To find the number halfway between \( \frac{1}{5} \) and \( \frac{1}{3} \), we can follow these steps:

### Step 1: Find a common denominator
The denominators are 5 and 3. The least common denominator (LCD) is 15.

- Rewrite \( \frac{1}{5} \) as:
  \[
  \frac{1}{5} = \frac{3}{15}
  \]
- Rewrite \( \frac{1}{3} \) as:
  \[
  \frac{1}{3} = \frac{5}{15}
  \]

### Step 2: Find the average
To find the halfway point, we take the **average** of \( \frac{3}{15} \) and \( \frac{5}{15} \).

\[
\text{Average} = \frac{\frac{3}{15} + \frac{5}{15}}{2} = \frac{8/15}{2} = \frac{8}{30}
\]

### Step 3: Simplify the result
\[
\frac{8}{30} = \frac{4}{15}
\]

### Final Answer
The number halfway between \( \frac{1}{5} \) and \( \frac{1}{3} \) is:
\[
\boxed{\frac{4}{15}}
\]

Would you like more details or have any questions?  

Here are 5 related questions you might find interesting:
1. How do you find the halfway point between two fractions with different signs?
2. What is halfway between 1/2 and 2/3?
3. How do you add and subtract fractions with unlike denominators?
4. What is the concept of the arithmetic mean and how does it apply to fractions?
5. How do you find the midpoint of two irrational numbers?

**Tip:** When working with fractions, always look for the least common denominator to simplify operations.

Learn how to calculate the halfway point between the fractions 1/5 and 1/3. This detailed step-by-step guide demonstrates how to find a common denominator, calculate the average, and simplify the result. Perfect for students in Grades 5-7.

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