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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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