Problem: Divisibility and Divisibility Rules There are many rules to determine i

Question

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. Using divisibility rules show that the following number is divisible by 9 but is not divisible by 11. The number is:

Given number: 7,176,825,942,116,027,211
*Note: You want to use divisibility rules. Do not attempt to use long division and do not just use your

calculator.

Instructions:

Research the topic of divisibility.

Research the divisibility rules for 9 and 11.

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. Once you determine the results, include the following information in a report, in this order:
a. Explain (in a few sentences) the topic of divisibility, including any correct terms that apply. b. Explain in words the divisibility rule of 9. Give an example using another number to help

the explanation.
c. Show how the given number is divisible by 9. Work out all your steps.
d. Explain in words the divisibility rule of 11. Give an example using another number to help

the explanation.
e. Show how the given number is not divisible by 11. Work out all your steps.

** You only have to discuss divisibility rules of 9 and 11.

You must locate a minimum of 2 sources to help you complete this project. You must include at

least one book or E-book (other than your textbook) and one website. Your sources should explain the topics of the problem (divisibility and divisibility rules) and have examples that help you with the problem.

On a separate sheet of paper, correctly cite, in MLA format, the sources that you located to complete the assignment. If you need help for citations in MLA format, go to http://www.easybib.com/.

Be sure to do the entire project typed neatly.

Explanation / Answer

divisibility rule of 9 add all digits of the given number if it is equal to 9 then the number is divisible by 9.

divisibility rule of 11 add all the even and position digits of the number whose difference should be zero then the number is divisible by 11 .

Given number: 7,176,825,942,116,027,211

add all the digits 7+1+7+6+...........+1 = 72 =9 so the number is divisible by9.

in the given number we have 19 digits so we have 10 odd and 9 even digits starting from units digit as odd

add all the odd digit place numbers from units digit onwrds...1+2+2+....+7 =43

add all digits of even digits place numbers 1+7+0+....+1 =29

the difference between them is not a multiple of11 or zero so the number is not divisible by 11.

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