Numbers Between Rational Numbers Discussion
Math 8 Q1 (Pre-Algebra) / The Number System
Numbers Between Rational Numbers Discussion
In your journal, you identified careers that involve irrational numbers. You brainstormed or researched jobs that use pi or Euler’s number to do their work.
Imagine that your friend loves to plan parties, and he wants to be an event planner someday. He does not think he needs to know how to find a number between two rational numbers. He also says he will never use pi again in his life after math class. You think of some of the tasks he might need to do as an event planner:
Decide how many cakes to order when a party could have as few as 50 people and as many as 100 people.
Choose a round table that is the correct size to fit six people.
Make a prediction about how much to budget for the decorations at a party when the customer is still deciding between $10 floral arrangements and $30 floral arrangements.
In your post, explain to your friend how he will use the skill of finding a number between two rational numbers in his dream career:
Choose one of the examples from the list above, and represent the example with a mathematical statement.
Summarize to your friend why he will need both rational and irrational numbers as an event planner.
First off, I would explain to my friend that finding a number between two rational numbers is actually a very useful skill for event planning. Let's take the example of deciding how many cakes to order for a party. Say we have a minimum of 50 people and a maximum of 100 people attending the party. In order to make sure we have enough cakes to serve all the guests, we need to find a number between 50 and 100 that represents a reasonable estimate of the number of people who will actually attend. This will help us determine how many cakes to order.
For example, let's say we estimate that around 75 people will attend. This number is between 50 and 100, and it helps us make a more accurate decision on how many cakes to order.
Next, I would explain to my friend that as an event planner, he will come across situations where he needs to work with both rational and irrational numbers. Rational numbers, such as whole numbers and fractions, will be used in practical situations like counting guests, measuring quantities, and calculating costs. On the other hand, irrational numbers like pi or Euler's number may come up in tasks such as calculating the circumference of a circular table or estimating the amount of decorations needed.
In summary, as an event planner, my friend will need to find a number between two rational numbers to make accurate estimations and decisions, such as how many cakes to order. Additionally, understanding both rational and irrational numbers will allow him to successfully plan events by applying mathematical concepts to practical situations.
tell me how many cakes to order when a party could have as few as 50 people and as many as 100 people.
To determine how many cakes to order for a party with a minimum of 50 people and a maximum of 100 people, we can find a reasonable number between the given range as an estimate of the expected attendance.
One possible approach could be to take the average of the minimum and maximum values. Adding the two numbers together and dividing by 2 will give us the average:
(50 + 100) / 2 = 150 / 2 = 75
So, a reasonable estimate for the number of people attending the party could be around 75. Thus, it would be prudent to order enough cakes to accommodate this estimated number.
how many cakes
Based on the estimated attendance of 75 people, the number of cakes to order will depend on the serving size and the desired portion per person.
Let's assume that each cake can serve 12 people. To determine the number of cakes needed, we can divide the estimated number of people attending the party by the serving size:
75 people / 12 people per cake = 6.25 cakes
Since we cannot order a fractional number of cakes, it would be best to round up to ensure there are enough cakes for everyone. Therefore, we would need to order at least 7 cakes for the party.
As an event planner, your friend may not initially see the direct connection between finding a number between two rational numbers and his dream career. However, it is important to understand that mathematical skills play a crucial role in event planning.
Let's take the example of deciding how many cakes to order for a party that could have as few as 50 people and as many as 100 people. To ensure that there is enough cake for everyone, your friend needs to find a suitable number between these two rational numbers (50 and 100). By finding a middle number, such as 75, he can approximate the number of cakes needed to cater to a crowd of varying sizes.
Mathematical Statement: Find a number between 50 and 100 that represents the estimated number of guests at the party.
In addition to finding numbers between rational numbers, it is also essential for your friend to have a basic understanding of irrational numbers, such as pi. For instance, when choosing a round table that can fit six people, he needs to consider the diameter of the table. Since the value of pi (approximately 3.14) is needed to calculate the circumference of the table, he cannot dismiss it completely. By using pi in a formula, he can determine the appropriate table size to accommodate the desired number of guests.
Furthermore, a successful event planner needs to make predictions about various aspects of a party, including budgeting for decorations. Let's assume the customer is deciding between $10 floral arrangements and $30 floral arrangements. Your friend can use his knowledge of finding numbers between rational numbers to estimate the budget for decorations. By considering different options and their corresponding budgets, he can find a rational number between $10 and $30, which represents a reasonable assumption to make for the customer's final decision.
In summary, both rational and irrational numbers are important for an event planner. Finding numbers between rational numbers helps in tasks like estimating the number of cakes or budgeting for decorations, while understanding irrational numbers like pi supports calculations involving measurements and dimensions. By recognizing the significance of these mathematical skills, your friend can enhance his abilities as an event planner and ensure the success of his future parties.
As an event planner, your friend may not see the immediate connection between their dream career and finding a number between two rational numbers. However, this skill is actually quite useful in various aspects of their job. Let's explore one of the examples from the list provided:
Example: Deciding how many cakes to order when a party could have as few as 50 people and as many as 100 people.
To solve this problem, your friend needs to find a number between the given range to determine the appropriate quantity of cakes. In this case, they would need to find a rational number between 50 and 100 that represents a reasonable estimate for the number of people expected at the party. This estimation will help ensure that they order an adequate amount of cakes without wasting resources or leaving guests unsatisfied.
Mathematical statement: Find a number x such that 50 < x < 100. This statement represents the task of finding a rational number between the given range.
Now, let's summarize why your friend will need both rational and irrational numbers as an event planner:
1. Rational numbers: Rational numbers, such as whole numbers, fractions, and decimals, are used to represent precise quantities and measurements. As an event planner, your friend will need to work with rational numbers to determine the appropriate quantity of resources, such as food, materials, and seating arrangements.
2. Irrational numbers: Although your friend may think they will never use pi again after math class, irrational numbers like pi and Euler's number (e) have practical applications in event planning. For example, if your friend needs to calculate the circumference of a round table to seat six people, they would need to use pi (approximately 3.14) to find the correct size table. Similarly, when making predictions about budgets for decorations, irrational numbers may be involved in calculations to estimate costs, proportions, or ratios.
By understanding and utilizing both rational and irrational numbers, your friend will be able to make informed decisions, accurate estimations, and efficient plans while organizing events. These mathematical skills will help them ensure the success and smooth execution of parties, making them a competent and reliable event planner.