# Fractions, Compassion, and Sharing

My son approached me and asked, “I can’t remember which is bigger: one-half or one-twelfth?”

This, of course, led to an impromptu math lesson.  We talked about fractions.  I explained that the denominator – the bottom number – of a fraction tells you how many equal parts something is divided into.  I explained that the numerator – the top number – of a fraction tells you how many of those equal parts you’re discussing.

I launched into the classic example of a cake, channeled directly from one of my elementary school teachers many years ago.  “Let’s say we had a choice between two ways to cut a cake,” I expounded.  “We could divide the cake into two equal pieces.  Or we could divide that same cake into twelve equal pieces.  If you wanted a big piece of cake, how would you want me to cut it?”

My son stood there and thought in silence.

This seemed like an easy problem.  I began to wonder where I lost him in my explanation.

After a few more moments of silence, I asked, “Do you understand the question?”

My son looked at me with his eyes open wide and replied, “Well, it would depend on how many other people there are.”

It was my turn to be confused, “What do you mean?”

“Well,” he replied, “The cake that was cut in two would have bigger slices, but it wouldn’t be fair if there were more than two people.”

Now I stood in silence, as a smile slowly came over my face.  He went on, “Not everyone could have a slice.  We should make sure that everyone who wants a slice could have one.  So how to cut the cake should depend on how many people are there.”

My son understood fractions.  He didn’t understand how you could decide which way to slice a cake until you accounted for other factors.  Yes, my love, life is often more complicated than simple math might lead us to believe.  Thank you for reminding me that even in our everyday discussions about numbers, our thinking should account for sharing and compassion.

And, like all days, we both learned something.