Let's break down the expression step by step:

Given:
$\frac{1}{3} - \frac{1}{8} \div \frac{3}{8} + \frac{2}{3}$

Step 1: Division operation

First, handle the division part: $\frac{1}{8} \div \frac{3}{8} = \frac{1}{8} \times \frac{8}{3} = \frac{1}{3}$

So, the expression now becomes: $\frac{1}{3} - \frac{1}{3} + \frac{2}{3}$

Step 2: Simplification

Now, simplify the subtraction and addition: $\frac{1}{3} - \frac{1}{3} = 0$

Thus, the remaining expression is: $0 + \frac{2}{3} = \frac{2}{3}$

Final Answer:

$\frac{2}{3}$

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

Here are 5 related questions:

1. What happens when we divide fractions with unlike denominators?
2. How do you simplify complex fractional expressions?
3. Can you explain how to handle mixed operations (addition, subtraction, multiplication, and division) with fractions?
4. What are the common strategies to add and subtract fractions?
5. How do you convert improper fractions to mixed numbers?

Tip: When dividing fractions, remember to multiply by the reciprocal of the second fraction.