Question
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
Upstudy AI Solution
Tutor-Verified Answer
Answer
Sara ran \(\frac{4}{7}\) of the total distance around the track.
Solution
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.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
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. 🏃♀️💨
