Motor Daddy wrote:1 divided by 3 means each of the parts are .333... You have .333.../1.0. and that can't be reduced. Plus, there is a remaining part, the 4th part, which when added to the other 3 parts equals 1.0.

You can't have 1 of 3 equal parts when there are 4 parts.

What you are claiming is that you have 1 of 3 equal parts of 1.0, when in fact there are 4 parts. 3 parts of .333... and 1 part that is the remainder.

Yes, when we try to find the result of "1/3" by using long division in base 10, that is precisely what happens. We all know that. You don't have to repeat it.

However, we also know that when we try to find the result of "1/3" by using long division in base 3, we get \(0.1_3\). How do you explain that? What makes base 10 system so special in your eyes?

If all you're saying is that 1/3 has no representation in base 10, then that's not much of a revelation. It's really just a banality that pretty much everyone agrees with. There is really no need for you to prove that to us. What you have to do, but you're not doing, is show to us how "The result of 1 divided by 3 has no representation in base 10" logically leads to "1 divided by 3 has no result". You never did that. And judging by the looks of it, you will never do it.

One the other hand, we have shown to you that many things in real life are one third of (or three times less) than something else. An example is a banana that is one third of a group of three bananas. In that case, a banana can be seen as the result of dividing one thing (a group of three bananas) into three equally sized sub-groups. Your response to this was to deny that that is an instance of dividing one by three.

"1 divided by 3" can not divide 12 eggs into 3 equal parts.

It can because "12 eggs" is at the same time "1 group of twelve eggs". It's not merely 12 things, it's also 1 thing.

12 divided by 3 does that.

Yes but not exclusively.

"12 inches" and "1 feet" are two different expressions of one and the same length. If you can cut "12 inches" into 3 equal lengths, you can also cut "1 feet" into 3 equal lengths.

Your problem is that you don't quite understand what decimal numbers are. In fact, you don't seem to be aware that a lot of them are no more than fractions (which you do not consider to be numbers.) "0.2" means no more than "The result of dividing 2 by 10". When someone asks you "What's the result of 1 divided by 5?" you have no problem answering with "0.2" even though that's merely a shorter way of saying "It's 2 divided by 10". But when you ask "What's 1 divided by 3?" and someone says "It's 1/3" you get all upset.