5/(9/11+4/11) Use the rules for order of operations to evaluate the following expression. Write the solution as a mixed number or a fraction in lowest terms.

Let's evaluate the expression \( \frac{5}{\frac{9}{11} + \frac{4}{11}} \) step by step, following the order of operations:

1. **Add the fractions** in the denominator:
   \[
   \frac{9}{11} + \frac{4}{11} = \frac{9 + 4}{11} = \frac{13}{11}
   \]

2. **Rewrite the expression**:
   \[
   \frac{5}{\frac{13}{11}} = 5 \times \frac{11}{13}
   \]
   Since dividing by a fraction is the same as multiplying by its reciprocal, we multiply 5 by \( \frac{11}{13} \).

3. **Multiply the fractions**:
   \[
   5 \times \frac{11}{13} = \frac{5 \times 11}{13} = \frac{55}{13}
   \]

4. **Convert to a mixed number**:
   Divide 55 by 13:
   \[
   55 \div 13 = 4 \text{ with a remainder of } 3
   \]
   So, \( \frac{55}{13} = 4 \frac{3}{13} \).

Thus, the solution to the expression is \( 4 \frac{3}{13} \) or \( \frac{55}{13} \).

Would you like any further details or clarification on this? 

Here are 5 related questions to explore:
1. How do you simplify complex fractions with different denominators?
2. What is the process for converting improper fractions to mixed numbers?
3. How do you add or subtract fractions with unlike denominators?
4. Can you explain the concept of reciprocal in division of fractions?
5. How does the order of operations affect the outcome of expressions?

**Tip:** When dividing by a fraction, always multiply by its reciprocal to simplify the process.

Learn how to evaluate the fraction expression 5/(9/11 + 4/11) step by step. This solution covers adding fractions, applying the reciprocal rule for division, and converting the result into a mixed number. Suitable for students in Grades 5-7.

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