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The simplified form of the given expression \( \frac{1}{2}r - \frac{1}{9}r + \frac{3}{2} + 5 \) is:

\[
\frac{7}{18}r + \frac{13}{2}
\]

Would you like further details or have any questions about this process?

Here are five related questions to deepen understanding:
1. How do you combine terms with different denominators?
2. What are the steps to simplify algebraic expressions with fractions?
3. How can you find a common denominator for fractional terms?
4. How would this expression change if a constant were added or subtracted?
5. How does distribution affect the simplification of expressions with multiple terms?

**Tip:** When simplifying expressions, always combine like terms and find a common denominator for fractional terms to streamline your calculations.

Simplify the expression: \( \frac{1}{2}r - \frac{1}{9}r + \frac{3}{2} + 5 \).

Learn how to simplify the algebraic expression \( \frac{1}{2}r - \frac{1}{9}r + \frac{3}{2} + 5 \) by combining like terms and finding a common denominator. This problem covers key algebraic concepts and is suitable for students in Grades 6-8.

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