## Fair Sharing?

Katie: Mom, can I have a whole doughnut with my milk?

Me: I think there is only one left in the bag.  How about a piece for daddy and me?

Katie: I can give you a quarter (aka, one fourth and not the coin :-)).

Me: A quarter for both or a quarter each?

Katie: A quarter each.

Me: And then how much will be left for you?

Katie is having some trouble figuring this out so I decide to help out.

Me: How many pieces do you need to split something into to make a quarter?

Katie: Four.

Me: So if you give one quarter to me and one to your dad, then how many quarters will be left for you?

Katie: Two.

Me: And two quarters is the same as…

I show her four fingers and split them into two and two.

Katie: One half!

At this point we actually look into the doughnut bag and it turns out that there are one and a half donuts in there.

Katie: That means I can have a whole doughnut.

Me: No, I think that means that you still get a half and daddy and I will split the whole one.

Katie: I guess that’s fair since everyone will then get a half, but before I was going to get more than you…

We ended up giving her about three-quarters of a doughnut and she was very happy.