7. ReasoningNolan Listed The Weights Of Oranges In A Box In The Frequency Table. Which Is Greater, The Total Weight Of The 6.25-ounce Oranges Or The Total Weight Of The 7.25-ounce Oranges? How Much More?
Reasoning with Frequency Tables
In mathematics, frequency tables are used to display the distribution of data. When dealing with a box of oranges, understanding the weight distribution is crucial. In this article, we will explore how to reason with frequency tables to determine the total weight of 6.25-ounce oranges and 7.25-ounce oranges in a box.
The Frequency Table
The frequency table provided by Nolan lists the weights of oranges in a box as follows:
| Weight (ounces) | Frequency |
|---|---|
| 6.25 | 5 |
| 7.25 | 1 |
Calculating Total Weight
To determine the total weight of each type of orange, we need to multiply the weight by the frequency and then add the results.
Total Weight of 6.25-Ounce Oranges
To calculate the total weight of 6.25-ounce oranges, we multiply the weight by the frequency:
6.25 ounces/orange × 5 oranges = 31.25 ounces
Total Weight of 7.25-Ounce Oranges
To calculate the total weight of 7.25-ounce oranges, we multiply the weight by the frequency:
7.25 ounces/orange × 1 orange = 7.25 ounces
Comparing Total Weights
Now that we have calculated the total weight of each type of orange, we can compare them to determine which is greater.
Which is Greater?
The total weight of 6.25-ounce oranges (31.25 ounces) is greater than the total weight of 7.25-ounce oranges (7.25 ounces).
How Much More?
To determine how much more the total weight of 6.25-ounce oranges is greater than the total weight of 7.25-ounce oranges, we subtract the smaller total weight from the larger total weight:
31.25 ounces - 7.25 ounces = 24 ounces
Therefore, the total weight of 6.25-ounce oranges is 24 ounces more than the total weight of 7.25-ounce oranges.
Conclusion
In conclusion, by using a frequency table and performing calculations, we can determine the total weight of each type of orange in a box. In this case, the total weight of 6.25-ounce oranges is greater than the total weight of 7.25-ounce oranges, with a difference of 24 ounces.
Understanding Weight Distribution in a Box of Oranges: Key Takeaways
- Frequency tables are used to display the distribution of data.
- To calculate the total weight of each type of orange, multiply the weight by the frequency and add the results.
- Compare the total weights to determine which is greater.
- Subtract the smaller total weight from the larger total weight to determine how much more the larger total weight is greater.
Q: What is a frequency table, and how is it used to display data?
A: A frequency table is a table used to display the distribution of data. It lists the different values or categories of data and the number of times each value or category occurs. In the context of the box of oranges, the frequency table lists the weights of the oranges and the number of oranges with each weight.
Q: How do I calculate the total weight of each type of orange in a box?
A: To calculate the total weight of each type of orange, you multiply the weight of the orange by the number of oranges with that weight. For example, if there are 5 oranges that weigh 6.25 ounces each, the total weight of those oranges would be 6.25 ounces/orange × 5 oranges = 31.25 ounces.
Q: How do I compare the total weights of different types of oranges?
A: To compare the total weights of different types of oranges, you simply compare the two total weights. In the case of the box of oranges, the total weight of the 6.25-ounce oranges (31.25 ounces) is greater than the total weight of the 7.25-ounce oranges (7.25 ounces).
Q: How do I determine how much more one total weight is greater than another?
A: To determine how much more one total weight is greater than another, you subtract the smaller total weight from the larger total weight. In the case of the box of oranges, the total weight of the 6.25-ounce oranges (31.25 ounces) is 24 ounces more than the total weight of the 7.25-ounce oranges (7.25 ounces).
Q: What if there are multiple types of oranges with different weights? How do I calculate the total weight of all the oranges?
A: If there are multiple types of oranges with different weights, you would calculate the total weight of each type of orange separately and then add the total weights together. For example, if there are 5 oranges that weigh 6.25 ounces each and 1 orange that weighs 7.25 ounces, the total weight of all the oranges would be 31.25 ounces + 7.25 ounces = 38.5 ounces.
Q: Can I use a frequency table to display data other than weights?
A: Yes, you can use a frequency table to display data other than weights. Frequency tables can be used to display any type of data, such as the number of students in a class, the number of books on a shelf, or the number of cars in a parking lot.
Q: How do I create a frequency table?
A: To create a frequency table, you need to list the different values or categories of data and the number of times each value or category occurs. You can then use this information to create a table that displays the frequency of each value or category.
Q: What are some common uses of frequency tables?
A: Frequency tables are commonly used in statistics and data analysis to display the distribution of data. They are also used in business and economics to display sales data, customer demographics, and other types of data.
Conclusion
In conclusion, frequency tables are a powerful tool for displaying data and understanding weight distribution in a box of oranges. By following the steps outlined in this article, you can create a frequency table, calculate the total weight of each type of orange, compare the total weights, and determine how much more one total weight is greater than another.