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.