What is negative 33 times negative 53? (-33 x -53)

What is negative 33 times negative 53?

33 times 53 is 1749, but what is the answer if both 33 and 53 are negative numbers? Here we will determine if the answer to negative 33 times negative 53 is positive 1749 or negative 1749.

There are many different ways to explain and determine if the answer to negative 33 times negative 53 is -1749 or +1749 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 -1749 is the correct answer using basic algebra.

We will test if -1749 is correct by setting up the equation negative 33 times negative 53 equals negative 1749, and then simplifying the equation to see if it is true.

(-33) (-53) = (-1749)

Divide both sides of the equation by (-53) :

		(-33) (-53)
		(-53)

		(-1749)
		(-53)

The numerator and denominator on the left side both have (-53) which even each other out and can be removed:

(-33) =

		(-1749)
		(-53)

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

(-33) =

		(1749)
		(53)

A numerator of 1749 and denominator of 53 on the right side is the same as 1749 divided by 53 which is 33. Now we end up with this untrue equation:

(-33) = (33)

-33 is NOT equal to 33, thus we have proven that negative 33 times negative 53 is not equal to -1749. The answer must therefore be 1749:

-33 x -53 = 1749

The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 33 times negative 53 will always have a positive answer.

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