What is negative 78 times negative 34? (-78 x -34)

What is negative 78 times negative 34?

78 times 34 is 2652, but what is the answer if both 78 and 34 are negative numbers? Here we will determine if the answer to negative 78 times negative 34 is positive 2652 or negative 2652.

There are many different ways to explain and determine if the answer to negative 78 times negative 34 is -2652 or +2652 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 -2652 is the correct answer using basic algebra.

We will test if -2652 is correct by setting up the equation negative 78 times negative 34 equals negative 2652, and then simplifying the equation to see if it is true.

(-78) (-34) = (-2652)

Divide both sides of the equation by (-34) :

		(-78) (-34)
		(-34)

		(-2652)
		(-34)

The numerator and denominator on the left side both have (-34) which even each other out and can be removed:

(-78) =

		(-2652)
		(-34)

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

(-78) =

		(2652)
		(34)

A numerator of 2652 and denominator of 34 on the right side is the same as 2652 divided by 34 which is 78. Now we end up with this untrue equation:

(-78) = (78)

-78 is NOT equal to 78, thus we have proven that negative 78 times negative 34 is not equal to -2652. The answer must therefore be 2652:

-78 x -34 = 2652

The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 78 times negative 34 will always have a positive answer.

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