what is the midway point between 3 2/3 and 5 1/6

To find the midway point between \(3 \frac{2}{3}\) and \(5 \frac{1}{6}\), we can follow these steps:

1. **Convert the mixed numbers to improper fractions**:
   - \(3 \frac{2}{3} = \frac{11}{3}\)
   - \(5 \frac{1}{6} = \frac{31}{6}\)

2. **Find a common denominator**:
   - The least common denominator (LCD) of 3 and 6 is 6.
   - Convert \(\frac{11}{3}\) to a fraction with denominator 6:  
     \(\frac{11}{3} = \frac{22}{6}\).

3. **Add the two fractions**:
   - \(\frac{22}{6} + \frac{31}{6} = \frac{53}{6}\).

4. **Divide by 2 to find the midpoint**:
   - \(\frac{53}{6} \div 2 = \frac{53}{6} \times \frac{1}{2} = \frac{53}{12}\).

5. **Convert \(\frac{53}{12}\) back to a mixed number**:
   - \(\frac{53}{12} = 4 \frac{5}{12}\).

Thus, the midway point between \(3 \frac{2}{3}\) and \(5 \frac{1}{6}\) is \(4 \frac{5}{12}\).

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Here are 5 related questions for you to explore:

1. How do you convert mixed numbers to improper fractions?
2. What are other methods for finding the midpoint of two numbers?
3. How do you find the least common denominator (LCD) of fractions?
4. How do you multiply and divide fractions?
5. Can you calculate the average of three mixed numbers?

**Tip**: When dividing fractions, remember that dividing by a fraction is the same as multiplying by its reciprocal.

Learn how to find the midpoint between 3 2/3 and 5 1/6 with this step-by-step guide. This problem involves converting mixed numbers to improper fractions, finding a common denominator, and calculating the midpoint. Suitable for students in Grades 6-8.

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