What is negative 4 times negative 81?




4 times 81 is 324, but what is the answer if both 4 and 81 are negative numbers? Here we will determine if the answer to negative 4 times negative 81 is positive 324 or negative 324.

There are many different ways to explain and determine if the answer to negative 4 times negative 81 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 4 times negative 81 equals negative 324, and then simplifying the equation to see if it is true.

(-4) (-81) = (-324)

Divide both sides of the equation by (-81) :

   
(-4) (-81)
 
   
(-81)
 =
   
(-324)
 
   
(-81)

The numerator and denominator on the left side both have (-81) which even each other out and can be removed:

  (-4) =
   
(-324)
 
   
(-81)

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

  (-4) =
   
(324)
 
   
(81)

A numerator of 324 and denominator of 81 on the right side is the same as 324 divided by 81 which is 4. Now we end up with this untrue equation:

(-4) = (4)

-4 is NOT equal to 4, thus we have proven that negative 4 times negative 81 is not equal to -324. The answer must therefore be 324:

-4 x -81 = 324


The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 4 times negative 81 will always have a positive answer.

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What is negative 4 times negative 82?
Here is the next problem on our list that we have explained and calculated.


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