# Math Evistigetion Project

1020 words 5 pages
NINETUPLES
CABUGCABUG NATIONAL HIGH SCHOOL
President Roxas, Capiz
S.Y. 2012-2013

Researcher: Mizraim Tirol Ruan Cyrrene Vallejera Ma. Krizza Vergara

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

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.