1 St Grade Math Worksheets Adding With The Number 4 From Fractions to Calculus

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From Fractions to Calculus

So you want to learn higher math? Calculus, you say? Well, let me state right here and now that if you don’t master fractions, guess what? Did I hear what I think you said? Yes, that’s right. You will never learn calculus.

A big part of the problem in learning higher mathematics is that so much of it depends on having first mastered the basics like fractions. Too many students in calculus courses still have trouble performing routine duties such as finding the least common denominator of two fractions with unusual denominators. I say unusual because most common denominators can be reckoned with. However, when two denominators from another world come jamming on the scene, this often presents big trouble; for most students have forgotten things like decomposing composite numbers into primes, and from there getting the least common denominator.

Fractions are trouble because they have two heads, so to speak: the numerator serves as one of these heads, and the denominator, the other. You cannot simply add or subtract fractions the way you would ordinary numbers, and even though multiplication and division present no extraordinary problems, you still must contend with the two heads in these operations as well.

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

So how do you master fractions? Become familiar with them the way you would a good friend. Realize that fractions are nothing more than the quotient of two integers. 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 easier 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 into 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 1 of 5/1 by 7 to get 35/7. Fractions like 5/1 and 35/7 are known as equivalent fractions.

Remember that before adding or subtracting two fractions that they have the same denominator. If not, you must first find the least common denominator (see my ebook on fractions). With just this information outlined here, you can master fractions and then master calculus. Without it, you may as well just skip enrolling in that calc course after all.

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