How To Add Fractions With Different Denominators Math Is Fun 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 say right here and now that if you don’t master fractions, guess what? Did I hear what I think you said? Yes, that is correct. You will never learn calculus.

A big part of the problem with learning higher math is that a lot of it depends on having first mastered the basics like fractions. Too many students in calculus courses still have trouble performing routine tasks, such as finding the least common denominator of two fractions with unusual denominators. I say unusual because the most common denominators can be counted. However, when two denominators from another world enter the picture, this often presents big problems; because most students have forgotten things like breaking down composite numbers into prime numbers, and from there getting the lowest common denominator.

Fractions are problems because they have two heads, so to speak: the numerator serves as one of those heads, and the denominator serves as the other. You can’t simply add or subtract fractions as you would with ordinary numbers, and while multiplication and division present no extraordinary problems, you also have to contend with both heads in these operations.

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

So how do you master fractions? Get to know them like you would a good friend. Note that fractions are nothing more than the quotient of two whole numbers. This is a fraction like 4/27 is just 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: so 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 make 5 a fraction with a denominator of 7, multiply the 5 and 1 of 5/1 by 7 to get 35/7. Fractions such as 5/1 and 35/7 are known as equivalent fractions.

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

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