Multiples of Four
Date: 03/01/99 at 02:09:10 From: felicity Subject: Multiples of Four My mathematics homework sheet says that 0 is a multiple of four, but I cannot see how as four does not go into 0 but it goes into the rest: 4 8 12. I think multiples of four start with four. All the examples on my page start with 0. What do you think? Thanks.
Date: 03/01/99 at 05:26:43 From: Doctor Reno Subject: Re: Multiples of Four I have looked through definitions of multiples on the Web and in textbooks here at home, and even in a dictionary! I think I have an explanation for the confusion. According to all the definitions I found, a multiple is a quantity into which another can be divided with zero remainder. Therefore, the multiples of four *would* be 0, 4, 8, 12, etc. (4 *does* go into zero: 0 / 4 = 0). However, no reference I found listed 0 as a multiple of any number, and I think this is because it isn't useful to us. If we need to know the least common multiple of 3 and 4, we would list them like this: multiples of 3: 3, 6, 9, 12, 15... multiples of 4: 4, 8, 12, 16... and we can quickly see that 12 is the least common multiple. But if we include 0 on these lists, then 0 would *always* be the least common multiple of any pair of numbers. And that would not help us when we needed to use the least common multiple in order to find the least common denominator of two or more fractions. Zero can never be the denominator of a fraction, and that is probably another important reason why textbooks do not usually include it as a multiple of any number. So, I think that by definition, zero could be considered a multiple of 4, but since it is of no use to us we don't include it in a list of multiples. Your textbook is an exception. Have you asked your teacher about this? I would be interested in what your teacher or others have to say about it! - Doctor Reno, The Math Forum http://mathforum.org/dr.math/
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