Question
2. Rebecea uses \( \frac{3}{4} \) gallon of paint to col 1 wall. She has 3 gallons of paint. Draw model to show how many walls she can paint.
Ask by Young Franklin. in the United States
Jan 31,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Rebecea can paint 4 walls with 3 gallons of paint.
Solution
To determine how many walls Rebecea can paint with her available paint, let's break down the problem step-by-step and create a simple model to visualize the solution.
### **Given:**
- **Paint used per wall:** \( \frac{3}{4} \) gallon
- **Total paint available:** 3 gallons
### **Objective:**
Find out how many walls Rebecea can paint with 3 gallons of paint.
### **Step 1: Set Up the Calculation**
To find the number of walls she can paint, divide the total amount of paint by the amount of paint used per wall:
\[
\text{Number of Walls} = \frac{\text{Total Paint}}{\text{Paint per Wall}} = \frac{3 \text{ gallons}}{\frac{3}{4} \text{ gallon per wall}}
\]
### **Step 2: Perform the Division**
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{3}{\frac{3}{4}} = 3 \times \frac{4}{3} = 4
\]
So, Rebecea can paint **4 walls** with 3 gallons of paint.
### **Model Representation:**
Imagine the 3 gallons of paint as a whole that needs to be divided into portions, each representing the paint needed for one wall (\( \frac{3}{4} \) gallon).
1. **Total Paint (3 gallons):**
```
|---------|---------|---------|
0 1 2 3 (gallons)
```
2. **Paint per Wall (\( \frac{3}{4} \) gallon):**
- Each wall requires 0.75 gallons.
3. **Dividing the Total Paint:**
- **Wall 1:** 0 to 0.75 gallons
- **Wall 2:** 0.75 to 1.5 gallons
- **Wall 3:** 1.5 to 2.25 gallons
- **Wall 4:** 2.25 to 3 gallons
```
|---Wall 1---|---Wall 2---|---Wall 3---|---Wall 4---|
0 0.75 1.5 2.25 3 (gallons)
```
Each segment represents the paint used for one wall. As shown, 3 gallons of paint are divided into four segments of \( \frac{3}{4} \) gallon each.
### **Conclusion:**
Rebecea can paint **4 walls** with her 3 gallons of paint.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To visualize how many walls Rebecea can paint with 3 gallons of paint, you can create a simple bar model. Represent each gallon as a separate bar. Since she uses \( \frac{3}{4} \) gallon of paint for one wall, divide each gallon bar into four equal parts. Shading in three parts of each bar represents the amount used for each wall. You’ll find that from 3 gallons, she can shade in enough parts to paint 4 full walls (as \( \frac{3}{4} \times 4 = 3 \)). With this model, you can clearly see that Rebecea can paint a total of 4 walls using the 3 gallons of paint available. This hands-on method makes counting and understanding ratios much easier and more visually appealing!
