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. \( 1 \frac{100}{4} \)

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: \[ \boxed{26} \]