If you divide the numerator and denminator of a fraction by a common factor will the resulting fraction always be in simplest form?

Answer 1

No!

For example: 50/100 the numerator and denominator have a common factor of:

1, 2, 5, 10, 25, 50

If you take the number 2, which is one of the smallest common factors, you will be left with:

25/50 which is not in simplest form.

But, if you take the largest common factor, 50, and you use this instead, you will end up with:

1/2 which is the simplest form.

So, you must divide the numerator and the denominator by the LARGEST common factor for this to be true.