Don is making a picture frame with a length of 27 1/4 inches and a width of 11 3/8 inches. He has a piece of wood 6 1/2 feet long. After he cuts off the wood he needs to make the frame, how long will the remaining piece of wood be?

To solve this, we'll first determine the total length of wood needed for the picture frame and then subtract this from the length of the available wood.

### Step 1: Convert Measurements to the Same Units
We need to work in consistent units. Let’s convert everything to inches.

1. **Piece of wood (in feet to inches):**
   \[
   6 \frac{1}{2} \text{ feet} = 6 \times 12 + \frac{1}{2} \times 12 = 72 + 6 = 78 \text{ inches}
   \]

2. **Frame dimensions:**
   - Length = \( 27 \frac{1}{4} \) inches
   - Width = \( 11 \frac{3}{8} \) inches

### Step 2: Determine the Total Length of Wood Needed
Don needs to cut 4 pieces of wood for the frame: 2 pieces for the length and 2 pieces for the width.

- **Length:** \( 2 \times 27 \frac{1}{4} = 2 \times \frac{109}{4} = \frac{218}{4} = 54.5 \) inches
- **Width:** \( 2 \times 11 \frac{3}{8} = 2 \times \frac{91}{8} = \frac{182}{8} = 22.75 \) inches

Total length of wood needed:
\[
54.5 + 22.75 = 77.25 \text{ inches}
\]

### Step 3: Subtract the Wood Used from the Total Wood
The remaining length of wood after Don cuts what he needs is:
\[
78 \text{ inches} - 77.25 \text{ inches} = 0.75 \text{ inches}
\]

### Final Answer:
Don will have **0.75 inches** of wood remaining after making the picture frame.

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

Here are some related questions:
1. How do you convert mixed fractions to improper fractions?
2. How can you simplify measurements in feet and inches?
3. How would you handle different units in a similar problem?
4. What are other real-life scenarios involving cutting materials?
5. How can you calculate perimeter for rectangular objects?
6. What are some tips for measuring materials precisely?
7. How do mixed fractions work in calculations?
8. What happens if Don makes a mistake and cuts too much?

Tip: Always double-check your measurements before cutting to avoid waste.

Learn how to calculate the remaining length of wood after making a picture frame with detailed step-by-step solution. This problem covers measurement conversion, area calculation for rectangular objects, and subtraction of measurements. Suitable for students in Grades 6-8.

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