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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 5

How to turn two fractions summed into one larger fraction

$$\left({a \over b}\right)+\left({c \over d}\right) = {(ad+bc) \over bd}$$
Description:

This follows from the fact that you can find a common denominator between two fractions by multiplying the numerator and denominator of each fraction by the other's denominator, like so:

$${3 \over 5}+{1 \over 3} = {(3*3) \over (5*3)} + {(1*5) \over (3*5)} = {9 \over 15} + {5 \over 15} = {14 \over 15}$$ or, written as in the above rule: $${3 \over 5}+{1 \over 3} = {(3*3) \over (5*3)} + {(1*5) \over (3*5)} = {(1*5)+(3*3) \over (3*5)}$$
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