If a faucet dripped 1/4 cups in 1 2/4 hours.How many cups did it drip in 1 hour?

1 2/4  =  1 1/2  =  3/2

You can set up a proportion:  (1/4) / (3/2)  =  x / 1

Cross multiply:  1 · (1/4)  =  (3/2) · x

--->                          1/4  =  (3/2)x

Multiply both sides by 2/3:  (2/3)·(1/4)  =  (2/3)·(3/2)x

--->                                              2/12  =  x

--->                                               1/6  =  x

--->   Answer:  1/6^th of a cup