Yes the awnser is in one sentence

Question

Joe's mother had 1/3 of an apple pie left. Joe cut the remaining pie into 4 equal pieces and ate one piece. What fraction of the whole pie did that one piece equal?

Answer 1

The one piece he ate was ¼ of ⅓ of the pie=1/12.

If Joe had taken a quarter of the pie that was taken away, Joe would have eaten ¼ of ⅔ of the pie, that is, ⅙ of the pie.

To avoid the fractions think of the original pie divided like a clock into 12 pieces. So the pie that was left could look like a 20-minute slice, or 4 pieces. These would be the pieces Joe had to choose from. He ate one, so he ate one twelfth of the whole pie. (You can also see that just 3 pieces of pie remained. Together they would look like a 15-minute slice, or quarter of the pie.)

If 4 pieces of his mother’s pie were left and Joe had eaten a quarter of the other 8 pieces, he would have eaten 2 pieces (10-minute slice) which make a sixth of the original pie.