Divisibility and Divisibility Rules

Research the topic of divisibility.

Divisibility is the process by which an integer is divided by a fixed divisor without carrying out division but by analyzing the digits (Kremer & Kjell, 2004)

Research the divisibility rules for 9 and 11.

A number is divisible by 9 if the sum of all individual digits is divisible by 9 (Posamentier et al., 2018). For example, take the number 4,356. It is divisible by 9 since the sum of all its digits is divisible by 9. This is because 4+3+5+6 = 18. 18 divided by 9 = 2; hence 4,356 is divisible by 9.

Using the divisibility rules found, determine how the given number is divisible by 9 and is not divisible by 11.

Our given number, 7176825942116027211, is divisible by 9 since the sum of its digits is 72, which is divisible by 9. Therefore, 7+1+7+6+8+2+5+9+4+2+1+1+6+0+2+7+2+1+1= 72. 72 divided by 9 = 8. Hence 7176825942116027211 is divisible by 9.

A number is divisible by 11 if the alternating sum of its digits from left to right is divisible by 11 (Posamentier et al., 2018). This means that the number is not divisible by 11 if the alternating sum is not divisible by 11. For example, 4563 is not divisible by 11 since 4-5+6-3 = 2. 2 is not divisible by 11, and so is the number 4563.

Our number 7176825942116027211 is not divisible by 11 because 7-1+7-6+8-2+5-9+4-2+1-1+6-0+2-7+2-1+1 = 14. 14 is not divisible by 11; hence 7176825942116027211 is not divisible by 11.

References

Kremer, Ilan, and Kjell G. Nyborg (2004). “Divisible-good auctions: The role of allocation rules.” RAND Journal of Economics . pp. 147-159.

Posamentier, Alfred S., and Christian Spreitzer (2018). The Mathematics of Everyday Life. Prometheus Books.

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MATH 1100 (Hybrid): Math/Analytical Project

Problem: Divisibility and Divisibility Rules

There are many rules to determine if a number is divisible by other smaller numbers. In basic arithmetic courses, you learned divisibility and discussed a few common divisibility rules. Your task is to determine if the given number is divisible by 9 but is not divisible by 11.

Divisibility and Divisibility Rules

Given number: 7176825942116027211

*Note: You want to use divisibility rules. Do not attempt to use long division and do not just use your calculator.

Instructions:

1. Research the topic of
2. Research the divisibility rules for 9 and
3. Using the divisibility rules found, determine how the given number is divisible by 9 and is not divisible by 11.

**Note: I am telling you that the number IS divisible by 9 and IS NOT divisible by 11. Do not try to show the opposite  of this statement.

4. Include the following information in a report, in this order:
   1. Explain (in a few sentences) the topic of divisibility, including any correct terms that
   2. Explain in your own words the divisibility rule of
   3. Give an example using another number to help the
   4. Show how the given number is divisible by 9. Work out all your
   5. Explain in your own words the divisibility rule of
   6. Give an example using another number to help the
   7. Show how the given number is not divisible by 11. Work out all your
5. You must locate a minimum of 2 sources to help you complete this project. More than two sources, though not required, can be used if it helps to give detail to the
   1. You must use at least one book or E-book (other than your textbook). Do not use the dictionary for your
   2. You must use at least one website. Do not use Wikipedia.
   3. Your sources should explain the topics of the problem (divisibility and divisibility rules) and have examples that help you with the
   4. Your sources should be relevant to the project and not just be a math source because it has math in the
6. Correctly cite, in MLA format, the sources that you located to complete the assignment. If you need help for citations in MLA format, you can try using the website EasyBib
7. Be sure to do the entire project typed neatly

Papers will be compared for similarity.

Plagiarism is against the academic honesty policy and will receive a zero.

*Note: A detailed Grading Rubric is provided on Canvas and on the assignment submission link

The due date for the project is listed on Canvas.

The Math/Analytical Project must be submitted through Canvas. Directions for submitting can be found in the Course Syllabus and on Canvas.

This document has been reviewed for accessibility.