What is negative 36 times negative 9?




36 times 9 is 324, but what is the answer if both 36 and 9 are negative numbers? Here we will determine if the answer to negative 36 times negative 9 is positive 324 or negative 324.

There are many different ways to explain and determine if the answer to negative 36 times negative 9 is -324 or +324 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 -324 is the correct answer using basic algebra.

We will test if -324 is correct by setting up the equation negative 36 times negative 9 equals negative 324, and then simplifying the equation to see if it is true.

(-36) (-9) = (-324)

Divide both sides of the equation by (-9) :

   
(-36) (-9)
 
   
(-9)
 =
   
(-324)
 
   
(-9)

The numerator and denominator on the left side both have (-9) which even each other out and can be removed:

  (-36) =
   
(-324)
 
   
(-9)

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

  (-36) =
   
(324)
 
   
(9)

A numerator of 324 and denominator of 9 on the right side is the same as 324 divided by 9 which is 36. Now we end up with this untrue equation:

(-36) = (36)

-36 is NOT equal to 36, thus we have proven that negative 36 times negative 9 is not equal to -324. The answer must therefore be 324:

-36 x -9 = 324


The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 36 times negative 9 will always have a positive answer.

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What is negative 36 times negative 10?
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