Bag End, Halimath 1391

Frodo looked up from his writing lessons and saw Sam standing at the doorway, board in hand that he used when learning lessons with Bilbo. The tween smiled at his friend who looked rather forlorn.

"I'm that sorry, Mr. Frodo, but could you help me again with my sums? Mr. Bilbo been teaching me more, but I think with all the time off during the summer, I've forgotten half of what he taught me."

"It'll come back to you, my Sam," the tween assured. He patted the seat beside him. "Why don't you come here and we can go over some of what you've already learned and then you can show me where you are stuck."

The lad brightened immediately and rushed over. "Oh, thank you, Mr. Frodo! I love the way you make all the learning into a big story. It's that fun!"

The child sat right down and showed Frodo the hard board with the problems Bilbo had written out for Sam to solve.

"Well, let's start back toward the beginning," Frodo said, "though you probably don't need it all, but the more you do it, the easier it will be to remember. Now let's say, you and I are going to be having biscuits as part of tea. We have four to eat between us and we want to have an even amount for both of us. How many would each of us have?"

Sam thought and he drew the biscuits just as Frodo had earlier in the year and then counted them out. "Two," he said.

Frodo patted his friend's back. "Very good, my Sam! Now, let's..."

The tween stopped when he saw Sam draw another two more. "What are you doing, Sam?"

"Those are for Mr. Bilbo, for wouldn't he be joining us?"

Frodo thought quickly. "No, he's sick." As soon as he saw Sam's stricken expression, he knew he had made a mistake.

"Oh, that's just awful," the child said and then drew another biscuit that had something on the top of it. "Then he should have more if he's not feeling well and it should have some jam on it, unless he's sick to his stomach and then he'd probably just have some ginger tea like my mum makes."

Frodo scrambled for a way to keep this lesson on track. "But...he's sick in...in Rivendell, Sam."

"Could we take it to him then? I know the Elves must have food that is that wonderful, but wouldn't he be missing some hobbit food? And we should bring him some of my mum's soup because it is that good to eat when you're not feeling right."

Frodo grew a tad desperate. "I don't think it would keep, Sam. Rivendell is a long way away."

"Then maybe we could use some of that special bread that Mr. Bilbo says the Elves have that stays good forever and ever or close to it and bake it into the biscuits and then it would stay fresh. We could go out and look for the Elves in the woods and see if any could help us. Didn't you say it was autumn when it is most likely we could see them?"

All this talk of food was making Frodo hungry. "Well, Sam, I don't know if they'd be likely to part with that bread or not."

"Maybe if we bought them something to give in exchange they would. My mum makes the best raspberry tarts you've ever had."

The tween resigned himself to the fact that there was going to be no easy way back to the lesson he had started out with. "I know, my Sam, because I've had them, and her soup and tea, and they are very wonderful, but I don't think we'd be able to keep them hot, and who wants to drink cold soup or tea?"

That stopped the child for a moment and Frodo held his breath. Sam though was not to be stopped. He furrowed his brow in thought and then said, "I think just the tarts then, Mr. Frodo. We could carry the tea bags with us and surely the Elves would have their own fire and we could warm up the tea then. I could ask my mum later whether she could make any. 'Tis too bad we can't take the soup."

"Yes, we can ask later," Frodo agreed with an emphasis on the last word. "Now, let's get back to the lesson, my Sam."

He looked at the problems that Bilbo had written on the board for his student to solve and then drew another biscuit and divided it into three equal parts. "Now..."

"Who's getting the third part if Mr. Bilbo ain't here?"

"Well, we'll leave that part to Merry. You remember when he came last Yule?"

"Yes, he was that fun, Mr. Frodo. But I don't think you should have me have an equal part, with Mr. Merry being gentry and all. He should have a bigger part than me."

"But that would spoil what you need to learn, Sam. You'll just have to pretend that you are on the same level." He thought quickly. "You can make believe that you are Mayor, how's that?"

The child's expression quickly informed him that would not work. "That ain't right, Mr. Frodo, begging your pardon. My Gaffer's always said, 'You'll be gardener of Bag End one day, and you're the son of a gardener and a grandson of a gardener. Don't ever think of anything else above your station. Naught use putting any daft ideas into your head of being anyone else your own self.'"

"Well, I'm not saying it's real, Sam, just pretend."

The lad still didn't look comfortable so Frodo knew he had to think of something else. "Well, we can pretend it is my heart. Here's Bilbo's part, here's Merry's and here's yours." In each equal part, he drew the initial for them. Then he looked up at Sam and dared him with his eyes to make a comment and was surprised when his friend looked more distressed than ever.

"But, Mr. Frodo! That leaves no room for you! Surely you love your own self!"

Frodo bit back a sigh. "Of course I do, Sam, but you need to learn about third's in this lesson and that's what I am trying to tell you. Now, Bilbo makes up one-third of my heart, Merry makes up another third and that makes it two-thirds, and you make up the last third. So that's my whole heart." He didn't go into all the other cousins that held a piece of his heart also, including his newest Tookish one. He wished fervently, though he knew in vain, that Sam wouldn't bring it up.

Sam opened his mouth, but before he could speak, Bilbo popped his head in.

Frodo felt he could have perished with relief. Never before he had felt so worn out. Bilbo smiled and winked at him.

"Ready for elevenses, my lads?"

That revived the tween straightaway. He and Sam answered the old hobbit "Yes!" at the same time, almost as though they spoke with the same voice, though course, Sam had added, "Mr. Bilbo," to his affirmation. They raced out of the room and into the kitchen where the old hobbit had tea, biscuits and jam waiting. Bilbo smiled at them as they scrambled onto chairs.

"Have you been learning a lot, Sam, my lad?" Bilbo asked.

"Oh, yes, Mr. Bilbo! I do so love it! Let me show you."

He cut one biscuit into even thirds. One he put extra butter and jam on because he knew Mr. Frodo liked it that way and the other way just with jam and handed them to his tutors. The other third he kept to himself and slathered with jam. He still didn't think it right that he have the same amount as his betters, but he did want to show how much he had learned and what a good teacher Mr. Frodo was. "Now, Mr. Bilbo, you have one-third, Mr. Frodo has one-third, and that's two-thirds together and I have the other and that makes up the whole thing."

"Wonderful, Sam!" Bilbo praised and the child's face lit up. "Now tomorrow, we'll learn fourths, but perhaps Frodo will have to do that lesson, because I am going to be away in the morning at the market."

Sam's face grew even brighter while Frodo's looked a bit panic-stricken and he begged his uncle silently for a reprieve, but Bilbo only smiled and sipped his tea contentedly.

Sam took his friend's hand. "I'm that glad you are going to be teaching me still, Mr. Frodo!" he said and how could Frodo refuse that, looking into the child's shining eyes?

Very true it was that Sam held part of his heart and a bigger part all the time. Frodo didn't know how to explain it yet to the lad, but it was possible to love more than one person at the same time with your whole heart, and he knew his friend would be one of these he would add to that.

But that had nothing to do with sums.