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 $$ \frac{ ext { many more yards of ribbon does she need to buy? }}{5 \frac{1}{4}+2 \frac{2}{8}} $$ $$ \begin{array}{lll} ext { (8) } & 5 \frac{1}{4}=5 \frac{2}{8} & 5 \frac{2}{8}+2 \frac{7}{8}=7 \frac{9}{8}=\end{array} $$

Question

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 $$ \frac{	ext { many more yards of ribbon does she need to buy? }}{5 \frac{1}{4}+2 \frac{2}{8}} $$ $$ \begin{array}{lll}	ext { (8) } & 5 \frac{1}{4}=5 \frac{2}{8} & 5 \frac{2}{8}+2 \frac{7}{8}=7 \frac{9}{8}=\end{array} $$

UpStudy AI · Accepted Answer

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.
Rosa needs to buy $$ 2 \frac{3}{8} $$ yards of ribbon.

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