Math Is Fun Forum

atran

Member

Registered: 2013-07-12

Posts: 91

Division Pages

Hi,

I've read two pages on division, but none includes measurement division. It'll be nice if the author explains and mentions the two types of division.

Thanks...

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Division Pages

hi atran

Why?  Division is division; the rest is just 'examples in context'.  I have taught maths for many years and have never even met the term 'measurement' division (I had to google it just to work out what you meant); nor the other one, the name of  which I've managed to forget already (part....something ?).

I encourage my students/pupils to think about the problem and what maths they can bring to bear on it.  If they conclude that division is needed then they either use a calculator or do the working on paper; but why burden them with an extra word that is just for (unnecessary?) classification purposes.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

atran

Member

Registered: 2013-07-12

Posts: 91

Re: Division Pages

Hi Bob;

Conceptually, division describes two distinct but related settings. Partitioning involves taking a set of size a and forming b groups that are equal in size. The size of each group formed, c, is the quotient of a and b. Quotative division involves taking a set of size a and forming groups of size c. The number of groups of this size that can be formed, b, is the quotient of a and c.

If the number in each group is known, and you are trying to find the number of groups, then the problem is referred to as a quotative division problem. Quotative division may also be called measurement, or repeated subtraction. You are, in effect, counting or measuring the number of times you can subtract the divisor from the dividend.

If the number of groups is known, and you are trying to find the number in each group, then the problem is referred to as a partitive division problem. Partitive division may also be called equal groups, or sharing and distribution. You are, in effect, partitioning the dividend into the number of groups indicated by the divisor and then counting the number of items in each of the groups.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Division Pages

This is my introductory page on Division: http://www.mathsisfun.com/numbers/division.html

Happy to hear suggestions.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Division Pages

hi atran,

Thanks for the definitions.  I still think it is an arbitrary and unnecessary way of trying to separate division into types of division.  I cannot see that it helps with learning about division and it is certainly incomplete.

What about;

I suppose if, say, D = 20 miles and T = 5 hours, you could think of dividing 20 into 5 equal groups with 4 mph in each, but then

would have to involve making groups of 4mph until 20 is reached.  It just doesn't seem to work for most of the maths I know.

And which classification is involved here:

In number theory, division is defined as the reverse of multiplication.  As multiplication is commutative ( ab = ba ) I think all division of type 1 can be re-written as division of type 2.  Hence, all problems can be done either way.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

SteveB

Member

Registered: 2013-03-07

Posts: 595

Re: Division Pages

I managed to get some good academic qualifications in maths without them, but I did in fact see a website after reading the above
post where yes apparently there are two types of division in discrete mathematical situations where you have whole numbers of an
item and you are describing the difference I think between two ways of thinking about a division, but where numerically speaking
it does not really matter as far as I could tell. If you divide 24 by 6 you get 4. Both of these numbers could be the number of items
in the group or the number of groups themselves. Understanding the real thing that is being thought about is important in division
perhaps in primary school teaching, but I would not wany to teach the primary school child confusing terms. I wonder whether in
Sets and Groups in university teaching it becomes relevant to a integer based or discrete maths topic.
There are some concepts in those sorts of "foundations" maths modules that do have this sort of feature.
For instance "parity" being even or odd being a useful term in some proofs in a proof where you need to refer to both together and
wish to keep the proof concise. So yes terms like that can sometimes be introduced like that to help the clarity of a maths topic.