1 dozen eggs divided by 3 is 4 eggs. But 1 dozen eggs is not a whole/unity, it is 12 whole eggs. Dividing 1 egg in 3 results in shell, white, and yolk. Pie, like scrambled eggs, is not practically divisible in the way a whole egg is divisible, but if you disagree, show me .3333 (bar) of a dozen scrambled eggs or a piece of pie.
1 dozen is a quantity of 1 and a unit of measure of “dozen.” It is the same thing as saying 1 mile, you have a quantity of 1 and a unit of measure of mile.
If you split 1 mile into 2 equal parts, the distance for each part is .5 mile, not 880 yards.
Two different equations:
1/2 = .5
1760/2 = 880
We are using the unit of measure mile, and there is 1 of them not 1760 of them so you end up with 2 parts of .5, not 2 parts of 880.
Ok, fine. But I’m only eating one piece of pie that is .3…, one that is .6…, & one that is .9…, for a total of .18… (a whole pie) and THAT is FINAL! Don’t even ask for a piece, cuz…
I don’t have to because that’s not what I’m saying. That’s your own invention.
“1 meter divided by 2 equals 50 centimeters” is not equivalent to “1 divided by 2 equals 50”. We’re dividing “1 meter” by “2” to get “50 centimeters”. We are NOT dividing “1” by “2” to get “50”.
Centimeters has nothing to do with dividing 1 meter into 2 equal parts. The math is 1/2=.5 and .5 x 2 = 1. There is no “50” part of that math.
Why don’t you just say 1 meter divided by 2 equals 500 millimeters?? Why not claim 1 meter divided by 2 equals 19.6850 inches??? How about you just write the fraction 1/2=19.6850 because that is what you are claiming??
Why can’t you understand that we are not dividing 100 into 2 equal parts we are dividing 1 into 2 equal parts?
You know the difference between 1/2=.5 and 100/2=50, right?
“1 group of three pies” divided by “3” is “1 pie”. But it is also “1/3 groups of three pies”. So “1 pie” and “1/3 group of three pies” are equivalent expressions. That’s the point. The point is to show you a real world example of “1/3”. The number of groups of three pies in a single pie is 1/3 and that is a real world example of 1/3. It’s a proof that 1/3 exists. Base-10 notation and long division cannot change that fact.
Noone is claiming that 1 divided by 3 is 1. That’s your own invention.
And noone is trying to divide 3 into 3 equal parts. That, again, is your own invention.
I’m taking “1 group of three pies” and dividing it into “3” equal parts. That’s what I’m actually doing. And the result of that is both “1 pie” and “1/3 groups of three pies”. And I am doing that in order to show you a real world example of “1/3”. The universe has lots of numerical properties. One of them is the number of people alive. The value of that property at the present moment, we are told, is between 7 and 8 billions. There are many other numerical properties. For example, there is the average human height. In order to show you that 1/3 exists, all I have to do is show you a property of the universe that is numerical and that is 1/3. And that’s what I did. I told you that the number of trios ( i.e. groups of three people ) in any person of your choice is exactly 1/3; or rather, that the number of groups of pies in any pie of your own choice is exactly 1/3.
All you’re really doing is you’re complaining that I’m not using long division in order to calculate the base-10 representation of 1 divided by 3. And you’re doing so because you erroneously think that if a number cannot be represented in base-10 that it does not exist. That’s really all there is to it. You think that if we do not have a word for something that that something does not exist; that if we don’t have the word “horse” for horses that horses do not exist; that if we do not have a base-10 representation of 1/3 that 1/3 does not exist.