What is negative 5 times negative 39?




5 times 39 is 195, but what is the answer if both 5 and 39 are negative numbers? Here we will determine if the answer to negative 5 times negative 39 is positive 195 or negative 195.

There are many different ways to explain and determine if the answer to negative 5 times negative 39 is -195 or +195 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 -195 is the correct answer using basic algebra.

We will test if -195 is correct by setting up the equation negative 5 times negative 39 equals negative 195, and then simplifying the equation to see if it is true.

(-5) (-39) = (-195)

Divide both sides of the equation by (-39) :

   
(-5) (-39)
 
   
(-39)
 =
   
(-195)
 
   
(-39)

The numerator and denominator on the left side both have (-39) which even each other out and can be removed:

  (-5) =
   
(-195)
 
   
(-39)

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

  (-5) =
   
(195)
 
   
(39)

A numerator of 195 and denominator of 39 on the right side is the same as 195 divided by 39 which is 5. Now we end up with this untrue equation:

(-5) = (5)

-5 is NOT equal to 5, thus we have proven that negative 5 times negative 39 is not equal to -195. The answer must therefore be 195:

-5 x -39 = 195


The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 5 times negative 39 will always have a positive answer.

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What is negative 5 times negative 40?
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