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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 9

Factors in the numerator of a fraction that are the same as the denominator can be cancelled

$${ac+bc \over c} = a+b$$
Description:

Division can be thought of as 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 to where we started. This rule is an extension of that fact. 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 ${bc \over c} = b$, from that 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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