What is negative 3 times negative 37? (-3 x -37)

What is negative 3 times negative 37?

3 times 37 is 111, but what is the answer if both 3 and 37 are negative numbers? Here we will determine if the answer to negative 3 times negative 37 is positive 111 or negative 111.

There are many different ways to explain and determine if the answer to negative 3 times negative 37 is -111 or +111 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 -111 is the correct answer using basic algebra.

We will test if -111 is correct by setting up the equation negative 3 times negative 37 equals negative 111, and then simplifying the equation to see if it is true.

(-3) (-37) = (-111)

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

		(-3) (-37)
		(-37)

		(-111)
		(-37)

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

(-3) =

		(-111)
		(-37)

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

(-3) =

		(111)
		(37)

A numerator of 111 and denominator of 37 on the right side is the same as 111 divided by 37 which is 3. Now we end up with this untrue equation:

(-3) = (3)

-3 is NOT equal to 3, thus we have proven that negative 3 times negative 37 is not equal to -111. The answer must therefore be 111:

-3 x -37 = 111

The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 3 times negative 37 will always have a positive answer.

Negative Times Negative Calculator
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