Reunited(11)

“Maybe there is no reason, Brett. Maybe someone just made that up to confuse math students.”

“There’s got to be a reason.”

“Geez…Okay, do you have any graph paper?”

“Nope.”

“We need to make a number line.”

“I stopped making number lines in sixth grade, Kath.”

“Well, humor me. Get some notebook paper and draw some vertical lines so we have graph paper.”

“Okay.” He complied. “Why are we doing this again?”

“Because I don’t know the answer to your question.”

“You don’t?”

“No.”

“How can you be so good at math, then?”

“Because I learn the rules. I follow them. I get the right answer. I don’t have to understand why.”

“Wow. I never would have thought…”

“Well, I never would have thought you’d care about why the rules of math are what they are. I’d have thought you just wanted to get your C and play baseball.”

“I do.”

“Don’t worry. You will, with me tutoring you.”

He smiled. “I know.”

“So you got your graph paper ready?”

“Yup.” He handed it to her. Kathryn quickly wrote out a number line starting in the middle with zero and going horizontally and vertically into positive and negative integers.

“Okay. Now, what is your exact question?”

“Well, positive numbers are numbers greater than zero, right?”

“Yeah.”

“And negative numbers are less than zero.”

“Right.”

“When you add two positives together, you get a positive.”

“Yup.”

“And when you add two negatives you get a negative.”

“You got it so far.”

“It makes sense so far. When you multiply two positives you get a positive. I don’t get why you wouldn’t get a negative when you multiply two negatives. I mean, when you think about it, multiplying is just adding, only adding more than once, you know? So if you get negative when you add two negatives, why don’t you get negative when you multiply two negatives?”

Wow. Impressive. He’d really thought this out. Determination gripped her. She’d find the answer for him. Clearly, he understood the concepts of addition and multiplication and how they were related. There had to be a reason for this stupid rule. There just had to be.

“Okay, let’s look at two times two.” Kathryn drew a line two blocks to the right horizontally from zero, and two blocks upward vertically from zero. “If we tie these together with coordinates, we get a volume of four on the graph, see?”

“Yeah.”

“Now if we do the same with negative two times negative two—” She drew a line two blocks to the left side from zero, then two blocks downward from zero. She shaded in the area. “It’s still a volume of four. See?”

“Yeah. But I still don’t get it.”

She scoffed. “To tell you the truth, neither do I. Did you order the pizza yet?”

“Yeah. While you were getting the drinks.”

“Okay, let’s think of how multiplication works. Two times two means two sets of two, right?”

“Yeah. And two sets of two would be four.”

“Good. And you understand why two times negative two is negative four?”

“Yeah, of course. Two sets of negative two would be negative four. That makes sense.”

“Good. It makes sense to me, too. So really, all we need to do is figure out why negative two sets of negative two equals positive four.”

“Yup.”

“Okay, no problem.” Kathryn rolled her eyes. “Would you like to know about the existence of God or the meaning of life? That might be easier.”

Brett laughed. Oh, he had an attractive husky laugh. She sighed.

“Do you have any math homework you need help with? Maybe when the pizza comes we can tackle this question. I work better on a full stomach.”

Brett laughed again. “Me, too. Yeah, here’s my homework assignment. Can you check it for me?”

Kathryn went through the problems with him and found he had done a pretty good job. Just as she finished helping him with the corrections, the doorbell rang and the pizza arrived.

“The iced tea’s gone, and Deb doesn’t have any pop. We should have ordered some Coke,” Kathryn said.

“No problem. Ice water’s fine.” He winked. “She does have ice, doesn’t she?”

Kathryn’s heart skipped a beat. He’d actually winked at her! “I think so. I’ll get us some. And some plates and napkins. Give me a sec.”

“I’ll be right here.”

When she returned Brett had already polished off a piece of pizza.

“You must be hungry,” she said.

“Always. Here.” He handed her a piece. She took a bite and set it on a plate.

“So I’ve been thinking,” he said.

“About what?”

“About our positive and negative problem.”

“This is really bugging you, isn’t it?”