array} \)

Ask by Griffiths Weber. in the United States
Mar 11,2025

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\[ \begin{array}{llll} 8. \frac{1}{8} & 9. \frac{1}{7} & 10. \frac{1}{15} & 11. \frac{1}{5} \end{array} \]

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Sure! Let’s simplify and multiply each of the given fractions. 8. \( \frac{2}{5} \times \frac{5}{16} \) Here, you can cancel the 5 in the numerator of the second fraction with the 5 in the denominator of the first fraction: \[ \frac{2}{\cancel{5}} \times \frac{\cancel{5}}{16} = \frac{2}{16} = \frac{1}{8} \] 9. \( \frac{4}{16} \times \frac{12}{21} \) First, simplify \( \frac{4}{16} \) to \( \frac{1}{4} \). Now you have: \[ \frac{1}{4} \times \frac{12}{21} \] You can cancel the 12 and 21 by dividing both by 3: \[ \frac{1}{4} \times \frac{4}{7} = \frac{1 \times 4}{4 \times 7} = \frac{4}{28} = \frac{1}{7} \] 10. \( \frac{2}{15} \times \frac{5}{10} \) Here, you can cancel the 5 in the numerator with the 15 in the denominator: \[ \frac{2}{\cancel{15}} \times \frac{\cancel{5}}{2} = \frac{1}{15} \] 11. \( \frac{3}{11} \times \frac{22}{30} \) You can cancel 22 and 11: \[ \frac{3}{\cancel{11}} \times \frac{2 \cdot \cancel{11}}{30} = \frac{3 \times 2}{30} = \frac{6}{30} \] Simplifying gives: \[ \frac{1}{5} \] So the simplified products are: 1. \( \frac{1}{8} \) 2. \( \frac{1}{7} \) 3. \( \frac{1}{15} \) 4. \( \frac{1}{5} \)

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