Sinking to the lowest common denominator

A recent study concludes that Americans are falling behind other nations when it comes to fractions and long division, according to Scientific American. Below is the transcript of a recent fifth grade math class:

“Class, get out your math books and turn to the chapter on fractions.”

“Aw, Ms. Crabapple, I hate fractions. Can’t we just sit here and count how many times Josh yawns? That could get us into higher math.”

“Now Johnny, you know one of the reasons you’re having to do summer school is because you haven’t mastered fractions. And your long division leaves much to be desired as well.”

“I always get denominators and numerators confused, Ms. Crabapple. And you can forget about dividends.”

“That’s what I mean, Johnny. Your deficiency in splitting numbers is holding you back. When you learn to divide as well as you add and subtract, you’ll be a fine math student.”

“But I don’t want to be a math student, Ms. Crabapple. I want to be a Major League baseball player. And if that doesn’t work out, I’ll be a truck driver.”

“Fractions and long division are important no matter what career you choose. For instance, what was your batting average in Little League last season?”

“Well, not to brag, but I hit .450. Coach said I had good hand-eye coordination.”

“OK, Johnny, how did you figure out your batting average?”

“Uh, I didn’t figure it out myself. The coach kept up with it.”

“Aha. So how do you know for sure that you hit .450? What if the coach was wrong and your average was really just .200? How would you know the difference?”

“But my coach is smart and wouldn’t make a mistake. Besides, he uses a calculator.”

“What if you were a coach someday. How would you figure your players’ averages if you don't understand the concept?”

“Umm, I guess I’d find a player who was smart in math.”

“But Johnny, what if all your players were like you and didn’t like long division and never learned how to figure batting averages?”

“Ms. Crabapple, I don’t think I’ll ever coach Little League. It sounds too hard.”

“Nothing’s too hard when you learn how to do it, Johnny. It’s like dividing fractions. Once you learn the tricks, it’s easy.”

“That’s always been hard for me, Ms. Crabapple. I forget if I’m supposed to multiply the top numbers or the bottom numbers.”

“That’s why we’re going to study fractions, Johnny. Then when you really need the skill, you’ll have it.”

“But I think I can get along without fraction skills, Ms. Crabapple. Why would I need them?”

“Here’s an example, Johnny. You and Josh want to split up two leftover apple pies. The first pie has one-third left and the second pie is three-eighths. How much does each of you get?”

“I’m not really crazy about apple pie, Ms. Crabapple, but thanks all the same.”

“This is a hypothetical question, Johnny. Pretend it’s something you like a lot.”

“Well, if that’s the case, I guess I’d cut both 'pecan' pies in two and we’d each take half of each one.”

“Let me put it another way, then. You can’t cut the pies but have to each take one pie plate. How do you know which one gets more pie?”

“You mean, which is bigger, one-third or three-eighths?”

“Yes, Johnny. How do you figure out which is the larger pie?”

“I give up, Ms. Crabapple.”

“First you find the lowest common denominator — the bottom numbers. What’s the lowest number that both three and eight will divide into?”

“Uh, three goes into nine and 12 and 15 and 18 and 21 and 24. OK, eight goes into 24.”

“That’s right, Johnny, the lowest common denominator is 24. Now, how many 24ths are there in one-third and in three-eighths? Three into 24 is eight so one-third is eight-24ths.

“Eight into 24 is three. Three times three is nine, so three-eighths is nine-24s.”

“I get it, Ms. Crabapple. The one-third pie is a little bit smaller than the three-eighths pie.”

“Good, Johnny. Now do you understand?”

“Yes ma’am. But I’d still rather count Josh’s yawns.”

Larry Penkava is a writer for Randolph Hub. Contact: 336-302-2189, larrypenkava@gmail.com.