Reducing Fractions Questions

Now when I reduce fractions while multiplying I am getting confused. I know I can cross cancel AND do vertical reduction.

Now when i do the problem:

18/12 ÷ 35/70

I reduce to

3/2 ÷ 1/2

I then FLIP...cross cancel and multiply like so:

3/2 • 2/1

Cross cancel the 2's

3/1 • 1/1 = 3/1

This problem is correct. However. When I do the same thing with the following problem, I get an incorrect answer. What am I doing wrong?

240/10 ÷ 65/100

I reduced to

24/1 ÷ 13/20

I then...cross canceled 20 and 24.....flipped...and multiply like so:

6/1 • 13/5

Flip and multiply

6/1 5/13 = 30/13

that is the wrong answer. it should be 36 and 12 over 13.

What did I do wrong and why is it wrong?