cake cut into slices and need fractions

Question

Sister made cheesecake. She cut the cake into 15 equal slices, but only 8 slices were eaten. The next day you took 1/3 of the remaining cake. What fraction of the original cake was left? How much was left when you took 1/3 of the remaining cake?

Answer 1

15 slices and 8 are eaten leaving 7 slices

 

the next day you took 1/3 of 7 which is 7/3, ie 2 and 1/3 slices, that leaves you 4 2/3 slices  (or 14/3 see below)

 

The fraction of the original cake left is 4 2/3 slices divided by 15 total slices, do it this way:

 

Convert 4 2/3 to 14/3 by multiplying 4*3 and then adding 2.  Now divide 14/3 by 15/1, or multiply 14/3 by the reciprocal which is 1/15:  14/3 * 1/15 = 14/45