Multiply/divide fraction/fraction

[brucec30]

I have been in automotive repair for 30 years, have taught electronics and automotive for years on the college level and have degrees in Digital electronics and also Computer service technology. I have problems understanding fractional multiplication or division. In whole numbers to multiply is to add repeatedly, to divide is to subtract repeatedly. When dealing with fraction to fraction these methods do not work (also served well as a reverse check of your work). I know 1/4 x 1/2=1/8, can someone explain to me why this is so and how you can prove it? Thanks!