Question 691032: what is the difference between dividing a set of objects into three equal groups and dividing the same set of objects into groups of three?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! It's just a difference of words.
It will only mean something in the context of the problem.
The calculation is the same.
If you are evenly dividing among 3 pirates a loot of gold coins,
you are expected to divide a set of objects into three equal groups.
One way of doing it, is to start dealing the coins as you would deal cards.
You would deal a first round of three coins, a second round of 3 coins, a third one, and so on.
Each round is a group of 3 coins, so you would be really
dividing the same set of objects into groups of three.
From the point of view of the person doing the calculations,
dividing a set of objects into three equal groups,
and dividing the same set of objects into groups of three
could mean arranging those objects into a grid pattern,
with 3 rows (or 3 columns) of equal length,
and rows turn into columns as you rotate the grid a quarter of a turn.
The apparent difference is in which of the factors of a product is seen as a divisor.
We know that 3 x 8 = 24, with 3 and 8 as factors and 24 as product.
From there, we can get two division statements:
24 / 8 = 3 (with 8 as divisor and 3 as a quotient) and
24 / 3 = 8 (with 3 as divisor and 8 as a quotient).
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