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The problem in the image involves adding and subtracting fractions to determine how much more paint is needed.

Let's break it down:

- The painter has \( 5 \frac{1}{3} \) gallons of paint.
- It takes \( 4 \frac{4}{9} \) gallons of paint for the family room.
- It will take \( 6 \frac{2}{9} \) gallons of paint for the living room.

We need to find how much more paint is needed by:

1. Finding the total amount of paint required (for both rooms).
2. Subtracting the available paint to determine how much more is needed.

### Step 1: Convert the mixed numbers into improper fractions.
- \( 5 \frac{1}{3} = \frac{16}{3} \)
- \( 4 \frac{4}{9} = \frac{40}{9} \)
- \( 6 \frac{2}{9} = \frac{56}{9} \)

### Step 2: Calculate the total paint required for the family room and living room.
The total paint required is:
\[
\frac{40}{9} + \frac{56}{9} = \frac{96}{9} = \frac{32}{3}
\]

### Step 3: Compare the total paint required with the available paint.
Now, subtract the available paint from the required paint:
\[
\frac{32}{3} - \frac{16}{3} = \frac{16}{3}
\]

### Conclusion:
The painter needs an additional \( \frac{16}{3} \) gallons of paint, or \( 5 \frac{1}{3} \) gallons.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. How do you subtract mixed numbers without converting them to improper fractions?
2. How would the answer change if the painter had more than \( 5 \frac{1}{3} \) gallons of paint?
3. What are some real-world applications of using fractions in measurements?
4. Can you add fractions with different denominators directly?
5. What is the importance of finding a common denominator in fraction problems?

**Tip:** When adding or subtracting fractions, always ensure that they have a common denominator before performing the operation.

A painter has 5 1/3 gallons of paint. It takes 4 4/9 gallons to paint the family room. It is estimated that 6 2/9 gallons are required to paint the living room. How much more paint is needed?

Learn how to solve a problem involving the addition and subtraction of fractions. This detailed solution walks through converting mixed numbers into improper fractions, finding the total amount of paint needed, and calculating how much more is required. Ideal for students in Grades 5-7.

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