https://file.aiquickdraw.com/mathbot/file/1726660579482myx0h75a.jpg

The expression in the image is as follows:

\[
\left( 1 + \frac{13}{27} \right) \times 2 \times \frac{11}{12} \div 3 \times \frac{1}{9}
\]

We will solve it step by step.

### Step 1: Simplify the mixed fraction
Convert \( 1 + \frac{13}{27} \) to a single fraction:
\[
1 + \frac{13}{27} = \frac{27}{27} + \frac{13}{27} = \frac{40}{27}
\]

### Step 2: Multiplying and Dividing
Now, simplify the rest of the expression:

\[
\frac{40}{27} \times 2 \times \frac{11}{12} \div 3 \times \frac{1}{9}
\]

#### Step 2.1: Multiply \( \frac{40}{27} \times 2 \):
\[
\frac{40}{27} \times 2 = \frac{80}{27}
\]

#### Step 2.2: Multiply \( \frac{80}{27} \times \frac{11}{12} \):
\[
\frac{80}{27} \times \frac{11}{12} = \frac{880}{324}
\]

Simplify \( \frac{880}{324} \) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
\[
\frac{880 \div 4}{324 \div 4} = \frac{220}{81}
\]

#### Step 2.3: Divide by 3:
\[
\frac{220}{81} \div 3 = \frac{220}{81} \times \frac{1}{3} = \frac{220}{243}
\]

#### Step 2.4: Multiply by \( \frac{1}{9} \):
\[
\frac{220}{243} \times \frac{1}{9} = \frac{220}{2187}
\]

### Final Answer:
The simplified result of the expression is:
\[
\frac{220}{2187}
\]

Would you like further details on any of the steps?

Here are some related questions for further practice:
1. How do you convert a mixed fraction to an improper fraction?
2. What are the steps to multiply two fractions?
3. How do you simplify a fraction after multiplying?
4. How do you divide one fraction by another?
5. What is the greatest common divisor, and how is it used to simplify fractions?

**Tip:** When working with fractions, always remember to simplify at the end by finding the greatest common divisor of the numerator and denominator.

Solve the expression (1 + 13/27) × 2 × (11/12) ÷ 3 × (1/9).

Learn how to solve the expression involving fractions: (1 + 13/27) × 2 × (11/12) ÷ 3 × (1/9). This step-by-step guide walks through simplifying fractions, converting mixed fractions to improper fractions, and solving arithmetic operations. Suitable for Grades 6-8.

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