Find 1/4 divided by 3/8.
The answer to your question is 3/4.
I can't give you a mathematical reason why you multiply by the reciprocal when dividing fractions -- it's just something you do, and it all works out!
So, the reciprocal of 3/8, which is the divisor, is 8/3. You multiply this inverted fraction by 1/4 to get your answer of 1/4 divided by 3/8:
1/4 * 8/3 = 8/12.
This simplifies to 3/4.