2 Rosa needs \( 5 \frac{1}{4} \) yards of ribbon for a crafts project. She already has \( 2 \frac{7}{8} \) yards of ribbon. How \( \frac{\text { many more yards of ribbon does she need to buy? }}{5 \frac{1}{4}+2 \frac{2}{8}} \) \( \begin{array}{lll}\text { (8) } & 5 \frac{1}{4}=5 \frac{2}{8} & 5 \frac{2}{8}+2 \frac{7}{8}=7 \frac{9}{8}=\end{array} \)

To determine how many more yards of ribbon Rosa needs to buy for her crafts project, we can follow these steps: **Given:** - **Total ribbon needed:** \( 5 \frac{1}{4} \) yards - **Ribbon Rosa already has:** \( 2 \frac{7}{8} \) yards **Objective:** Find the additional yards of ribbon Rosa needs to purchase. **Step 1: Convert Mixed Numbers to Improper Fractions** First, let's convert both mixed numbers to improper fractions to make the calculations easier. 1. **Total ribbon needed:** \[ 5 \frac{1}{4} = \left(5 \times 4\right) + 1 = 21 \text{ eighths} = \frac{21}{4} \] 2. **Ribbon Rosa already has:** \[ 2 \frac{7}{8} = \left(2 \times 8\right) + 7 = 23 \text{ eighths} = \frac{23}{8} \] **Step 2: Subtract the Existing Ribbon from the Total Needed** To find out how much more ribbon is needed, subtract the amount Rosa already has from the total required. \[ \frac{21}{4} - \frac{23}{8} \] **Step 3: Find a Common Denominator** The denominators are 4 and 8. The least common denominator (LCD) is 8. Convert \(\frac{21}{4}\) to eighths: \[ \frac{21}{4} = \frac{21 \times 2}{4 \times 2} = \frac{42}{8} \] **Step 4: Perform the Subtraction** \[ \frac{42}{8} - \frac{23}{8} = \frac{42 - 23}{8} = \frac{19}{8} \] **Step 5: Convert Back to a Mixed Number** \[ \frac{19}{8} = 2 \frac{3}{8} \] **Conclusion:** Rosa needs to buy **\( 2 \frac{3}{8} \) yards** of ribbon to have enough for her crafts project.