# Math Evistigetion Project

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

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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.