A whole what, a whole group? if you are asking if 3 bananas can be 1.0 group then yes, I agree.
Do you agree that 3 bananas divided into 3 parts means each part is 1.0 banana? Yes?
Do you agree that 1 divided by 3 will never equal 1.0? So you acknowledge that dividing 1 group into 3 equal parts can not equal 1.0, right? How could 1 group divided by 3 equal 1.0?
What you are claiming is that you can divided 1 group of money into 4 equal parts and end up with 4 parts, each being 1 dollar.
Each part is .25 of a group, not 1.0 dollar. We are not dividing 4 dollars into 4 parts, we are dividing 1 group into 4 parts. Each part is .25, not 1.0.
1/3 is indeed a number. So is 100/3. In general, every fraction is a number.
I find it strange that Motor Daddy is perfectly fine saying that “0.25” is a number but not at all fine saying that “1/3” is a number. Why? Because “0.25” is a shorthand for “2/10 + 5/100”. It’s a sum of two fractions. If fractions aren’t numbers, how can sums of fractions be numbers?
I am anticipating a response such as “0.25 is not a sum of fractions” But that would be wrong.
1 group divided into 2 equal parts means you end up with 2 equal parts of .5 group, not 2.0 groups. You don’t end up with 2 groups, you end up with 2 parts each being .5 group.
Maybe that confuses you, so look at this:
1 gallon divided into 4 equal parts means each part is .25 gallon. So you end up with 4 equal .25 parts, that total 1.0 gallon.
Now you say, But .25 of a gallon is 1 quart, because there are 4 quarts in a gallon.
But look, 1 divided by 4 = .25, not 4.0. You end up with 4 equal parts, each part being .25 of a gallon. You do not end up with 4.0 units of anything, you end up with 4 equal parts that are each .25 gallon.
So 45 people isn’t a group of people?
And two sets of 45 people isn’t two groups of people?
So I guess you assume that when you have 57 people - what you really have is only half of a group of 114 people - or is it only 1/3 of a group of 171 people?
You seem rather free with your language and assumptions mate-- anything to try to win an argument (typical liberal actually).
My response is “2”. There are 2 apples. But I can also say “There are 5-3 apples on the table” which isn’t wrong but merely useless because you already know that. As a general rule, questions such as “What’s 5-3 equal to?” are looking for a decimal equivalent of the stated number, in this case, “5-3”. “5-3” is in itself a number, it’s merely not a decimal expression of a number. Decimal expressions have the form “. . . + a2 ^ (9 + 1)^1 + a1 x (9 + 1)^0 + b1 x (9 + 1)^-1 + b2 x (9 + 1)^-2 + . . .” where “a” and “b” represent integers between 0 and 9. Number 20, for example, is a short hand for “2 x (9 + 1)”.
You defined the group to be 100 people.
You want to divide the group into 2 equal parts.
The division goes like this: 1 group divided by 2 in order to arrive at a number per part. There is no 100 part of that division, there is 1 group being divided into 2 equal parts. The answer is .5 group per part. Again, no mention of people, just how much of the group per part. 1 divided by 2 = .5 group, not 50 people.
If you want to divide the 100 people into 2 equal parts then it would be 100 divided by 2, so 50 people per part. Notice the difference between 100 divided by 2 and 1 divided by 2?
If you try to divide each remainder of 1 / 3 by 1/10 over and over (as base_10 long division does) in an effort to eventually get to an even 1/3 - as MD says - you will never get there.
Of course that doesn’t mean that a whole cannot be divided in even 1/3rds. It merely means that you cannot do it that way.
That is why the issue of other bases comes up - “try dividing the whole in a different way”. And of course - if you divide it in the right way (not base_10) it works just fine.
My argument has been that you don’t have to use long division at all - but then he decides to play words games in denial (“it isn’t a group if you cut it in half - only half a group”).
Which is irrelevant to your non-sequitur conclusion that a whole CANNOT be divided into 3 equal parts.
All you are really saying is that you cannot use long division to calculate a decimal expression of 1/3 of a whole.
Of course everyone already knew that – which is why they/we have all been automatically going to the next steps - not using base_10 long division when trying to divide 1 by 3.
No - YOU cannot.
The rest of us can do it quite easily – because we aren’t blinding ourselves from the obvious.
Not being able to divide a ratio into a decimal representation has nothing at all to do with whether a true division can be performed - THAT is your non-sequitur issue with common reasoning.
When you choose to narrow words to only mean what you want when you want (“it isn’t a group if it is divided”) –
And your response is to fixate on the first two sentences of my post and ignore all the rest (:
Again, you’re asking for a base 10 representation of 1/3. And once again, I tell you that there is no such representation. However, that does not mean that one cannot divide a whole in 3 equal parts. Feel free to prove that logical connection with an argument of some sort (strict deductive argument would be the most preferrable.)
“1/3” is not a good answer because “1/3” is not a number but a fraction. Yet, percentages are perfectly fine even though percentages themselves are fractions too. “20%” is merely a shorthand for “20/100”. According to his own logic, they aren’t numbers; yet, he treats them as such.
Again, what he’s asking everyone to do, but not explicitly stating, is to tell him what’s the decimal equivalent of 1/3. And he already got that answer from many of us here, that answer being: there is no such thing. But he keeps asking that question over and over again rather than doing what needs doing.
1/3 is 1 of 3 parts. In order to have 1 of 3 of those parts there must first be 3 equal parts.
12 eggs CAN BE divided into 3 equal parts, and the 3 parts are each 4 eggs, and 1/3 is 4 eggs, 2/3 is 8 eggs, and 3/3 is 12 eggs.
1/3 is ONE THIRD (1 of 3), just like 1/4 is One Quarter (1 of 4), and 1/10 is One Tenth (1 of 10).
Sure, 1/3 is also 1 divided by 3, but it is not limited to dividing 1.0 into 3 equal parts. 1/3 is 1 of 3 parts. It could be 1 of 3 parts of 12, or 1 of 3 parts of 30, or 1 of 3 parts of 15.
1/3 is 1 of 3 parts. To have 1/3 is to have 1 of 3 equal parts.
You can divide 12 into 3 equal parts and have 1 of those parts, which is 4.
You can divide 30 into 3 equal parts and have 1 of those parts, which is 10.
You can divide .9 into 3 equal parts and have 1 of those parts, which is .3
You can also have 2 of 3 of those parts, or 2/3 of 12 is 8, 2/3 of 30 is 20, and 2/3 of .9 is .6
1/3 of 3 pizzas is 1 pizza
1/3 of 12 pizzas is 4 pizzas.
But you CANT divide 1 pizza into 3 equal parts in order to have 1 of those 3 equal parts. You can’t take a 1/3 slice of a pizza because you can’t cut the damn thing into 3 equal parts to begin with!
“ But you CANT divide 1 pizza into 3 equal parts in order to have 1 of those 3 equal parts. You can’t take a 1/3 slice of a pizza because you can’t cut the damn thing into 3 equal parts to begin with!”
Ecmandu replies:
Yet we do it everyday. Impossible?
You also contradicted yourself… saying 12 pizzas this and 15 pizzas that.
This is the problem you’re having …
Bases. You don’t understand them.
What about base 12 or base 15?
Anytime we use a placeholder, (zero in base 10), when we do that, we’re in another base.
This is hard for people to understand.
The number 12 in base 10 is actually now, base 12. Yes. The symbols don’t change, but the placeholder caused a base change.