Lourdes is listening to an audio book that is 9 hours long. She has Whole listened for $$ 6 \frac{1}{6} $$ hours so far. How many hours of listening time are left? a. Fill in the whole box. b. Number model with unknown: c. A different way to solve a mixed-number subtraction problemc

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Let's solve the problem step by step:

**Problem Statement:**
Lourdes is listening to a 9-hour audiobook. She has listened for $$ 6 \frac{1}{6} $$ hours so far. How many hours of listening time are left?

---

### **a. Fill in the Whole Box**

Assuming "filling in the whole box" refers to setting up the subtraction with whole numbers separated from fractions:

1. **Total Time (Whole Number):** 9 hours
2. **Time Listened (Whole Number):** 6 hours
3. **Fractional Part of Time Listened:** $$ \frac{1}{6} $$ hours

So, the subtraction setup focusing on whole numbers is:

$$
\boxed{9\ \text{(Total Hours)}\ -\ 6\ \text{(Listened Hours)}}
$$

---

### **b. Number Model with Unknown**

Let's represent the problem using an equation where $$ x $$ is the unknown amount of time left:

$$
\text{Total Time} - \text{Time Listened} = \text{Time Left}
$$

Plugging in the known values:

$$
9\ \text{hours} - 6 \frac{1}{6}\ \text{hours} = x
$$

So, the number model is:

$$
9 - 6 \frac{1}{6} = x
$$

---

### **c. A Different Way to Solve a Mixed-Number Subtraction Problem**

Instead of subtracting the mixed numbers directly, you can convert them to improper fractions or separate the whole numbers from the fractions. Here's an alternative method:

1. **Convert Whole Number to a Mixed Number:**
   - Represent 9 hours as $$ 8 \frac{6}{6} $$ hours (since $$ 8 + \frac{6}{6} = 9 $$).

2. **Set Up the Subtraction:**
   $$
   8 \frac{6}{6} - 6 \frac{1}{6}
   $$

3. **Subtract the Whole Numbers and Fractions Separately:**
   - **Whole Numbers:** $$ 8 - 6 = 2 $$
   - **Fractions:** $$ \frac{6}{6} - \frac{1}{6} = \frac{5}{6} $$

4. **Combine the Results:**
   $$
   2 \frac{5}{6}\ \text{hours left}
   $$

**Final Answer:**
$$
9 - 6 \frac{1}{6} = 2 \frac{5}{6}\ \text{hours left}
$$

---

**Summary:**
- **a.** Filled whole boxes with 9 and 6.
- **b.** Number model: $$ 9 - 6 \frac{1}{6} = x $$.
- **c.** Converted 9 to $$ 8 \frac{6}{6} $$ and subtracted to find $$ 2 \frac{5}{6} $$ hours left.
There are 2 and 5/6 hours of listening time left.

Lourdes is listening to an audio book that is 9 hours long. She has Whole listened for \( 6 \frac{1}{6} \) hours so far. How many hours of listening time are left? a. Fill in the whole box. b. Number model with unknown: c. A different way to solve a mixed-number subtraction problemc

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