What is negative 8 times negative 32? (-8 x -32)

What is negative 8 times negative 32?

8 times 32 is 256, but what is the answer if both 8 and 32 are negative numbers? Here we will determine if the answer to negative 8 times negative 32 is positive 256 or negative 256.

There are many different ways to explain and determine if the answer to negative 8 times negative 32 is -256 or +256 using mathematical terms such as additive inverse and mathematical laws like the Distribute Law.

We will take a different approach - process of elimination: We will simply test if -256 is the correct answer using basic algebra.

We will test if -256 is correct by setting up the equation negative 8 times negative 32 equals negative 256, and then simplifying the equation to see if it is true.

(-8) (-32) = (-256)

Divide both sides of the equation by (-32) :

		(-8) (-32)
		(-32)

		(-256)
		(-32)

The numerator and denominator on the left side both have (-32) which even each other out and can be removed:

(-8) =

		(-256)
		(-32)

The numerator and denominator on the right side both have a minus sign (-) which even each other out and can be removed:

(-8) =

		(256)
		(32)

A numerator of 256 and denominator of 32 on the right side is the same as 256 divided by 32 which is 8. Now we end up with this untrue equation:

(-8) = (8)

-8 is NOT equal to 8, thus we have proven that negative 8 times negative 32 is not equal to -256. The answer must therefore be 256:

-8 x -32 = 256

The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 8 times negative 32 will always have a positive answer.

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