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

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 9

Multiplication and division (by the same number) cancel each other out

```{ac+bc \over c} = a+b```

Division is the inverse of multiplication: if ``{a \over b} = c`` then ``b*c = a``. This means that the fraction ``{ac \over c}`` is equal to ``a``, since we are multiplying ``a`` by ``c`` and then immediately dividing it by ``c`` again, which puts us right back where we started. Since we know that ``{ac+bc \over c} = {ac \over c} + {bc \over c}`` (see rule 8), and based on the above we can see that ``{ac \over c} = a`` and ``{bc \over c} = b``, we have our result: ``a+b``.

```{(4*5)+(2*5) \over 5} = {4*5 \over 5}+{2*5 \over 5} = 4+2```
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A little bit about

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

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.

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