https://file.aiquickdraw.com/mathbot/file/1727405791588lh54mf1s.jpg

The expression in the image is:

\[
3 \frac{2}{3} \times 1 \frac{5}{6} \div \frac{4}{5}
\]

Let's break this down step by step.

### Step 1: Convert Mixed Numbers to Improper Fractions
1. \( 3 \frac{2}{3} \) can be written as:
   \[
   3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{11}{3}
   \]
2. \( 1 \frac{5}{6} \) can be written as:
   \[
   1 \frac{5}{6} = \frac{1 \times 6 + 5}{6} = \frac{11}{6}
   \]

Now the expression becomes:
\[
\frac{11}{3} \times \frac{11}{6} \div \frac{4}{5}
\]

### Step 2: Division of Fractions
Dividing by a fraction is the same as multiplying by its reciprocal. So,
\[
\div \frac{4}{5} = \times \frac{5}{4}
\]
Now the expression becomes:
\[
\frac{11}{3} \times \frac{11}{6} \times \frac{5}{4}
\]

### Step 3: Multiply the Fractions
Now multiply all the numerators and denominators:
\[
\frac{11 \times 11 \times 5}{3 \times 6 \times 4} = \frac{605}{72}
\]

### Step 4: Simplify (if needed)
The fraction \(\frac{605}{72}\) is already in its simplest form, as 605 and 72 have no common factors.

So, the result is:
\[
\frac{605}{72}
\]

Would you like further clarification or any additional details?

Here are five related questions:
1. How do you convert mixed numbers to improper fractions?
2. Why is dividing by a fraction the same as multiplying by its reciprocal?
3. Can you simplify the fraction \(\frac{605}{72}\) using another method?
4. How would the result change if the numbers in the fractions were different?
5. What are other real-world applications of operations with fractions?

**Tip:** When multiplying or dividing fractions, always check if you can simplify the numbers early to avoid working with large values.

Learn how to solve the mixed fraction expression 3 2/3 × 1 5/6 ÷ 4/5. This problem demonstrates converting mixed numbers to improper fractions and applying division and multiplication of fractions step by step. Suitable for Grades 6-8.

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