To solve the expression \( \frac{5}{8} + \frac{1}{8} \div \frac{2}{3} - \frac{3}{6} \), we need to follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). Here's the step-by-step solution:

1. **Division:** 
   \[
   \frac{1}{8} \div \frac{2}{3} = \frac{1}{8} \times \frac{3}{2} = \frac{1 \times 3}{8 \times 2} = \frac{3}{16}
   \]

2. **Addition and Subtraction:**
   \[
   \frac{5}{8} + \frac{3}{16} - \frac{3}{6}
   \]

3. **Finding a common denominator:**
   - The denominators are 8, 16, and 6. The least common denominator (LCD) for 8 and 16 is 16, but we'll consider 48 (the least common multiple of 8, 16, and 6).

   Convert each fraction:
   \[
   \frac{5}{8} = \frac{30}{48}, \quad \frac{3}{16} = \frac{9}{48}, \quad \frac{3}{6} = \frac{24}{48}
   \]

4. **Perform the operations:**
   \[
   \frac{30}{48} + \frac{9}{48} - \frac{24}{48} = \frac{30 + 9 - 24}{48} = \frac{15}{48}
   \]

5. **Simplify the fraction:**
   \[
   \frac{15}{48} = \frac{5}{16} \quad (\text{dividing both the numerator and the denominator by 3})
   \]

So, the final answer is:
\[
\frac{5}{16}
\]

Would you like more details or have any questions about the steps?

Here are 8 related questions to expand your understanding:
1. How do you find the least common denominator for a set of fractions?
2. What are the rules for dividing fractions?
3. How can you simplify a fraction to its lowest terms?
4. How would you solve the expression if the fractions had different denominators initially?
5. Can you explain why the order of operations is important in solving math problems?
6. How does multiplying fractions differ from adding them?
7. What are some real-life examples where you might need to add, subtract, or divide fractions?
8. How would the solution change if the subtraction was done before the division?

**Tip:** Always simplify fractions at the end to make your answer easier to understand.

Learn how to solve the expression 5/8 + 1/8 ÷ 2/3 - 3/6 step-by-step. Understand the order of operations, find common denominators, and simplify fractions to reach the final answer of 5/16. Suitable for Grades 6-8.

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