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Let's solve the problem step by step:

Given:
- \(\frac{1}{2}\) gallon of paint covers \(\frac{1}{12}\) of a wall.
- We need to find how many quarts of paint are needed to cover the entire wall.

### Step 1: Determine how many gallons of paint are needed for the whole wall.

If \(\frac{1}{2}\) gallon covers \(\frac{1}{12}\) of the wall, we can set up a proportion to find how many gallons cover the entire wall.

Let \(x\) be the number of gallons needed to cover the whole wall:
\[
\frac{1}{2} \text{ gallon} : \frac{1}{12} \text{ of wall} = x \text{ gallons} : 1 \text{ of wall}
\]

Solving for \(x\):
\[
x = \frac{1}{2} \times \frac{1}{\frac{1}{12}} = \frac{1}{2} \times 12 = 6 \text{ gallons}
\]

So, 6 gallons of paint are required to cover the entire wall.

### Step 2: Convert gallons to quarts.

Since 1 gallon is equal to 4 quarts:
\[
6 \text{ gallons} \times 4 \text{ quarts per gallon} = 24 \text{ quarts}
\]

### Answer
24 quarts of paint are needed for the entire wall.

Would you like more details or have any questions about the solution?

### Related Questions:
1. If a gallon of paint covers \(\frac{1}{8}\) of a wall, how many gallons are needed to cover the entire wall?
2. How many quarts are in 10 gallons?
3. If 3 quarts of paint cover \(\frac{1}{4}\) of a wall, how much paint is required to paint half of the wall?
4. What is the conversion factor from gallons to pints?
5. How many square feet can 1 quart of paint cover if 1 gallon covers 350 square feet?

### Tip:
When working with unit conversions, always double-check the conversion factors to ensure accuracy in your calculations!

If 1/2 gallon of paint covers 1/12 of a wall, how many quarts of paint are needed for the entire wall?

Learn how to calculate the number of quarts of paint required to cover a full wall when given partial coverage information. This solution involves setting up a proportion and converting gallons to quarts, suitable for students in Grades 6-8.

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