The problem asks to calculate how much fencing is required for two adjacent rectangular pastures. The dimensions given are:

• Length = $50 \frac{5}{8}$ yards
• Width = $30 \frac{2}{9}$ yards

Since there are two adjacent rectangular pastures, the fencing needed will enclose both pastures together. We can visualize the total fenced area as a large rectangle divided into two smaller rectangles. This means the middle fencing only needs to be counted once between the two pastures.

To find the total fencing, we calculate the perimeter of the combined rectangle:

Step 1: Convert mixed fractions to improper fractions

1. $50 \frac{5}{8}$ yards = $\frac{405}{8}$ yards
2. $30 \frac{2}{9}$ yards = $\frac{272}{9}$ yards

Step 2: Find the total perimeter

The combined perimeter (P) for two adjacent rectangular pastures has the following formula: $P = 2 \times \text{Length} + 3 \times \text{Width}$ We multiply the width by 3 because the middle fence between the two pastures needs to be added.

Substitute the values: $P = 2 \times \frac{405}{8} + 3 \times \frac{272}{9}$

Let's calculate this value to find the total fencing needed.The total fencing required is $\frac{2303}{12}$ yards, which simplifies to approximately 191.92 yards.

Would you like a further breakdown or explanation?

Here are some related questions to extend your understanding:

1. How do you calculate the perimeter of a single rectangular pasture?
2. What would the perimeter be if the two pastures were not adjacent?
3. Can you use decimals instead of fractions in the calculation?
4. How would the answer change if the pastures were square instead of rectangular?
5. How do you simplify mixed fractions in these types of problems?

Tip: When working with mixed numbers, converting them to improper fractions can make calculations easier!