Exploration of the Number 9 and the Impact It Has on the Combination of Numbers on the 4 Basic Operations of Mathematics
Journal Title: Journal of Education and Literature - Year 2015, Vol 4, Issue 3
Abstract
This paper shows that the number 9 is unique and it has characteristics which are peculiar when compared to other numbers. When a number which is not a multiple of 9 is divided by 9, the result is always a repeating decimal with a unique pattern. The study of 9 has shown that if any number is divided by 3 or 6, provided that number is not a multiple of either 3 or 6, the result will be a repeating decimal because 3 and 6 have a special relationship with 9. The paper has tried to show the impact 9 has on other numbers in terms of addition, subtraction, multiplication and division and a number of formulas have been derived such as a + b = ab – (a x 10k – a) where ab ≠ a x b and k is the number of digits of b, to show that 9 is a special number. The study also shows that a ÷ 9, where a is not a multiple of 9 and a < 9, then a ÷ 9 = 0.aaaaaa..(a will be recurring), ab ÷ 99, where ab is not a multiple of 99 and ab < 99, then ab ÷ 99 = 0.abababab…..(ab will be recurring).The methods used in solving some problems were interesting to the learner and the teacher of mathematics not forgetting the mathematician. Studying the behavior of 9 is very enriching to the learner for it helps the learner to develop mathematical inquiry skills and at same time be able to develop mathematical reasoning, critical thinking and appreciate the importance of logic. The process of combining numbers to find the product, sum or difference has been shown and explained; such as 3 + 34 = 334 – 297 = 37. In this case the first step was to bring together or combine 3 and 34 in the order they are appearing to get 334 and then subtract 297 which is a multiple of 9.
Authors and Affiliations
Kwenge Erasmus
Keywords
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