Integral Multiples

Date: 9/7/96 at 22:56:29
From: Anonymous
Subject: Fraction of Numbers That....

  What fraction of the integral multiples of 3, between 1 and 100, are 
also integral multiples of 4?

Date: 9/8/96 at 0:20:48
From: Doctor Mike
Subject: Re: Fraction of Numbers That....

Dear  Melissa,
  
This is a really interesting way of asking the question.  For me
to answer it I will have start with a slightly different question.

I first want to know HOW MANY integral multiples of 3 there are
between 1 and 100.  I will just count them.  There are 3*1, 3*2, 3*3,
and so on up to 3*31, 3*32, 3*33 (which is 99, so it is the last one), 
so there are 33 of them in all.  

Now, HOW MANY of them are integral multiples of 4? Since 3 is a prime 
number, I am looking for those multiples of 3 where the multiplying 
factor is a multiple of 4, or 3*4, 3*8, 3*12, 3*16, 3*20, 3*24, 3*28, 
3*32, so there are 8.
 
Now we have enough information to answer your original question. 
There are 33 of these multiples of 3, and 8 of them are multiples
of 4, so the fraction answer is 8/33 , which is about 24 percent.
  
I hope this helps.  

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