Integral MultiplesDate: 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/ |
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