a fat quarter measures about 18" x 22"; a linear quarter yard measures 9" x 42" (1/4th of 36"=9" x width of fabric)
1/8th fabric is 4 1/2" x 42"
the first quilt class i signed up for was a turning twenty...years ago. i bought the pattern at the lqs when i signed up buy finances were an issue and i went to walmart and picked out my fabrics...was quite happy with my selections when i walked into the class with 20 1/4 yard cuts...which the instructor promptly threw aside and let me know if i wanted to participate in this class i was going to have to buy fatquarters. she was teaching special cutting instructions that could not be done with my quarter yard cuts. at the time i had no idea there was a difference. i had been sewing for 30+ years then and had bought lots of 1/4 yard cuts of fabric...so, long-short...that quilt wound up being a bit (spendy) and i learned my lesson. when buying fabric for appliques unless they are big i usually buy linear 1/4's it seems to me like i get alot more out of a (regular) 1/4 than out of a fq. i dont know if it is true, but it seems like it