# Algebrarules.com

The most useful rules of basic algebra,
free, simple, & intuitively organized
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Howdy! Here are a few very handy rules of algebra. These basic rules are useful for everything from figuring out your gas mileage to acing your next math test — or even solving equations from the far reaches of theoretical physics. Happy calculating!

## Algebra Rule 7

#### Reversing a subtraction in both the numerator and the denominator of a fraction leaves the fraction's value unchanged

$${(a-b) \over (c-d)} = {(b-a) \over (d-c)}$$
Description:

Reversing the order of a subtraction operation creates the inverse result: 5-3 = 2; 3-5 = -2. A consequence of this is that for a fraction in which both the numerator and denominator contain a subtraction (ie, they each contain a negative term), if both those subtractions are reversed, the value of the fraction remains the same. This is because if the sign of both the numerator and denominator of a fraction is changed, the fraction's value remains the same.

$${3-5 \over 2-1} = {-2 \over 1} = {5-3 \over 1-2} = {2 \over -1} = -2$$or$${-3 \over 4} = -0.75 = {3 \over -4}$$ or $${-3 \over -4} = 0.75 = {3 \over 4}$$
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## A little bit about algebrarules.com

Algebra rules is a project by two of the folks who run The Autodidacts.

A couple of autodidact math enthusiasts, we were looking for all the rules of basic algebra concisely presented in one place. We couldn’t find such a place, so we made Algebrarules.com

These simple rules — applied with a pinch of imagination and a dash of arithmetic — can divide, conquer, and solve just about any practical algebra problem.

If you find errata in the math, bugs in the code of Algebrarules.com, or just want to say Eh, please send us a letter or join us on our roost: @rulesofalgebra.