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The problem you're asking about is how to find the average of the fractions \( \frac{3}{5} \), \( \frac{5}{12} \), and \( \frac{2}{3} \).

### Step 1: Add the fractions
To find the average, first add the fractions together. To do this, you need a common denominator.

The least common denominator (LCD) of \( 5 \), \( 12 \), and \( 3 \) is \( 60 \).

- Convert \( \frac{3}{5} \) to a fraction with denominator \( 60 \):
  \[
  \frac{3}{5} = \frac{3 \times 12}{5 \times 12} = \frac{36}{60}
  \]
- Convert \( \frac{5}{12} \) to a fraction with denominator \( 60 \):
  \[
  \frac{5}{12} = \frac{5 \times 5}{12 \times 5} = \frac{25}{60}
  \]
- Convert \( \frac{2}{3} \) to a fraction with denominator \( 60 \):
  \[
  \frac{2}{3} = \frac{2 \times 20}{3 \times 20} = \frac{40}{60}
  \]

Now, add the fractions:
\[
\frac{36}{60} + \frac{25}{60} + \frac{40}{60} = \frac{36 + 25 + 40}{60} = \frac{101}{60}
\]

### Step 2: Divide by the number of fractions
Since there are 3 fractions, divide the sum by 3 to find the average:
\[
\text{Average} = \frac{\frac{101}{60}}{3} = \frac{101}{60} \times \frac{1}{3} = \frac{101}{180}
\]

### Final Answer:
The average of the fractions \( \frac{3}{5} \), \( \frac{5}{12} \), and \( \frac{2}{3} \) is \( \frac{101}{180} \).

Would you like more details or have any questions?

Here are five related questions:
1. How do you find the least common denominator of two or more fractions?
2. What is the process for simplifying a fraction after addition?
3. Can you find the average of more complex fractions, such as those with variables?
4. How does multiplying fractions by a reciprocal simplify division problems?
5. How do you convert a mixed number to an improper fraction?

**Tip:** When adding fractions, always ensure that you are working with a common denominator before summing the numerators.

In Mathematics, average is defined as the ratio of the sum of the values divided by the total number of the values. What is the average of 3/5, 5/12, and 2/3?

Learn how to calculate the average of fractions 3/5, 5/12, and 2/3 with a step-by-step guide. This problem explores key arithmetic concepts such as adding fractions with different denominators and applying the formula for averages. Suitable for students in Grades 6-8.

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