Emma has n containers. She will put 3/4 berries into each container.
Which expression represents the total amount of berries, in cups, that Emma will put into the containers?
The Correct Answer and Explanation is:
To determine the total amount of berries that Emma will put into her n containers, where she places ( \frac{3}{4} ) of a cup of berries into each container, we need to formulate an expression that represents this scenario.
Given:
- Number of containers = ( n )
- Amount of berries in each container = ( \frac{3}{4} ) cup
The total amount of berries can be calculated by multiplying the number of containers by the amount of berries placed in each one. Therefore, the expression for the total amount of berries is:
[
\text{Total berries} = n \times \frac{3}{4}
]
This can also be written as:
[
\text{Total berries} = \frac{3n}{4}
]
Explanation:
- Understanding the Components:
- Containers (n): This variable represents the number of individual containers that Emma has. It is a fundamental part of our equation because it tells us how many times we will be adding the amount of berries.
- Berries per Container: The fraction ( \frac{3}{4} ) signifies that each container will receive three-quarters of a cup of berries. This measurement indicates a partial quantity, emphasizing that Emma is not filling each container to its full capacity but is distributing a specific amount.
- Multiplication for Total Calculation:
- When calculating total amounts in scenarios involving repetition (like filling multiple containers), multiplication is the appropriate operation. Each container receives ( \frac{3}{4} ) cup, and with ( n ) containers, we multiply ( n ) by ( \frac{3}{4} ) to find the total amount.
- This multiplication reflects the idea that the same quantity of berries is being added multiple times—once for each container.
- Result Interpretation:
- The resulting expression ( \frac{3n}{4} ) gives a straightforward formula that allows Emma to calculate the total amount of berries she will need based on how many containers she is using. If she knows the value of ( n ), she can substitute it into the formula to find the total amount of berries needed.
In conclusion, the expression ( \frac{3n}{4} ) effectively captures the relationship between the number of containers and the total quantity of berries, allowing for easy calculation and understanding of the distribution of berries across the containers.