What is negative 45 times negative 37? (-45 x -37)

What is negative 45 times negative 37?

45 times 37 is 1665, but what is the answer if both 45 and 37 are negative numbers? Here we will determine if the answer to negative 45 times negative 37 is positive 1665 or negative 1665.

There are many different ways to explain and determine if the answer to negative 45 times negative 37 is -1665 or +1665 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 -1665 is the correct answer using basic algebra.

We will test if -1665 is correct by setting up the equation negative 45 times negative 37 equals negative 1665, and then simplifying the equation to see if it is true.

(-45) (-37) = (-1665)

Divide both sides of the equation by (-37) :

		(-45) (-37)
		(-37)

		(-1665)
		(-37)

The numerator and denominator on the left side both have (-37) which even each other out and can be removed:

(-45) =

		(-1665)
		(-37)

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

(-45) =

		(1665)
		(37)

A numerator of 1665 and denominator of 37 on the right side is the same as 1665 divided by 37 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 37 is not equal to -1665. The answer must therefore be 1665:

-45 x -37 = 1665

The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 45 times negative 37 will always have a positive answer.

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