Question
Three hikers equally shared One-half gallon of water. Explain how you would use an area model to find the amount of water each hiker drank.
Answers
GPT-4o mini
To use an area model to find out how much water each hiker drank when three hikers equally shared one-half gallon of water, we can visualize the problem as follows:
1. **Understand the Total Amount of Water**: We start with a total of 1/2 gallon of water.
2. **Create the Area Model**:
- Draw a rectangle to represent the total amount of water, which is 1/2 gallon. You could represent the total rectangle width to represent 0 to 1 (where 1 represents 1 gallon), and mark off 0 to 1/2 within that range to indicate the total area.
3. **Divide the Area**:
- Since we are sharing this amount of water equally among three hikers, we need to divide the area (or rectangle) into 3 equal parts. Each part will represent the share of the water for one hiker.
4. **Calculate Each Hiker's Share**:
- To find the amount of water each hiker gets, we can calculate 1/2 divided by 3. This is done by multiplying by the reciprocal of 3:
\[
\text{Amount for each hiker} = \frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}
\]
5. **Label the Model**:
- Within the rectangle, shade or label each of the 3 equal parts to show that each hiker got 1/6 gallon of water.
6. **Conclusion**:
- Each hiker drank 1/6 gallon of water.
By using the area model and dividing the rectangle into 3 equal sections, we visualize how the total amount of water is distributed among the hikers, and we can clearly see that each hiker receives 1/6 gallon of water.
1. **Understand the Total Amount of Water**: We start with a total of 1/2 gallon of water.
2. **Create the Area Model**:
- Draw a rectangle to represent the total amount of water, which is 1/2 gallon. You could represent the total rectangle width to represent 0 to 1 (where 1 represents 1 gallon), and mark off 0 to 1/2 within that range to indicate the total area.
3. **Divide the Area**:
- Since we are sharing this amount of water equally among three hikers, we need to divide the area (or rectangle) into 3 equal parts. Each part will represent the share of the water for one hiker.
4. **Calculate Each Hiker's Share**:
- To find the amount of water each hiker gets, we can calculate 1/2 divided by 3. This is done by multiplying by the reciprocal of 3:
\[
\text{Amount for each hiker} = \frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}
\]
5. **Label the Model**:
- Within the rectangle, shade or label each of the 3 equal parts to show that each hiker got 1/6 gallon of water.
6. **Conclusion**:
- Each hiker drank 1/6 gallon of water.
By using the area model and dividing the rectangle into 3 equal sections, we visualize how the total amount of water is distributed among the hikers, and we can clearly see that each hiker receives 1/6 gallon of water.