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 and using multiple …show more content…

Example:
1107= 9 x 123
7011= 9 x 779
1701= 9 x 189
0117= 9 x 13
7101= 9 x 789

IV. Justifying Conjectures
Conjecture #1 A number is a multiple of 9 if the sum of the digit is divisible by nine.
17=1+7=18
18÷9=2 As shown, 17 has the digits 1 and 7. 1 is added to 7 and we get the sum of 18. 18 is divided by 9 and we get the answer 2. 2 is a whole number so 18 is a multiple of 9. Then then count by 9.. 9 18 The sum of the given example “17” 27 So as shown in the figure above 17 is a multiple of 9.
Conjecture #2 The tens digit increases by 1 while the ones digit decrease by 1.
108,117,126,135,144,153,162,171,180,189,198,207,216,225
-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. For three digit multiple of 9, ones unit digit are all the same number.
Conjecture#3 The reverseof the given digit but still have a multiple of 9.
The other possibilities is when you rearrange the digit, it is still the multiple of 9.
Example:
1107= 9 x 123
7011= 9 x 779
1701= 9 x 189
0117= 9 x 13
7101= 9 x 789

V. Summary of Conjectures
Conjecture #1 A number is a multiple of 9 if the sum of the digit is divisible by nine.
Conjecture #2 The tens digit increases by 1 while the ones digit decrease by 1.
Conjecture#3 The reverseof the given digit but still have a multiple of 9. VI.