What is negative 9 times negative 5?




9 times 5 is 45, but what is the answer if both 9 and 5 are negative numbers? Here we will determine if the answer to negative 9 times negative 5 is positive 45 or negative 45.

There are many different ways to explain and determine if the answer to negative 9 times negative 5 is -45 or +45 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 -45 is the correct answer using basic algebra.

We will test if -45 is correct by setting up the equation negative 9 times negative 5 equals negative 45, and then simplifying the equation to see if it is true.

(-9) (-5) = (-45)

Divide both sides of the equation by (-5) :

   
(-9) (-5)
 
   
(-5)
 =
   
(-45)
 
   
(-5)

The numerator and denominator on the left side both have (-5) which even each other out and can be removed:

  (-9) =
   
(-45)
 
   
(-5)

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

  (-9) =
   
(45)
 
   
(5)

A numerator of 45 and denominator of 5 on the right side is the same as 45 divided by 5 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 5 is not equal to -45. The answer must therefore be 45:

-9 x -5 = 45


The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 9 times negative 5 will always have a positive answer.

Negative Times Negative Calculator
Here you can multiply another two negative numbers together.

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Here is the next problem on our list that we have explained and calculated.


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