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NINETUPLES
CABUGCABUG NATIONAL HIGH SCHOOL
President Roxas, Capiz
S.Y. 2012-2013
Researcher: Mizraim Tirol Ruan Cyrrene Vallejera Ma. Krizza Vergara
Mrs. Roselyn Palorma Adviser
NINETUPLES I. Introduction :
A mathematical investigation is defined as a collection of worthwhile problem-solving tasks that has multi-dimensional content, is an open-minded, permitting several acceptable solutions and is often embedded in a focus question. In addition, a mathematical investigation involves a number of processes, which includes ---- researching outside sources to gather information, collecting data through such means as surveying, observing or measuring, collaborating with each team member taking specific jobs*…show more content…*

III. Conjectures Conjecture #1 A number is a multiple of 9 if the sum of the digit is divisible by nine. Testing/verifying conjecture #1 This Conjecture #1 is applicable to the big numbers that are higher than 9. For example: 26,847= 2+6+8+4+7=27 27÷9=3 As given iin the example given, 26,847. We added 2,6,8,4and 7 to get the sum, 27 which is a perfect number. Perfect numbers are numbers that are equal to the sum of their proper factors. And we divided 27 by 9 so we get 3. Since the quotient is a whole number it is a multiple of 9. We know that 27 is a multiple of 9 because when we count.. 9 18 27 The sum of the given example “26,847” 36 So as shown in the figure above 27is a multiple of 9. Now single digits are not applicaple to this conjecture for example 1,2,3,4,5,6,7 and 8. Since they are single digit there is no other numbers or digits that can be added to them. Conjecture #2 The tens digit increases by 1 while the ones digit decrease by 1. Testing/verifying conjecture #2 9,18,27,36,45,54,63,72,81,90,99 -For the tens digit it started from 0,1,2,3,4,5,6,7,8,9 and it is increasing by 1. While in the ones place it is decreasing by 1 like 9,8,7,6,5,4,3,2,1. Conjecture#3 The reverseof the given digit but still have a multiple of 9. Testing/Verifying Conjecture#3 Example: -317 x 9 = 2853 is a multiple of 9 which is equal to 317. When you reverse 2853 to 3582

III. Conjectures Conjecture #1 A number is a multiple of 9 if the sum of the digit is divisible by nine. Testing/verifying conjecture #1 This Conjecture #1 is applicable to the big numbers that are higher than 9. For example: 26,847= 2+6+8+4+7=27 27÷9=3 As given iin the example given, 26,847. We added 2,6,8,4and 7 to get the sum, 27 which is a perfect number. Perfect numbers are numbers that are equal to the sum of their proper factors. And we divided 27 by 9 so we get 3. Since the quotient is a whole number it is a multiple of 9. We know that 27 is a multiple of 9 because when we count.. 9 18 27 The sum of the given example “26,847” 36 So as shown in the figure above 27is a multiple of 9. Now single digits are not applicaple to this conjecture for example 1,2,3,4,5,6,7 and 8. Since they are single digit there is no other numbers or digits that can be added to them. Conjecture #2 The tens digit increases by 1 while the ones digit decrease by 1. Testing/verifying conjecture #2 9,18,27,36,45,54,63,72,81,90,99 -For the tens digit it started from 0,1,2,3,4,5,6,7,8,9 and it is increasing by 1. While in the ones place it is decreasing by 1 like 9,8,7,6,5,4,3,2,1. Conjecture#3 The reverseof the given digit but still have a multiple of 9. Testing/Verifying Conjecture#3 Example: -317 x 9 = 2853 is a multiple of 9 which is equal to 317. When you reverse 2853 to 3582

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