What is negative 3 times negative 34?




3 times 34 is 102, but what is the answer if both 3 and 34 are negative numbers? Here we will determine if the answer to negative 3 times negative 34 is positive 102 or negative 102.

There are many different ways to explain and determine if the answer to negative 3 times negative 34 is -102 or +102 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 -102 is the correct answer using basic algebra.

We will test if -102 is correct by setting up the equation negative 3 times negative 34 equals negative 102, and then simplifying the equation to see if it is true.

(-3) (-34) = (-102)

Divide both sides of the equation by (-34) :

   
(-3) (-34)
 
   
(-34)
 =
   
(-102)
 
   
(-34)

The numerator and denominator on the left side both have (-34) which even each other out and can be removed:

  (-3) =
   
(-102)
 
   
(-34)

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

  (-3) =
   
(102)
 
   
(34)

A numerator of 102 and denominator of 34 on the right side is the same as 102 divided by 34 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 34 is not equal to -102. The answer must therefore be 102:

-3 x -34 = 102


The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 3 times negative 34 will always have a positive answer.

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What is negative 3 times negative 35?
Here is the next problem on our list that we have explained and calculated.


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