6 items are filed under this topic.








Multiplication and repeated addition 
20161123 

From Anandmay: Hello
I was looking closely at early arithmetic where I found how we discovered properties of Arithmetic.
Like:2 x 3 = 3 x 2.
This can be proved by considering a 2D figure(actually,quadrilateral) having length consisting of 2 boxes of
1by1 dimensions and breadth of 3 boxes of the same dimensions.
Now,consider it again,but,this time,length of 3,and breadth of 2 of such 1 by 1 boxes.
We now notice that we can fit the 2 types of rectangles formed on each other precisely.
So the multiplicative property of commutativity is true for all natural numbers as we can generalize the result(in our mind,for self satisfaction).
Now,can you find me a nice satisfactory reason of why a fraction times a natural number equals the number times the fraction?
I mean, for example,i can understand the meaning of 3 x 2/3 to be three times 23rd,that is, 2/3+2/3+2/3.Fair enough.
But here is the problem:By definition and actual meaning of multiplication, a x b means the repeated sum of b,done 'a' times.
So what is the meaning of doing 2/3 x 3?The repeated addition of 3 how many times??2/3 times??Not making sense,right?And even
we have not proved yet the commutative property of numbers INCLUDING fractions.So how can we resolve this problem and make these things meaningful?
Thanks Answered by Penny Nom. 





2.236... 
20151013 

From Ann: 2.236...
What is the most specific category of numbers does this fall into? Rational or Irrational? Does the .... mean that it repeats? Answered by Harley Weston. 





Repeated decimals 
20150509 

From Vir: Years ago I (re?)discovered 'cyclic division'. For example: if you arrange the number along a circle and put the number 142857 at the centre
all the numbers taken cyclically, starting with 1, are fully divisible by 37. Whatever the starting point of this number, it remains fully divisible by 37.
what is more, the number can be formed by taking the digits clockwise as well as anticlockwise..This I call "full cyclic divisibility". In many cases, only clockwise cyclic divisibility is possible. But I have not come across a case where ONLY anticlockwise divisibility occurs. Thus clockwise cyclic divisibility seems to be favoured. Could this be construed as a sign of chirality in mathematics?.. Answered by Chris Fisher. 





Multiplication and order 
20110121 

From Janet: IN A MULTIPLICATION SENTENCE BASED ON A DRAWING..IS THERE ANY ORDER FOR THE MULTIPLICAND ANG MULTIPLIER FOR THE ANSWER TO RIGHT? Answered by Robert Dawson. 





Convert to multiplication 
20101023 

From angelina: how to covert 5+5+5=15 to multiplication Answered by Penny Nom. 





Kumon 
19981109 

From Kathy Steele: Perhaps I am not spelling this correctly,since there is nothing to be found on Kumin Math, but my search for info on this topic led to this site. My understanding is that it is a program of repeated drills. Do you have any additional information? I know that this will come up during Parent conferences since some of my Jr. High students are talking about it. Answered by Jack LeSage and Harley Weston. 


