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.