Question
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1. \( \frac{7}{8} \times \frac{2}{3}=\frac{\square \times 2}{8 \times \square}=\frac{\square}{24}=\frac{\square}{\square} \) 2. \( \frac{3}{4} \times \frac{5}{9}=\frac{\square \times 5}{4 \times \square}=\frac{15}{\square}=\frac{\square}{\square} \) 3. \( \frac{4}{5} \times \frac{1}{8}=\frac{\square \times 1}{5 \times \square}=\frac{\square}{\square}= \) \( \square \) 5. \( \frac{3}{5} \times \frac{3}{7}=\frac{\square \times \square}{\square \times \square}= \) \( \square \) 7. \( \frac{11}{12} \times \frac{2}{5} \) 8. \( \frac{2}{3} \times \frac{4}{5} \) 9. \( \frac{1}{6} \times \frac{2}{3} \) 10. \( \frac{3}{4} \) of \( \frac{1}{2} \)

Ask by Owen Nunez. in the United States
Jan 22,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

1. \(\frac{7}{12}\) 2. \(\frac{5}{12}\) 3. \(\frac{1}{10}\) 4. \(\frac{9}{35}\) 5. \(\frac{11}{30}\) 6. \(\frac{8}{15}\) 7. \(\frac{1}{9}\) 8. \(\frac{3}{8}\)

Solution

Let's solve each of the problems step by step. ### Problem 1 \[ \frac{7}{8} \times \frac{2}{3} = \frac{7 \times 2}{8 \times 3} = \frac{14}{24} \] Now, we can simplify \(\frac{14}{24}\): \[ \frac{14 \div 2}{24 \div 2} = \frac{7}{12} \] So, the final answer is: \[ \frac{7}{12} \] ### Problem 2 \[ \frac{3}{4} \times \frac{5}{9} = \frac{3 \times 5}{4 \times 9} = \frac{15}{36} \] Now, we can simplify \(\frac{15}{36}\): \[ \frac{15 \div 3}{36 \div 3} = \frac{5}{12} \] So, the final answer is: \[ \frac{5}{12} \] ### Problem 3 \[ \frac{4}{5} \times \frac{1}{8} = \frac{4 \times 1}{5 \times 8} = \frac{4}{40} \] Now, we can simplify \(\frac{4}{40}\): \[ \frac{4 \div 4}{40 \div 4} = \frac{1}{10} \] So, the final answer is: \[ \frac{1}{10} \] ### Problem 5 \[ \frac{3}{5} \times \frac{3}{7} = \frac{3 \times 3}{5 \times 7} = \frac{9}{35} \] So, the final answer is: \[ \frac{9}{35} \] ### Problem 7 \[ \frac{11}{12} \times \frac{2}{5} = \frac{11 \times 2}{12 \times 5} = \frac{22}{60} \] Now, we can simplify \(\frac{22}{60}\): \[ \frac{22 \div 2}{60 \div 2} = \frac{11}{30} \] So, the final answer is: \[ \frac{11}{30} \] ### Problem 8 \[ \frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15} \] So, the final answer is: \[ \frac{8}{15} \] ### Problem 9 \[ \frac{1}{6} \times \frac{2}{3} = \frac{1 \times 2}{6 \times 3} = \frac{2}{18} \] Now, we can simplify \(\frac{2}{18}\): \[ \frac{2 \div 2}{18 \div 2} = \frac{1}{9} \] So, the final answer is: \[ \frac{1}{9} \] ### Problem 10 \[ \frac{3}{4} \text{ of } \frac{1}{2} = \frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8} \] So, the final answer is: \[ \frac{3}{8} \] ### Summary of Answers 1. \(\frac{7}{12}\) 2. \(\frac{5}{12}\) 3. \(\frac{1}{10}\) 4. \(\frac{9}{35}\) 5. \(\frac{11}{30}\) 6. \(\frac{8}{15}\) 7. \(\frac{1}{9}\) 8. \(\frac{3}{8}\)

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The Deep Dive

Multiplying fractions can feel like a magical math dance! To solve these problems, you simply multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. For example, in the first equation \( \frac{7}{8} \times \frac{2}{3} \), you get \( \frac{7 \times 2}{8 \times 3} = \frac{14}{24} \). Boom! Simplify, and it's \( \frac{7}{12} \). Got some common mistakes creeping in? Watch out for multiplying incorrectly or forgetting to simplify your answer! A frequent pitfall is rushing to answer without checking that maximum simplification. For example, if you end up with \( \frac{14}{24} \) and think you're done—nope! It’s time to simplify to \( \frac{7}{12} \). Always double-check your simplifications!

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