Claire gives 1/2 of her crafts to her family. she then gives 1/3 of the remainder to her teachers and gives the rest to charity. what fraction of her crafts does she give to charity?

Let's say that Claire has 6 craft items. If she gives half (1/2) to her family, then she gives her family 3 items, with 3 left over that she keeps.

Then if she gives one-third (1/3) of that amount to her teachers, then she gives over 1 craft item with 2 left over that Clair keeps. 

The remaining 2 out of the original 6 leads to 2/6 = 1/3
Meaning that 1/3 of the craft items goes to charity

1/3

Step 1: 6x-10=1; step 2: 6x=11