What is negative 67 times negative 78? (-67 x -78)

What is negative 67 times negative 78?

67 times 78 is 5226, but what is the answer if both 67 and 78 are negative numbers? Here we will determine if the answer to negative 67 times negative 78 is positive 5226 or negative 5226.

There are many different ways to explain and determine if the answer to negative 67 times negative 78 is -5226 or +5226 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 -5226 is the correct answer using basic algebra.

We will test if -5226 is correct by setting up the equation negative 67 times negative 78 equals negative 5226, and then simplifying the equation to see if it is true.

(-67) (-78) = (-5226)

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

		(-67) (-78)
		(-78)

		(-5226)
		(-78)

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

(-67) =

		(-5226)
		(-78)

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

(-67) =

		(5226)
		(78)

A numerator of 5226 and denominator of 78 on the right side is the same as 5226 divided by 78 which is 67. Now we end up with this untrue equation:

(-67) = (67)

-67 is NOT equal to 67, thus we have proven that negative 67 times negative 78 is not equal to -5226. The answer must therefore be 5226:

-67 x -78 = 5226

The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 67 times negative 78 will always have a positive answer.

Negative Times Negative Calculator
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