What is negative 37 times negative 23? (-37 x -23)

What is negative 37 times negative 23?

37 times 23 is 851, but what is the answer if both 37 and 23 are negative numbers? Here we will determine if the answer to negative 37 times negative 23 is positive 851 or negative 851.

There are many different ways to explain and determine if the answer to negative 37 times negative 23 is -851 or +851 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 -851 is the correct answer using basic algebra.

We will test if -851 is correct by setting up the equation negative 37 times negative 23 equals negative 851, and then simplifying the equation to see if it is true.

(-37) (-23) = (-851)

Divide both sides of the equation by (-23) :

		(-37) (-23)
		(-23)

		(-851)
		(-23)

The numerator and denominator on the left side both have (-23) which even each other out and can be removed:

(-37) =

		(-851)
		(-23)

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

(-37) =

		(851)
		(23)

A numerator of 851 and denominator of 23 on the right side is the same as 851 divided by 23 which is 37. Now we end up with this untrue equation:

(-37) = (37)

-37 is NOT equal to 37, thus we have proven that negative 37 times negative 23 is not equal to -851. The answer must therefore be 851:

-37 x -23 = 851

The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 37 times negative 23 will always have a positive answer.

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