What is negative 13 times negative 82? (-13 x -82)

What is negative 13 times negative 82?

13 times 82 is 1066, but what is the answer if both 13 and 82 are negative numbers? Here we will determine if the answer to negative 13 times negative 82 is positive 1066 or negative 1066.

There are many different ways to explain and determine if the answer to negative 13 times negative 82 is -1066 or +1066 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 -1066 is the correct answer using basic algebra.

We will test if -1066 is correct by setting up the equation negative 13 times negative 82 equals negative 1066, and then simplifying the equation to see if it is true.

(-13) (-82) = (-1066)

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

		(-13) (-82)
		(-82)

		(-1066)
		(-82)

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

(-13) =

		(-1066)
		(-82)

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

(-13) =

		(1066)
		(82)

A numerator of 1066 and denominator of 82 on the right side is the same as 1066 divided by 82 which is 13. Now we end up with this untrue equation:

(-13) = (13)

-13 is NOT equal to 13, thus we have proven that negative 13 times negative 82 is not equal to -1066. The answer must therefore be 1066:

-13 x -82 = 1066

The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 13 times negative 82 will always have a positive answer.

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