What is negative 72 times negative 82? (-72 x -82)

What is negative 72 times negative 82?

72 times 82 is 5904, but what is the answer if both 72 and 82 are negative numbers? Here we will determine if the answer to negative 72 times negative 82 is positive 5904 or negative 5904.

There are many different ways to explain and determine if the answer to negative 72 times negative 82 is -5904 or +5904 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 -5904 is the correct answer using basic algebra.

We will test if -5904 is correct by setting up the equation negative 72 times negative 82 equals negative 5904, and then simplifying the equation to see if it is true.

(-72) (-82) = (-5904)

Divide both sides of the equation by (-82) :

		(-72) (-82)
		(-82)

		(-5904)
		(-82)

The numerator and denominator on the left side both have (-82) which even each other out and can be removed:

(-72) =

		(-5904)
		(-82)

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

(-72) =

		(5904)
		(82)

A numerator of 5904 and denominator of 82 on the right side is the same as 5904 divided by 82 which is 72. Now we end up with this untrue equation:

(-72) = (72)

-72 is NOT equal to 72, thus we have proven that negative 72 times negative 82 is not equal to -5904. The answer must therefore be 5904:

-72 x -82 = 5904

The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 72 times negative 82 will always have a positive answer.

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