What is negative 45 times negative 82? (-45 x -82)

What is negative 45 times negative 82?

45 times 82 is 3690, but what is the answer if both 45 and 82 are negative numbers? Here we will determine if the answer to negative 45 times negative 82 is positive 3690 or negative 3690.

There are many different ways to explain and determine if the answer to negative 45 times negative 82 is -3690 or +3690 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 -3690 is the correct answer using basic algebra.

We will test if -3690 is correct by setting up the equation negative 45 times negative 82 equals negative 3690, and then simplifying the equation to see if it is true.

(-45) (-82) = (-3690)

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

		(-45) (-82)
		(-82)

		(-3690)
		(-82)

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

(-45) =

		(-3690)
		(-82)

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

(-45) =

		(3690)
		(82)

A numerator of 3690 and denominator of 82 on the right side is the same as 3690 divided by 82 which is 45. Now we end up with this untrue equation:

(-45) = (45)

-45 is NOT equal to 45, thus we have proven that negative 45 times negative 82 is not equal to -3690. The answer must therefore be 3690:

-45 x -82 = 3690

The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 45 times negative 82 will always have a positive answer.

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