To solve this problem using the reciprocal method, we will follow these steps:

1. Understand the given quantities and relationships.
2. Use the reciprocal to find the total capacity.

Given:

• $\frac{2}{3}$ of the bottle is filled with $\frac{1}{2}$ liters of water.

We need to find the total capacity of the bottle.

Step-by-Step Solution

1. Determine the amount filled:

   $\frac{2}{3}$ of the bottle holds $\frac{1}{2}$ liters.

2. Set up the equation:

   Let $C$ be the total capacity of the bottle in liters.

   $\frac{2}{3}C = \frac{1}{2}$

3. Solve for $C$ using the reciprocal:

   To isolate $C$, multiply both sides of the equation by the reciprocal of $\frac{2}{3}$.

   The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.

   Multiply both sides by $\frac{3}{2}$:

   $C = \frac{1}{2} \times \frac{3}{2}$

4. Perform the multiplication:

   $C = \frac{1 \times 3}{2 \times 2} = \frac{3}{4}$

So, the total capacity of the bottle is $\frac{3}{4}$ liters.

Conclusion

The bottle can hold $\frac{3}{4}$ liters of water.

Would you like further details or have any questions?

Here are some related questions you might find helpful:

1. How do you calculate the reciprocal of a fraction?
2. What are other methods to find the total capacity of a container?
3. How can you convert between different units of volume?
4. How do you solve equations involving fractions?
5. What is the importance of understanding ratios and proportions?
6. How can you apply the concept of reciprocals in real-life situations?
7. How do you verify the solution to a problem involving reciprocals?
8. What are common mistakes to avoid when working with reciprocals?

Tip: When solving problems involving fractions, always double-check your calculations to ensure accuracy, especially when dealing with reciprocals and multiplication.