To find the value of the expression $\frac{1 \frac{2}{3}}{2 \frac{4}{5}}$, let’s follow these steps:

Step 1: Convert the Mixed Numbers to Improper Fractions

1. Convert $1 \frac{2}{3}$: $1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3}$

2. Convert $2 \frac{4}{5}$: $2 \frac{4}{5} = \frac{5 \times 2 + 4}{5} = \frac{14}{5}$

Step 2: Divide the Fractions

To divide $\frac{5}{3}$ by $\frac{14}{5}$, multiply $\frac{5}{3}$ by the reciprocal of $\frac{14}{5}$, which is $\frac{5}{14}$.

$\frac{5}{3} \div \frac{14}{5} = \frac{5}{3} \times \frac{5}{14} = \frac{25}{42}$

Final Answer

The value of the expression is: $\frac{25}{42}$

Would you like further details on any step, or have any questions?

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Here are 5 related questions to deepen understanding:

1. What is the value of $3 \frac{1}{4} / 1 \frac{3}{8}$?
2. How would you multiply $2 \frac{2}{7} \times 1 \frac{5}{9}$?
3. What is the reciprocal of $4 \frac{2}{3}$?
4. Can you simplify $\frac{5}{3} \times \frac{7}{5}$?
5. How can you convert a fraction like $\frac{25}{42}$ to a decimal?

Tip: Always convert mixed numbers to improper fractions before performing operations like division or multiplication.