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From Fractions to Calculus

So you want to learn higher math? Calculation, you say? Well, let me say here and now that if you haven’t mastered fractions, guess what? Did I hear what I think you said? Yes, it’s true. You will never learn the math.

A big part of the problem in learning higher math is that a lot of it depends on mastering the basics like fractions. Too many students in calculus classes still struggle with routine tasks such as finding the lowest common denominator of two fractions with unusual denominators. I say unusual because most of the common denominators can be taken into account. However, when two otherworldly denominators come into play, it often presents big problems; because most students have forgotten things like decomposing composite numbers into primes, and from there getting the lowest common denominator.

Fractions are problematic because they have two heads, so to speak: the numerator serves as one of these heads, and the denominator, the other. You can’t just add or subtract fractions like you would ordinary numbers, and while multiplication and division don’t present extraordinary problems, you have to deal with both heads in those operations as well.

In calculus, you often have to work with those “two-headed” beasts known as rationals, or fractions. You should be able to add and subtract them effortlessly when evaluating complex functions. Moreover, working with derivatives and integrals, you encounter these numbers so often that weakness in facing them will lead to expulsion from this discipline.

So how do you master fractions? Familiarize yourself with them as you would a good friend. Know that fractions are nothing more than the quotient of two whole numbers. That is, a fraction like 4/27 is nothing more than the number 4 divided by the number 27. Since many fractions have long or even infinite decimal representations, it is much more easy to work with a number as a fraction rather than a decimal. (See my article “Teach Your Kids Arithmetic – Fractions, Percents, and Decimals”)

Understand that you can represent any whole number as a fraction by putting 1 as the denominator: thus 3/1, 5/1 and 10/1. Any whole number can be converted to a fraction with a given denominator by multiplying both the numerator and denominator by the specified denominator. That is, if you want to convert 5 into a fraction with a denominator of 7, multiply the 5 and the 1 of 5/1 by 7 to get 35/7. Fractions such as 5/1 and 35/7 are called equivalent fractions.

Remember that before adding or subtracting two fractions, they have the same denominator. Otherwise, you need to find the lowest common denominator first (see my ebook on fractions). With just this information outlined here, you can master fractions and then master counting. Without it, you might as well not enroll in that calculus course after all.

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