At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To determine which track is longer, we compare the lengths of the opening track and the closing track. Here's the step-by-step analysis:
1. Convert the fractions to a common denominator for easy comparison:
- The opening track length is [tex]\(\frac{2}{5}\)[/tex] of an hour.
- The closing track length is [tex]\(\frac{1}{3}\)[/tex] of an hour.
- To compare these fractions, find a common denominator. The least common multiple of 5 and 3 is 15.
2. Convert each fraction to have a denominator of 15:
- For the opening track:
[tex]\[ \frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15} \][/tex]
- For the closing track:
[tex]\[ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \][/tex]
3. Compare the fractions:
- Now that both fractions have the same denominator, we can easily see which is larger by comparing their numerators:
[tex]\[ \frac{6}{15} \quad \text{(opening track)} \quad vs \quad \frac{5}{15} \quad \text{(closing track)} \][/tex]
- Since [tex]\(6 > 5\)[/tex], [tex]\(\frac{6}{15}\)[/tex] (the opening track) is longer than [tex]\(\frac{5}{15}\)[/tex] (the closing track).
4. Conclusion:
- The opening track, which is [tex]\(\frac{2}{5}\)[/tex] of an hour, is longer than the closing track, which is [tex]\(\frac{1}{3}\)[/tex] of an hour.
Therefore, the correct answer is:
Opening track
1. Convert the fractions to a common denominator for easy comparison:
- The opening track length is [tex]\(\frac{2}{5}\)[/tex] of an hour.
- The closing track length is [tex]\(\frac{1}{3}\)[/tex] of an hour.
- To compare these fractions, find a common denominator. The least common multiple of 5 and 3 is 15.
2. Convert each fraction to have a denominator of 15:
- For the opening track:
[tex]\[ \frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15} \][/tex]
- For the closing track:
[tex]\[ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \][/tex]
3. Compare the fractions:
- Now that both fractions have the same denominator, we can easily see which is larger by comparing their numerators:
[tex]\[ \frac{6}{15} \quad \text{(opening track)} \quad vs \quad \frac{5}{15} \quad \text{(closing track)} \][/tex]
- Since [tex]\(6 > 5\)[/tex], [tex]\(\frac{6}{15}\)[/tex] (the opening track) is longer than [tex]\(\frac{5}{15}\)[/tex] (the closing track).
4. Conclusion:
- The opening track, which is [tex]\(\frac{2}{5}\)[/tex] of an hour, is longer than the closing track, which is [tex]\(\frac{1}{3}\)[/tex] of an hour.
Therefore, the correct answer is:
Opening track
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.