What is negative 65 times negative 78? (-65 x -78)

What is negative 65 times negative 78?

65 times 78 is 5070, but what is the answer if both 65 and 78 are negative numbers? Here we will determine if the answer to negative 65 times negative 78 is positive 5070 or negative 5070.

There are many different ways to explain and determine if the answer to negative 65 times negative 78 is -5070 or +5070 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 -5070 is the correct answer using basic algebra.

We will test if -5070 is correct by setting up the equation negative 65 times negative 78 equals negative 5070, and then simplifying the equation to see if it is true.

(-65) (-78) = (-5070)

Divide both sides of the equation by (-78) :

		(-65) (-78)
		(-78)

		(-5070)
		(-78)

The numerator and denominator on the left side both have (-78) which even each other out and can be removed:

(-65) =

		(-5070)
		(-78)

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

(-65) =

		(5070)
		(78)

A numerator of 5070 and denominator of 78 on the right side is the same as 5070 divided by 78 which is 65. Now we end up with this untrue equation:

(-65) = (65)

-65 is NOT equal to 65, thus we have proven that negative 65 times negative 78 is not equal to -5070. The answer must therefore be 5070:

-65 x -78 = 5070

The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 65 times negative 78 will always have a positive answer.

Negative Times Negative Calculator
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