https://file.aiquickdraw.com/mathbot/file/1730323095124d7f7enh0.jpg

The expression in the image is:

\[
5 \frac{5}{7} \div 1 \frac{3}{5} \cdot 4 \frac{2}{3}
\]

To solve this, let's break it down into steps:

### Step 1: Convert the Mixed Numbers to Improper Fractions

1. \( 5 \frac{5}{7} = \frac{5 \cdot 7 + 5}{7} = \frac{35 + 5}{7} = \frac{40}{7} \)
2. \( 1 \frac{3}{5} = \frac{1 \cdot 5 + 3}{5} = \frac{5 + 3}{5} = \frac{8}{5} \)
3. \( 4 \frac{2}{3} = \frac{4 \cdot 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \)

Now the expression becomes:

\[
\frac{40}{7} \div \frac{8}{5} \cdot \frac{14}{3}
\]

### Step 2: Perform the Division

Dividing by a fraction is the same as multiplying by its reciprocal:

\[
\frac{40}{7} \cdot \frac{5}{8} \cdot \frac{14}{3}
\]

### Step 3: Simplify the Expression by Multiplying the Fractions

Multiply the numerators and denominators:

\[
\frac{40 \cdot 5 \cdot 14}{7 \cdot 8 \cdot 3}
\]

### Step 4: Simplify by Canceling Common Factors

1. Simplify \( \frac{40}{8} = 5 \), so the expression becomes:
   \[
   \frac{5 \cdot 5 \cdot 14}{7 \cdot 3} = \frac{25 \cdot 14}{21}
   \]

2. Simplify \( \frac{14}{7} = 2 \), so now we have:
   \[
   \frac{25 \cdot 2}{3} = \frac{50}{3}
   \]

### Final Answer

\[
\frac{50}{3} \quad \text{or as a mixed number: } 16 \frac{2}{3}
\]

Would you like a detailed breakdown of any part of the solution, or do you have any other questions?

Here are five related questions to extend this topic:

1. How do you multiply and divide mixed numbers directly without converting to improper fractions?
2. How do you simplify complex fractions in multi-step problems like this?
3. What strategies help in reducing fractions early in multi-step calculations?
4. How do you handle division and multiplication with negative fractions?
5. How do you convert a result in improper fraction form to a decimal?

**Tip:** Always simplify fractions step-by-step to make large multiplications easier and avoid calculation errors.

Learn how to solve the fraction expression 5 5/7 ÷ 1 3/5 · 4 2/3 by converting mixed numbers to improper fractions and simplifying the result. This problem involves key fraction concepts, suitable for Grades 6-8.

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