Division of 28 by 13

Date: 9/12/96 at 12:22:12
From: Alicia Z Menchaca
Subject: Division of 28 by 13

Can you divide seven into twenty-eight thirteen times?

Date: 9/12/96 at 17:42:56
From: Doctor Jodi
Subject: Re: Division of 28 by 13

Hi Alicia!  One of my favorite ways to look at division is by grouping
numbers.  For example, if I wanted to put 8 items into rows and 
columns, I could do this several ways.

I could make 2 rows and 4 columns:

**
**
**
**

(2 X 4)

or 4 rows and 2 columns:

****
****

(4 X 2)

Division is like grouping: You could also say that 8 divided by 4 
(rows) is 2 (columns).  Does that make sense?  

Is there any way to put 8 stars into 3 rows?  Sort of...

I can draw a picture like this:

***
***
**

I'm missing 1 star here.

Or I could do this instead

***
***

              and leave ** lonely stars somewhere else.

We have problems grouping 8 into 3 rows because 8 doesn't divide by 
3(rows) evenly.  We're left with either too few or two many stars.

You can do the same thing with the numbers you sent us.  If we put
twenty-eight stars into 7 rows here's what we get:

* * * * * * *
* * * * * * *
* * * * * * *
* * * * * * *

Do you see that there are 28 stars in those 7 rows and 4 columns?

What if we try using 13 rows?

Well, then the grouping doesn't work quite as well:

* * * * * * * * * * * * *
* * * * * * * * * * * * *
There are twenty-six.

We still have 2 stars:  ** and no good place to put them.

7 divides 28 evenly:  you get 4.  But 13 doesn't divide 28 evenly:  
you get 2 columns with 2 stars left over.

I hope this helps.  Let us know if you have any questions!

-Doctor Jodi,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/