Given:
- The container is filled with a liquid mixture consisting of 4 parts water and 6 parts milk.
- We need to draw off some of the mixture and fill it with water in such a way that the resulting mixture contains equal parts of water and milk.

Approach:
Let's assume that the container initially contains 10 parts of the mixture (4 parts water + 6 parts milk).
We need to find out how much of the mixture needs to be drawn off and replaced with water to obtain a 1:1 ratio of water and milk in the final mixture.

Solution:
Step 1: Assume the total quantity of the mixture in the container as 10 units (to simplify calculations).

Step 2: Calculate the initial quantities of water and milk in the container:
- Water in the mixture = (4/10) * 10 = 4 units
- Milk in the mixture = (6/10) * 10 = 6 units

Step 3: Let's assume x units of the mixture is drawn off and replaced with water.

Step 4: After drawing off x units of the mixture, the remaining quantities of water and milk in the container will be:
- Remaining water = 4 - (4/10) * x
- Remaining milk = 6 - (6/10) * x

Step 5: Now, we need to calculate how much water needs to be added to make the final mixture contain equal parts of water and milk. Let's assume y units of water are added.

Step 6: After adding y units of water, the final quantities of water and milk in the container will be:
- Final water = 4 - (4/10) * x + y
- Final milk = 6 - (6/10) * x

Step 7: According to the problem, the final mixture should contain equal parts of water and milk. So, the final water and milk quantities should be equal:
Final water = Final milk

Step 8: Set up the equation:
4 - (4/10) * x + y = 6 - (6/10) * x

Step 9: Simplify the equation:
2/10 * x = y - 2

Step 10: We know that the final mixture should contain equal parts of water and milk. So, the quantity of water added should be equal to the quantity of milk removed from the mixture.
Therefore, y = (4/10) * x

Step 11: Substitute the value of y in the equation from Step 9:
2/10 * x = (4/10) * x - 2

Step 12: Simplify the equation:
2x = 4x - 20
2x - 4x = -20
-2x = -20
x = -20 / -2
x = 10

Step 13: The quantity of the mixture that needs to be drawn off and replaced with water is 10 units.

Step 14: The total quantity of the mixture in the container is 10 units (as assumed in Step 1). And we need to draw off 10 units of the mixture.

Step 15: The fraction of the mixture that needs to be drawn off is:
Fraction = (10 units) / (10 units) = 1/