What is negative 3 times negative 35?




3 times 35 is 105, but what is the answer if both 3 and 35 are negative numbers? Here we will determine if the answer to negative 3 times negative 35 is positive 105 or negative 105.

There are many different ways to explain and determine if the answer to negative 3 times negative 35 is -105 or +105 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 -105 is the correct answer using basic algebra.

We will test if -105 is correct by setting up the equation negative 3 times negative 35 equals negative 105, and then simplifying the equation to see if it is true.

(-3) (-35) = (-105)

Divide both sides of the equation by (-35) :

   
(-3) (-35)
 
   
(-35)
 =
   
(-105)
 
   
(-35)

The numerator and denominator on the left side both have (-35) which even each other out and can be removed:

  (-3) =
   
(-105)
 
   
(-35)

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

  (-3) =
   
(105)
 
   
(35)

A numerator of 105 and denominator of 35 on the right side is the same as 105 divided by 35 which is 3. Now we end up with this untrue equation:

(-3) = (3)

-3 is NOT equal to 3, thus we have proven that negative 3 times negative 35 is not equal to -105. The answer must therefore be 105:

-3 x -35 = 105


The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 3 times negative 35 will always have a positive answer.

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What is negative 3 times negative 36?
Here is the next problem on our list that we have explained and calculated.


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