5. kyle puts ribbon around his rectangular bulletin board, which measures \( 24 \frac{3}{4} \) inches by \( 36 \frac{5}{8} \) inches. How much ribbon does he need?

To determine how much ribbon Kyle needs to put around his rectangular bulletin board, we need to calculate the perimeter of the rectangle. The perimeter \( P \) of a rectangle is given by the formula: \[ P = 2 \times (\text{length} + \text{width}) \] **Given Dimensions:** - Length = \( 36 \frac{5}{8} \) inches - Width = \( 24 \frac{3}{4} \) inches **Step 1: Convert Mixed Numbers to Improper Fractions** Convert both measurements to improper fractions for easier calculation. \[ 36 \frac{5}{8} = \frac{36 \times 8 + 5}{8} = \frac{288 + 5}{8} = \frac{293}{8} \] \[ 24 \frac{3}{4} = \frac{24 \times 4 + 3}{4} = \frac{96 + 3}{4} = \frac{99}{4} \] **Step 2: Find a Common Denominator and Add** To add these two fractions, they need to have the same denominator. The least common denominator (LCD) of 8 and 4 is 8. \[ \frac{99}{4} = \frac{99 \times 2}{4 \times 2} = \frac{198}{8} \] Now, add the two fractions: \[ \frac{198}{8} + \frac{293}{8} = \frac{198 + 293}{8} = \frac{491}{8} \] **Step 3: Calculate the Perimeter** Multiply the sum by 2 to find the perimeter: \[ P = 2 \times \frac{491}{8} = \frac{982}{8} = \frac{491}{4} \] Convert the improper fraction back to a mixed number: \[ \frac{491}{4} = 122 \frac{3}{4} \text{ inches} \] **Conclusion:** Kyle needs **\( 122 \frac{3}{4} \) inches** of ribbon to wrap around his bulletin board. **Answer:** Kyle needs \(122\, \frac{3}{4}\) inches of ribbon.