Math CentralQuandaries & Queries


Question from Kevin, a parent:

Make a fraction that cannot be simplified and has 24 as its denominator?

We have two responses for you

Hi Kevin.

In order to simplify a fraction, there needs to be a number that goes into both the numerator and the denominator. So if it cannot be simplified, there is no such number.

The factors of 24 are 2, 3, 4, 6, 8, 12, and 24. So as long as you choose a number that cannot be evenly divided by any of these, you have solved your problem.

In fact, there is a shortcut. Because 24 = 3 x 2 x 2 x 2, all the numbers that go into 24 evenly (that is, all its factors) must also themselves be divisible evenly by 2 or 3 (or both).

So really you just have to pick any number that you cannot divide evenly by 2 (so it is odd) or by 3.

Stephen La Rocque.



Two whole numbers are called co-prime if there is no prime number that divides them both. Hence the numerator and denominator must be co-prime.


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