Numbers Between Rational Numbers Discussion

Question

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.

Answer 1

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.

Answer 2

tell me how many cakes to order when a party could have as few as 50 people and as many as 100 people.

Answer 3

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.

Answer 4

how many cakes

Answer 5

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.