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Crazy Fraction Write up

For the crazy fraction mini project, we were given an algebraic problem, and were told that we were to determine if there was an answer to it or not. (And why.) Here was my answer:

Crazy Fraction Write Up

By Trevor Farrell

Within this brief report on my crazy fraction problem, I will include four basic elements of focus. These basic topics include the problem itself, the process used to solve the problem, the final solution to the problem, and finally, my reflection on the problem.

The Problem:

The basic premise of the crazy fraction problem is as follows:

The problem simply tells the person viewing it that to solve it, you must find a way to make “a,” “b,” and “c” true, which allows the viewer to put quite a bit creativity into solving the problem. Although the problem asks the solver to come up with as many values for “a,” “b,” and “c,” the question can be negated by providing the rule numbers go on forever, so therefore, as long as there is at least one answer to the problem, it can be solved again by simply by multiplying the digits used to solve it. So to make the problem more difficult to those who can solve it quickly, a challenge option is available, seen above.

The Process, and the Solution:

As the title of this problem indicates, it is all based on the principle of fractions. Beyond this, I feel as though the problem is forcing the person attempting to solve it to plug in random numbers for letters “a”, “b”, and “c”. When I first approached the problem with the logic that “a” must equal “b,” “b” must equal “c,” or that “c” must equal “a.” For example, if I used the number 2 for “a,” and 4 for “b,” then “c” must equal 4, so that “b” would be equal to “c.” However, this theory was quickly dismissed after some thought.

One example is simply expanding the horizons of the one solving the equation, including me. If “a” was 2, and “b” was 2, then “c” would be zero, proving that “b” doesn't have to be the same number. The most prominent example amongst my peers was any equation involving negative numbers. An example of this would be if “a” was 2, “b” was 1, then “c” would equal -2. This works backwards too, with the wonder of double negatives, which can allow for mathematical addition. If “a” equals -2, and “b” equals -1, then “c” would equal 2. The bottom line for the whole crazy fraction problem is that there is there is more than one method for solving it, depending on how you look at it.

The Reflection

After solving this problem, I got a better idea of not only a better understanding of subtracting and adding fractions, (especially after I was only capable of changing the bottom integer.) but I also got a better idea of what types of problems we would be doing, and how there would always be a pattern to everything we did in math. This project further reinforced my idea that math is not only a an art expression, but also in its own way, a language. To quote Albert Einstein, “Pure mathematics is in its way the poetry of logical ideas.”