How to work out 100 divided by 150 without a calculator?

100 / 150
I always simplify fractions by dividing the top and bottom of the fraction by the same numbers.  Choose simple numbers you can do in your head, like 2.
I know 100/2 = 50 and 150/2 = 75
so now I have the fraction 50/75
then simplify it even more.  Try dividing both top and bottom by 5s.  
50/5=10 and 75/5=15
so now I have the fraction 10/15
now keep dividing by 5s.
10/5=2 and 15/5=3
so 100/150 simplifies to 2/3, or in decimal form 0.6666666666 repeating