To solve \(\left( \frac{11}{10} + \frac{3}{10} \right) \div \frac{1}{9}\), follow these steps:

1. **Add the fractions inside the parentheses**:
   \[
   \frac{11}{10} + \frac{3}{10} = \frac{14}{10} = \frac{7}{5}
   \]

2. **Divide by \(\frac{1}{9}\)**:
   Dividing by a fraction is the same as multiplying by its reciprocal, so:
   \[
   \frac{7}{5} \div \frac{1}{9} = \frac{7}{5} \times \frac{9}{1} = \frac{7 \times 9}{5 \times 1} = \frac{63}{5}
   \]

3. **Convert to a mixed number**:
   \[
   \frac{63}{5} = 12 \frac{3}{5}
   \]

So, \(\left( \frac{11}{10} + \frac{3}{10} \right) \div \frac{1}{9} = 12 \frac{3}{5}\).

Would you like more details on any part of this solution?

Here are some related questions:
1. How do you simplify fractions with different denominators?
2. How can you convert improper fractions to mixed numbers?
3. What is the rule for dividing fractions?
4. How do you multiply fractions and simplify the result?
5. Can you show the steps for converting \(\frac{63}{5}\) into decimal form?

**Tip**: When dividing fractions, always remember to multiply by the reciprocal of the divisor.

This guide explains how to solve the problem (11/10 + 3/10) ÷ 1/9 using fraction addition, division, and converting improper fractions to mixed numbers. Learn the key concepts of fractions and arithmetic suitable for students in Grades 5-7.

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