One Way of Conceptualising Division:

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Figure 1:  The Division Operator.

Introduction:

What follows is a discussion of Partitive Division.

Body:

 

We want an implicit understanding of the operation of Division.

Let us take the equation:

8  ÷  4 = 2

and let us examine what is happening, conceptually, when this operation is being worked out.  Let us imagine our dividend:

8

as a Universal Set containing 8 elements:

Figure 2: A Universal Set containing the Dividend number of elements.  A Universal Set containing 8 elements.  The set {a,b,c,d,e,f,g,h} .

Let us say that we wished to divide these elements, evenly, amongst a divisor number of sets.  The divisor is:

4

in this instance.  So we wish to distribute 8 elements, evenly, amongst 4 sets:

Figure 3:  We have distributed a dividend number of elements, evenly, amongst a divisor number of sets.  The number of elements in each set is the quotient.  We have distributed 8 elements, evenly, amongst 4 sets.  2, the number of elements in each set, is the quotient.

If we distribute 8 elements, evenly, amongst 4 sets, then we obtain 2 elements in each set.  2 is the result of Division.  If we were doing “sums” in primary school, then 2 would be “the answer.”

We have taken 1 big set containing 8 elements:

{a,b,c,d,e,f,g,h}

and we have dispersed these elements evenly amongst 4 sets:

{a,b} {c,d} {e,f} {g,h}

The number of elements in each of these 4 sets, i.e.:

2

is the quotient.