For each of the expressions below, leverage the part-whole relationship between the divisor and dividend to simplify the fractions and solve for the quotient. Represent your work using the open array model. $$ 1 \frac{100}{4} $$

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To simplify the expression $$ 1 \frac{100}{4} $$ and solve for the quotient using the part-whole relationship and the open array model, follow these steps:

### Step 1: Understand the Mixed Number
The expression $$ 1 \frac{100}{4} $$ is a **mixed number**, which consists of:
- **Whole number part:** 1
- **Fractional part:** $$ \frac{100}{4} $$

### Step 2: Simplify the Fractional Part
Simplify $$ \frac{100}{4} $$:

$$
\frac{100}{4} = 25
$$

So, the mixed number becomes:

$$
1 \frac{100}{4} = 1 + 25 = 26
$$

### Step 3: Representing with the Open Array Model
The **open array model** visually represents the division of objects into equal groups. Here's how you can visualize $$ 100 \div 4 $$:

1. **Start with 100 Objects:** Imagine 100 identical objects (like dots or squares).

2. **Divide into 4 Equal Groups:** Arrange the 100 objects into 4 equal rows (groups).

3. **Determine the Number of Objects per Group:**

$$
\frac{100}{4} = 25
$$

Each of the 4 groups will have **25 objects**.

4. **Add the Whole Number:**

Since the mixed number includes a whole number 1, you add this to the quotient obtained from the fraction:

$$
1 + 25 = 26
$$

### Visual Representation:

```
Group 1: ●●●●●●●●●●●●●●●●●●●●●●●●●● (25 objects)
Group 2: ●●●●●●●●●●●●●●●●●●●●●●●●●● (25 objects)
Group 3: ●●●●●●●●●●●●●●●●●●●●●●●●●● (25 objects)
Group 4: ●●●●●●●●●●●●●●●●●●●●●●●●●● (25 objects)
```

Adding the whole number:

$$
\text{Total Quotient} = 1 + 25 = 26
$$

### Conclusion

By simplifying the mixed number and using the open array model to visualize the division, the **quotient** of $$ 1 \frac{100}{4} $$ is:

$$
\boxed{26}
$$
The quotient of $$ 1 \frac{100}{4} $$ is 26.

For each of the expressions below, leverage the part-whole relationship between the divisor and dividend to simplify the fractions and solve for the quotient. Represent your work using the open array model. \( 1 \frac{100}{4} \)

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