Let's break down this problem step by step.

Part A: Estimating the Area

We have a rectangle with the following dimensions:

• Length: $4 \frac{2}{3}$ yards
• Width: $3 \frac{1}{2}$ yards

To estimate the area, we'll round the dimensions to simpler whole numbers:

• Length: $4 \frac{2}{3} \approx 5$ (since $4 \frac{2}{3}$ is closer to 5)
• Width: $3 \frac{1}{2} \approx 3$ (since $3 \frac{1}{2}$ is closer to 3)

Now, we estimate the area: $\text{Estimated area} = 5 \times 3 = 15 \, \text{square yards}.$

For the rounding part:

• $4 \frac{2}{3} \approx 5$ rounds to 5.
• $3 \frac{1}{2} \approx 3$ rounds to 3.

Thus, the estimated area is about 15 square yards.

Part B: Actual Area of the Wall

To find the exact area, multiply the actual dimensions of the rectangle:

• Length: $4 \frac{2}{3} = \frac{14}{3}$ yards
• Width: $3 \frac{1}{2} = \frac{7}{2}$ yards

Now, calculate the area: $\text{Actual area} = \frac{14}{3} \times \frac{7}{2} = \frac{14 \times 7}{3 \times 2} = \frac{98}{6} = 16 \frac{1}{3} \, \text{square yards}.$

Final Answers:

• A. Estimated area of the wall is about 15 square yards.
• B. The actual area of the wall is $16 \frac{1}{3}$ square yards.

Would you like more details or have any further questions?

Here are some related questions:

1. How do you convert mixed numbers to improper fractions?
2. What are the steps for multiplying fractions?
3. How do you round mixed numbers to the nearest whole number?
4. What’s the difference between estimating and calculating exact values in geometry?
5. How do you calculate the area of irregular shapes?

Tip: When estimating areas, rounding dimensions to whole numbers can make the calculation faster, but remember it might be slightly off from the actual value!