Hello. My name is Glenn Philips.
Ronald Mack, my friend and classmate, asked me to explain why some whole numbers cannot be split into parts even though we sometimes speak of them that way.
First let me say I very much enjoyed reading the book Ronald wrote.
In that book, Ronald described the monthly poker game attended by his father and Georgie Sinkoff’s father. He wrote:
I think there are eight men who play, but they do it at a different house each time, so they’re only at my house one and a half times each year. (Okay. I know that it’s impossible to be at my house a half of a time. But twelve months divided by eight men does equal 1.5, so…Aha! I just called Glenn Philips. He said I am right, but there’s a better way to say it: They’re only at my house three times every two years.
Yes, it is impossible to be somewhere a half of a time. That’s because some things—like trips to the post office, or home runs, or Vice Presidents of the United States—cannot be split. There is no such thing as “half of a home run” or “half of a Vice President”
Here’s a way to look at the poker game question. Assume that the eight men who play are Messrs. A, B, C, D, E, F, G, and H. They agree to host the game each month at a different man’s home. Mr. A hosts in January…Mr. B in February…Mr. C in March…and so on. Look at the table below. After one year, half of the men (Messrs. A, B, C, and D) would have had two games at their homes, but the other half (Messrs. E, F, G, and H) would each have hosted only once. On average, each man would have hosted 1.5 games per year.
But as I told Ronald, it might be clearer if he said, “Each man hosted three games every two years.” That also averages 1.5 times a year.
I hope this explanation is clear. If you have further questions, please ask them below, and I (Glenn Philips) will answer.
(Cheesie writing now: Glenn is really smart. You can ask him super hard questions!)