What is negative 71 times negative 72? (-71 x -72)

What is negative 71 times negative 72?

71 times 72 is 5112, but what is the answer if both 71 and 72 are negative numbers? Here we will determine if the answer to negative 71 times negative 72 is positive 5112 or negative 5112.

There are many different ways to explain and determine if the answer to negative 71 times negative 72 is -5112 or +5112 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 -5112 is the correct answer using basic algebra.

We will test if -5112 is correct by setting up the equation negative 71 times negative 72 equals negative 5112, and then simplifying the equation to see if it is true.

(-71) (-72) = (-5112)

Divide both sides of the equation by (-72) :

		(-71) (-72)
		(-72)

		(-5112)
		(-72)

The numerator and denominator on the left side both have (-72) which even each other out and can be removed:

(-71) =

		(-5112)
		(-72)

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

(-71) =

		(5112)
		(72)

A numerator of 5112 and denominator of 72 on the right side is the same as 5112 divided by 72 which is 71. Now we end up with this untrue equation:

(-71) = (71)

-71 is NOT equal to 71, thus we have proven that negative 71 times negative 72 is not equal to -5112. The answer must therefore be 5112:

-71 x -72 = 5112

The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 71 times negative 72 will always have a positive answer.

Negative Times Negative Calculator
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