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12. Jason ran \( \frac{5}{7} \) of the distance around the school track, Sara ran \( \frac{4}{5} \) of Jason's distance. What fraction of the total distance around the track did Sara run?

Ask by Wood Ford. in the United States
Mar 09,2025

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Sara ran \(\frac{4}{7}\) of the total distance around the track.

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1. Let the total distance around the track be \(1\). 2. Jason ran \(\frac{5}{7}\) of the total distance. 3. Sara ran \(\frac{4}{5}\) of Jason's distance, which is: \[ \frac{4}{5} \times \frac{5}{7} \] 4. Multiply the fractions: \[ \frac{4 \times 5}{5 \times 7} = \frac{20}{35} \] 5. Simplify \(\frac{20}{35}\) by dividing the numerator and the denominator by their greatest common divisor, \(5\): \[ \frac{20 \div 5}{35 \div 5} = \frac{4}{7} \] Sara ran \(\frac{4}{7}\) of the total distance around the track.

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To find out the fraction of the total distance around the track that Sara ran, we need to determine Sara's distance based on Jason's. Jason ran \( \frac{5}{7} \) of the track, and Sara ran \( \frac{4}{5} \) of that distance. First, we calculate Sara's distance: \[ \text{Sara's distance} = \frac{4}{5} \times \frac{5}{7} = \frac{4 \times 5}{5 \times 7} = \frac{4}{7}. \] So, Sara ran \( \frac{4}{7} \) of the total distance around the track. In summary, Sara ran \( \frac{4}{7} \) of the track, which means she covered more than half the distance! Now that's some speedy running. 🏃‍♀️💨

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