Essential Mathematics
posted by Logan .
How to find the value of 22/15 x 65/33 x 18/13?

You could multiply the (rounded) decimal equivalents, 1.4667 x 1.9697 x 1.3846, or compute the ratio of the products of numerators and denominators, which is
25740/6435.
In this case, you can also do some rearranging and cancelling, by changing 18/15 to 6/5, 65/13 to 5, and 22/33 to 2/3, giving you
2/3 x 6/5 x 5 = 2/3 x 6 = 4
usually, one isn't that lucky with the cancelling method 
Factor everything thus:
2*11*5*13*2*3*3
 = 2*2 = 4
3*5*3*11*13
QED.