Thanks loads to Chop Suey for help with latex

I know this is going to be so simple, I just can't see it yet.

I am working on canceling down fractions to make them easier to work with.

For example

$\displaystyle

\frac{6}{8} = \frac{6/2}{8/2} = \frac{3}{4}

$

I understand how to do it and thought I was fine. Then the book I'm using throws the following at me and I can't understand how they got to their answer.

$\displaystyle

\frac{3}{7} * \frac{5}{6} = \frac{1}{7} * \frac{5}{2} = \frac{1*5}{7*2} = \frac{5}{14}

$

IN the book they say canceling is possible because 3 divides into both the 3 and the 6, which is true but I thought the numerator and the denominator were divided by their highest common factor to cancel down.

This has confused me.

I think I may have it figured out, however I don't want to get carried away with the wrong idea.

I can see the they are doing 6/3 = 2 then 3/3 = 1, obviously 7/5 doesn't work as it produces a decimal so this is not canceled down. I found out their method by looking at some other examples in the book, however when they explained canceling down they said to find the highest common factor of the numerator and denominator then divide the numerator and denominator by it.

e.g

$\displaystyle

\frac{24}{60} = \frac{24/6}{30/6} = \frac{4}{5}

$

Many thanks in advance.