To simplify the expression:

\[
\frac{17}{12} - \left(\frac{1}{6} + \frac{5}{18}\right)
\]

### Step 1: Simplify the terms inside the parentheses
Find a common denominator for \(\frac{1}{6}\) and \(\frac{5}{18}\). The least common denominator (LCD) of 6 and 18 is 18.

\[
\frac{1}{6} = \frac{3}{18}
\]

So:

\[
\frac{1}{6} + \frac{5}{18} = \frac{3}{18} + \frac{5}{18} = \frac{8}{18}
\]

Now simplify \(\frac{8}{18}\):

\[
\frac{8}{18} = \frac{4}{9}
\]

### Step 2: Subtract from \(\frac{17}{12}\)
Now subtract \(\frac{4}{9}\) from \(\frac{17}{12}\). We need a common denominator between 12 and 9, which is 36.

\[
\frac{17}{12} = \frac{51}{36}, \quad \frac{4}{9} = \frac{16}{36}
\]

Now subtract:

\[
\frac{51}{36} - \frac{16}{36} = \frac{51 - 16}{36} = \frac{35}{36}
\]

Thus, the simplified expression is:

\[
\frac{35}{36}
\]

Would you like further details on any step?

Here are 5 related questions to explore further:
1. How do you find the least common denominator of two fractions?
2. What are the steps to simplify a fraction like \(\frac{8}{18}\)?
3. How do you convert improper fractions to mixed numbers?
4. How would you add or subtract more than two fractions with different denominators?
5. How can you solve algebraic expressions that involve fractions?

**Tip:** Always look for opportunities to simplify fractions before performing arithmetic operations like addition or subtraction.

Simplify the fractional expression 17/12 - (1/6 + 5/18) by finding the least common denominator and performing arithmetic operations. Follow a step-by-step approach to solve this problem, suitable for Grades 6-8.

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