What is negative 9 times negative 82? (-9 x -82)

What is negative 9 times negative 82?

9 times 82 is 738, but what is the answer if both 9 and 82 are negative numbers? Here we will determine if the answer to negative 9 times negative 82 is positive 738 or negative 738.

There are many different ways to explain and determine if the answer to negative 9 times negative 82 is -738 or +738 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 -738 is the correct answer using basic algebra.

We will test if -738 is correct by setting up the equation negative 9 times negative 82 equals negative 738, and then simplifying the equation to see if it is true.

(-9) (-82) = (-738)

Divide both sides of the equation by (-82) :

		(-9) (-82)
		(-82)

		(-738)
		(-82)

The numerator and denominator on the left side both have (-82) which even each other out and can be removed:

(-9) =

		(-738)
		(-82)

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

(-9) =

		(738)
		(82)

A numerator of 738 and denominator of 82 on the right side is the same as 738 divided by 82 which is 9. Now we end up with this untrue equation:

(-9) = (9)

-9 is NOT equal to 9, thus we have proven that negative 9 times negative 82 is not equal to -738. The answer must therefore be 738:

-9 x -82 = 738

The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 9 times negative 82 will always have a positive answer.

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