What is negative 34 times negative 23? (-34 x -23)

What is negative 34 times negative 23?

34 times 23 is 782, but what is the answer if both 34 and 23 are negative numbers? Here we will determine if the answer to negative 34 times negative 23 is positive 782 or negative 782.

There are many different ways to explain and determine if the answer to negative 34 times negative 23 is -782 or +782 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 -782 is the correct answer using basic algebra.

We will test if -782 is correct by setting up the equation negative 34 times negative 23 equals negative 782, and then simplifying the equation to see if it is true.

(-34) (-23) = (-782)

Divide both sides of the equation by (-23) :

		(-34) (-23)
		(-23)

		(-782)
		(-23)

The numerator and denominator on the left side both have (-23) which even each other out and can be removed:

(-34) =

		(-782)
		(-23)

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

(-34) =

		(782)
		(23)

A numerator of 782 and denominator of 23 on the right side is the same as 782 divided by 23 which is 34. Now we end up with this untrue equation:

(-34) = (34)

-34 is NOT equal to 34, thus we have proven that negative 34 times negative 23 is not equal to -782. The answer must therefore be 782:

-34 x -23 = 782

The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 34 times negative 23 will always have a positive answer.

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