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Integral Multiples

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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

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.

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/
```
Associated Topics:
Middle School Fractions

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