Reducing Fractions

Updated: Sep 4, 2020

By the time I was taking second-semester calculus in college I was sick of reducing fractions. Answers in the back of my five-pound calculus book were often in the form of a reduced fraction, such as 11/16. The problem was my calculations provided answers like 143/208. It turns out the ratio 11/16 equals 143/208. They’re both the same answer, but 11/16 is the “reduced fraction” (simplest) form. I won’t go into the mathematics involved (Google: reducing fractions) but suffice it to say that after hours of eye-scraping effort to produce 143/208, I didn’t want to go through the additional task of reducing the ratio to the equivalent 11/16. This was before hand-held calculators provided a reducing fraction function. I knew of no “automatic” method of doing it. I had a programmable calculator in college, but such was no good if I didn’t have an algorithm (computer program) built to reduce fractions. Because I knew of no method, I decided to invent one myself. There were many suffering high school and college students across the world at the time who needed my help. I would not stop until I had discovered an algorithm that simplified 50/100 to 1/2, 21/28 to 3/4, and 117/91 to 9/7. My quest stretched into months until at last, I found a way. When I entered into my calculator 51/85, the program gave me 3/5. When I put in 95/171, the program provided 5/9. It even reduced decimal fractions like .3/1.35 to 2/9. I was ecstatic! I demonstrated it to all my non-engineering roommates who were not impressed. I wrote out my method in the neatest way I could (this took several attempts) and carried the paper as one might cradle an artifact from an ancient tomb to my calculus professor during his office hours. “Professor __________,” (I don’t remember his name), “I believe I have discovered something. I’ve found a way to reduce fractions. Would you look it over please, and what do you think?” I don’t believe he was in the mood to talk with students. With a pained expression that communicated something like, Spare me, he looked over my intellectual creation. As if trying to hold back disgust, he said, “This is Euclid’s algorithm for reducing fractions. You haven’t discovered anything.” He handed my paper back to me and went back to his calculations, or whatever they were. I almost started crying. I walked back to my room in my apartment where I lived with five other college roommates. Did my professor mean, the Euclid? There was no Internet back then, so I found the largest dictionary in the apartment and looked up the name. It said he lived around 300 BC. Euclid, it turns out, was one of the greatest mathematicians who ever lived and was one of the Founding Fathers of modern-day mathematics. Have you heard of Euclidian geometry? He’s the guy. And yes, I came up with the same algorithm he did, from scratch, with no awareness that such a thing ever existed. So, POO! on my calculus professor, who instead of treating me with derision, should have telephoned the Dean of the College of Mathematics that night and set up a dinner with the Dean, himself, and me, to talk with the smartest student either of them ever had in their careers. Who cares if my professor had no vision? The miracle was I was able to discern that he was the one who blew it, and not me. Creation brings with it joy and fulfillment. If we can produce something that helps make the world a better place, then bring it on!

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