To solve the expression \( \frac{7}{6} - \frac{10}{9} + \frac{55}{54} \), we need to find a common denominator for the fractions and then simplify.

### Step 1: Find a common denominator
The denominators are 6, 9, and 54. The least common multiple (LCM) of these numbers is 54.

- Convert \( \frac{7}{6} \) to have a denominator of 54:
  \[
  \frac{7}{6} = \frac{7 \times 9}{6 \times 9} = \frac{63}{54}
  \]
- Convert \( \frac{10}{9} \) to have a denominator of 54:
  \[
  \frac{10}{9} = \frac{10 \times 6}{9 \times 6} = \frac{60}{54}
  \]
- \( \frac{55}{54} \) already has a denominator of 54.

### Step 2: Combine the fractions
Now, perform the addition and subtraction:
\[
\frac{63}{54} - \frac{60}{54} + \frac{55}{54} = \frac{63 - 60 + 55}{54} = \frac{58}{54}
\]

### Step 3: Simplify the fraction
Simplify \( \frac{58}{54} \) by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2:
\[
\frac{58}{54} = \frac{58 \div 2}{54 \div 2} = \frac{29}{27}
\]

### Final Answer:
\[
\frac{7}{6} - \frac{10}{9} + \frac{55}{54} = \frac{29}{27}
\]

Would you like more details or have any questions about this?

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**Related Questions:**

1. How do you find the greatest common divisor (GCD) of two numbers?
2. What steps are involved in adding and subtracting fractions?
3. How can fractions be simplified after addition or subtraction?
4. How do you identify when a fraction is in its simplest form?
5. What is the importance of the LCM in operations with fractions?
6. Can you convert improper fractions to mixed numbers?
7. What methods can be used to check if your fraction simplification is correct?
8. How does the order of operations affect the calculation of fractions?

**Tip:** Always ensure that fractions are simplified to their lowest terms for the most accurate and clear representation of the result.

Learn how to solve the expression 7/6 - 10/9 + 55/54 step-by-step. This problem involves arithmetic operations with fractions and finding a common denominator. Suitable for students in Grades 7-9.

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