Question
Maria, Leah, and Jonas ran these distances on Saturday. - Maria ran \( \frac{5}{6} \) mile. - Jonas \( \operatorname{ran} \frac{2}{3} \) mile. Who ran the shortest distance? mile. Show your work.
Ask by Ward Harrington. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Jonas ran the shortest distance of \( \frac{2}{3} \) mile.
Solution
To determine who ran the shortest distance, we need to compare the distances run by Maria and Jonas.
1. **Identify the distances:**
- Maria ran \( \frac{5}{6} \) mile.
- Jonas ran \( \frac{2}{3} \) mile.
2. **Convert the fractions to a common denominator:**
- The denominators are 6 and 3. The least common denominator (LCD) is 6.
- Convert \( \frac{2}{3} \) to a fraction with a denominator of 6:
\[
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
\]
3. **Compare the distances:**
- Maria's distance: \( \frac{5}{6} \)
- Jonas's distance: \( \frac{4}{6} \)
4. **Determine the shorter distance:**
- Since \( \frac{4}{6} < \frac{5}{6} \), Jonas ran the shorter distance.
Thus, the answer is that Jonas ran the shortest distance of \( \frac{2}{3} \) mile.
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Simplify this solution The Deep Dive
To determine who ran the shortest distance, let's convert both distances to a common denominator. Maria ran \( \frac{5}{6} \) mile. Jonas ran \( \frac{2}{3} \) mile. To compare these, we need to convert \( \frac{2}{3} \) to a fraction with a denominator of 6: \[ \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \] Now, we can compare \( \frac{5}{6} \) and \( \frac{4}{6} \). Since \( \frac{5}{6} > \frac{4}{6} \), it follows that Jonas ran the shorter distance. The distances are: - Maria: \( \frac{5}{6} \) mile - Jonas: \( \frac{4}{6} \) mile Therefore, Jonas ran the shortest distance: \( \frac{4}{6} \) mile or approximately \( 0.67 \) miles.
