# Algebrarules.com

The most useful rules of basic algebra,
free, simple, & intuitively organized
X

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 a subtraction gives the inverse result: $5-3 = 2; 3-5 = -2$. In a fraction, if both the numerator and the denominator are inverted, the value of the fraction stays the same. So, if we reverse a subtraction in both the numerator and denominator, the value of the fraction is unchanged.

$${3-5 \over 2-1} = {-2 \over 1} = {5-3 \over 1-2} = {2 \over -1} = -2$$ or $${-3 \over -4} = 0.75 = {3 \over 4}$$
« Previous Rule Next Rule »

## 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.

## Support algebrarules.com

You may have noticed that there are no ads on this site. That’s because we think ads are nasty, privacy-invading distractions — and we don’t want you to be distracted from learning algebra!

This site is free to use, but it’s not free to run. If algebrarules.com has helped you, please consider donating so that we can keep the site running for years to come.