Yesterday I went to the lunch counter and bought one-quarter of a pizza for lunch. I went to the lunch room and cut it into three parts to share with two of my friends. What I ended up eating was one-third of one-quarter of a pizza. What fraction of the whole pizza did I eat?
Imagine that four people did exactly what I did. Each of us took one-quarter of the pizza and cut it in three. Thus the entire pizza was cut into 4 3 = 12 pieces, and I ate one piece. Thus I ate one-twelfth of the pizza. Hence one-third of one-quarter is one-twelfth.