Math CentralQuandaries & Queries


Question from Kenneth:


Can a fraction be an even or odd number? If not , why?

I thank you for your reply.

Hi Kenneth. A "fraction" is a whole number over any other whole number except zero. So 6/2 is a fraction. I think you know that it equals 3, which is another whole number and an odd number.

So there is an example showing that a fraction can indeed be an odd number.

Remember that there are other definitions related to fractions that are more restrictive. What I have described is called a "common fraction" or, more colourfully, a "vulgar fraction".

A "proper fraction" is one in which the numerator is smaller than the denominator when you omit the positive and negative signs.

Can you think of any "proper fractions" that can be odd or even numbers?

Hope this helps,
Stephen La Rocque


Hi Kenneth,

The terms even and odd only apply to integers. An integer is even if it is divisible by 2, or more precisely

an integer n is even if there is an integer k so that n = 2k. An integer is odd if it is not even.

In Stephen's example above 6/2 is equivalent to the integer 3 and so it makes sense to ask if it is even or odd.


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