A school organized a football tournament from 6th grade  5/6 middle school students , 3/4 of 7th graders and 4/5 among 8th graders If they look and If the number of students in all three classes is equal, more participation What grade did they get?

To find out which grade contributed more students to the football tournament, we can compare the fractions of students from each grade who participated, given that the total number of students in each grade is equal.

- **6th grade participation**: \( \frac{5}{6} \)
- **7th grade participation**: \( \frac{3}{4} \)
- **8th grade participation**: \( \frac{4}{5} \)

### Step 1: Find a common denominator
To compare the fractions, we need to rewrite them with a common denominator. The least common denominator (LCD) of 6, 4, and 5 is 60.

Convert each fraction:
- \( \frac{5}{6} = \frac{5 \times 10}{6 \times 10} = \frac{50}{60} \)
- \( \frac{3}{4} = \frac{3 \times 15}{4 \times 15} = \frac{45}{60} \)
- \( \frac{4}{5} = \frac{4 \times 12}{5 \times 12} = \frac{48}{60} \)

### Step 2: Compare the fractions
Now, we compare the fractions:
- 6th grade: \( \frac{50}{60} \)
- 7th grade: \( \frac{45}{60} \)
- 8th grade: \( \frac{48}{60} \)

### Conclusion:
- The 6th grade had the highest participation rate at \( \frac{50}{60} \).
- Therefore, **the 6th grade had more participation** in the football tournament.

Would you like any further details, or do you have any questions? 

Here are 5 related questions to explore:
1. How do you calculate the least common denominator (LCD)?
2. Why is it important to convert fractions to a common denominator before comparing them?
3. Can we visualize these fractions using a bar or pie chart for better understanding?
4. How would the participation numbers change if the class sizes were different?
5. How can we calculate the total number of students who participated from all grades combined?

**Tip**: When comparing fractions, always ensure that they have the same denominator to make accurate comparisons.

A school organized a football tournament from 6th grade 5/6 middle school students, 3/4 of 7th graders and 4/5 among 8th graders. If the number of students in all three classes is equal, more participation, what grade did they get?

Explore how to compare participation rates among 6th, 7th, and 8th graders in a football tournament. Understand fractions, least common denominators, and compare values with a detailed solution. Suitable for Grades 6-8.

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