https://file.aiquickdraw.com/mathbot/file/1729427092653t9nr0skx.jpg

The expression in the image appears to be a complex fractional expression involving both decimals and fractions. Here is a breakdown of the expression:

\[
\frac{
    \left( 13.75 + 9 \frac{1}{6} \right) \cdot 1.2 + \left( 6.8 - 3 \frac{3}{5} \right) \cdot \frac{5}{6}
}{
    \left( 10.3 - 8 \frac{1}{2} \right) \cdot \frac{5}{9} + \left( 3 \frac{2}{3} - 1 \frac{1}{6} \right) \cdot 56
} - 27 \frac{1}{6}
\]

### Steps to solve:
1. **Handle mixed numbers** by converting them to improper fractions or decimals.
2. **Perform addition and subtraction** inside the parentheses.
3. **Multiply the results** with the constants outside the parentheses.
4. **Simplify** the numerator and denominator.
5. **Divide the numerator by the denominator**.
6. **Subtract** the final value by \( 27 \frac{1}{6} \).

I will now work through these steps.

### Step 1: Convert Mixed Numbers
- \( 9 \frac{1}{6} = 9 + \frac{1}{6} = 9.1667 \)
- \( 3 \frac{3}{5} = 3 + \frac{3}{5} = 3.6 \)
- \( 8 \frac{1}{2} = 8.5 \)
- \( 3 \frac{2}{3} = 3.6667 \)
- \( 1 \frac{1}{6} = 1.1667 \)
- \( 27 \frac{1}{6} = 27.1667 \)

### Step 2: Simplify the Expression
1. Numerator:
   \[
   (13.75 + 9.1667) \cdot 1.2 + (6.8 - 3.6) \cdot \frac{5}{6}
   \]
   Simplifies to:
   \[
   (22.9167) \cdot 1.2 + (3.2) \cdot \frac{5}{6}
   \]

2. Denominator:
   \[
   (10.3 - 8.5) \cdot \frac{5}{9} + (3.6667 - 1.1667) \cdot 56
   \]
   Simplifies to:
   \[
   (1.8) \cdot \frac{5}{9} + (2.5) \cdot 56
   \]

### Step 3: Further Simplifications
1. Numerator:
   \[
   22.9167 \cdot 1.2 = 27.5
   \]
   \[
   3.2 \cdot \frac{5}{6} = 2.6667
   \]
   So, the numerator is:
   \[
   27.5 + 2.6667 = 30.1667
   \]

2. Denominator:
   \[
   1.8 \cdot \frac{5}{9} = 1
   \]
   \[
   2.5 \cdot 56 = 140
   \]
   So, the denominator is:
   \[
   1 + 140 = 141
   \]

### Step 4: Final Division and Subtraction
1. The fraction is:
   \[
   \frac{30.1667}{141} \approx 0.2139
   \]

2. Subtract:
   \[
   0.2139 - 27.1667 = -26.9528
   \]

### Final Answer:
\[
\boxed{-26.9528}
\]

Would you like further details or have any questions about the process?

Here are some related questions to explore further:
1. How do you convert mixed numbers to improper fractions?
2. Why is it important to simplify expressions inside parentheses first?
3. What is the difference between multiplying decimals and fractions?
4. How do you find common denominators in fraction operations?
5. What happens when the numerator of a fraction is larger than the denominator?

**Tip:** Always simplify expressions inside parentheses before performing multiplication or division operations.

Solve the complex fractional equation involving mixed numbers, decimals, and fractions as shown in the image.

Learn how to solve a complex fractional equation that involves mixed numbers, decimals, and basic arithmetic operations. This step-by-step solution simplifies the equation and demonstrates the conversion of mixed numbers to improper fractions, suitable for Grades 8-10 students.

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