Which math property is this demonstrating
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Which math property is this demonstrating

[From: ] [author: ] [Date: 12-08-13] [Hit: ]
This law exists to preserve the integrity of the distributive law.To see this,let a = -1, b = -1.5 and c = 1.a*(b + c) = ab + ac.......
Which property (in math) is this equation illustrating?
-1 x (-1.5) = 1.5

I can't seem to find the right one, so a definition of the property would be helpful, as well.
Thank you. :)

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What is being used is the Law of Signs for multiplication: the product of two numbers
with like signs is always positive and the product of two numbers with different signs
is always negative. This law exists to preserve the integrity of the distributive law.
To see this, let a = -1, b = -1.5 and c = 1.5 and consider the distributive law
a*(b + c) = ab + ac. Then the LHS would be -1*(-1.5 + 1.5) = -1*0 = 0 by a property
of 0. The RHS will be (-1)*(-1.5) + (-1)*(1.5) = (-1)*(-1.5) - 1.5 which will equal 0 only if
(-1)*(-1.5) = 1.5.

Edit: Distributive law and distributive property are the same thing, so you can go
with that along with the property of zero I used above. I needed both of these
properties to demonstrate that (-1)*(-1.5) = 1.5, but if have to answer with just
one it would be the distributive property. :)

-
Distributive:

- 1 x (- 1.5) = - 1(- 1.5) = - (- 1.5) = 1.5
 
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