Let's solve the expression step by step.

The given expression is:

\[
\frac{1}{8} + \frac{7}{18} \div \frac{7}{6}
\]

### Step 1: Simplify the division part

We can rewrite the division as multiplication by the reciprocal:

\[
\frac{7}{18} \div \frac{7}{6} = \frac{7}{18} \times \frac{6}{7}
\]

Now, simplify this expression:

\[
\frac{7}{18} \times \frac{6}{7} = \frac{7 \times 6}{18 \times 7} = \frac{42}{126}
\]

Simplify \( \frac{42}{126} \) by dividing both the numerator and the denominator by 42:

\[
\frac{42}{126} = \frac{1}{3}
\]

So, the division part simplifies to \( \frac{1}{3} \).

### Step 2: Add \( \frac{1}{8} \) and \( \frac{1}{3} \)

To add fractions, we need a common denominator. The least common denominator (LCD) of 8 and 3 is 24. Rewrite each fraction with a denominator of 24:

\[
\frac{1}{8} = \frac{3}{24}, \quad \frac{1}{3} = \frac{8}{24}
\]

Now, add the two fractions:

\[
\frac{3}{24} + \frac{8}{24} = \frac{11}{24}
\]

### Final Answer:

\[
\frac{1}{8} + \frac{7}{18} \div \frac{7}{6} = \frac{11}{24}
\]

Would you like any further details or explanations?

Here are 5 related questions to expand on this topic:
1. How do you simplify fractions with large numerators and denominators?
2. What is the general method for dividing fractions?
3. How do you find the least common denominator for adding fractions?
4. How do you multiply two fractions?
5. How do improper fractions fit into these types of problems?

**Tip:** Always remember to simplify fractions at the earliest step to make calculations easier!

Learn how to solve the expression 1/8 + 7/18 divided by 7/6 step by step. This problem involves adding and dividing fractions, finding the least common denominator, and simplifying. Suitable for students in Grades 6-8.

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