Why is 35/30 < 22/12 and how do you get it

You could divide the numerator and denominator of the fraction on the left side by 5,
and then divide the numerator and denominator of the fraction on the right side by 2,
and then you'll see why. 

If you still don't get it at that point, then multiply each side of the inequality by  6, and
it's sure to jump out at you.