$$ \frac76-\frac{10}{9}-\frac{55}{54} $$$$ 3 $$

To solve the expression $ \frac{7}{6} - \frac{10}{9} - \frac{55}{54} + 3 $, we should first 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 subtract the fractions:
\[
\frac{63}{54} - \frac{60}{54} - \frac{55}{54} = \frac{63 - 60 - 55}{54} = \frac{-52}{54}
\]

Simplify the fraction:
\[
\frac{-52}{54} = \frac{-26}{27}
\]

### Step 3: Add the integer $3$
Now, add $ 3 $ (which is $ \frac{81}{27} $ when expressed as a fraction with a denominator of 27):
\[
\frac{-26}{27} + \frac{81}{27} = \frac{-26 + 81}{27} = \frac{55}{27}
\]

So, the simplified result is:
\[
\frac{55}{27}
\]

### Final Answer:
\[
\frac{7}{6} - \frac{10}{9} - \frac{55}{54} + 3 = \frac{55}{27}
\]

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

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**Related Questions:**

1. How do you find the least common multiple of a set of numbers?
2. What are the steps to simplify a fraction?
3. How can you convert a mixed number into an improper fraction?
4. How do you add or subtract fractions with different denominators?
5. What is the process of converting an integer into a fraction with a specific denominator?
6. Why is it important to simplify fractions in mathematical expressions?
7. How do you determine if a fraction can be simplified further?
8. What role does the LCM play in adding and subtracting fractions?

**Tip:** When working with fractions, always try to simplify your final answer to its lowest terms for clarity and precision.

Learn how to simplify the expression $\frac{7}{6} - \frac{10}{9} - \frac{55}{54} + 3$. This problem involves finding common denominators for fractions and applying addition and subtraction of fractions. Suitable for Grades 6-8.

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