Portion the Fair-Divider

Her given name was Tithe, the same as the town, though she had been called Portion since she was ten, when she settled a quarrel between two brothers over a basket of apples by a method so clean that both brothers walked away satisfied. She had grown up caring, more than anything, that a share be fair — and she had learned that fairness in a mixed group was not about giving everyone the same, but about giving everyone their right proportion.

The method her mother taught her, and that Portion refined over the years, was always the same. You did not start by guessing anyone's share. You started by counting the total number of shares the ratio called for. If two households were to split the season in the ratio of three parts to two, that was three shares and two shares — five shares in all. Then you found what one share was worth, by dividing the whole pay by five. And once you knew the worth of a single share, every household's portion was simple: three shares for one, two for the other, and not a coin in dispute.

A steward from the RatioRealm academy passed through Tithe at settling-time and watched Portion divide a season's pay among seven households of different sizes without a single voice raised.

"You are sharing in a ratio," the steward said. "Dividing a whole into parts that hold a given proportion. Our students find it slippery — they try to guess the shares directly and tangle themselves. You count the shares first."

Portion had never left the valley. But she liked the thought of children learning to divide things so cleanly that no one felt cheated. She has taught sharing-in-a-ratio for six years.

In her classroom Portion keeps a bowl of twenty smooth counters. She begins the same way each year. "Two children are to share these twenty in the ratio two to three," she says. "How many does each get?" The children guess wildly. Portion stops them. "Don't guess the shares. Count them. Two parts and three parts — that is five shares in all. Now" — she tips the twenty counters out — "share the twenty into five equal shares. What is one share worth?" The children divide: twenty into five is four. "So one share is four counters," says Portion. "Now hand them out: two shares — eight — to the first child, three shares — twelve — to the second. Eight and twelve. They add back to twenty, and they stand in the ratio two to three, and no one can argue." The children see it: the whole trick was never the shares themselves but finding the one share first — the single unit that made all the rest fall out fairly.