83 times 2 is 166, but what is the answer if both 83 and 2 are negative numbers? Here we will determine if the answer to negative 83 times negative 2 is positive 166 or negative 166.
There are many different ways to explain and determine if the answer to negative 83 times negative 2 is -166 or +166 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 -166 is the correct answer using basic algebra.
We will test if -166 is correct by setting up the equation negative 83 times negative 2 equals negative 166, and then simplifying the equation to see if it is true.
(-83) (-2) = (-166)
Divide both sides of the equation by (-2) :
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| = |
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The numerator and denominator on the left side both have (-2) which even each other out and can be removed:
| (-83) = |
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The numerator and denominator on the right side both have a minus sign (-) which even each other out and can be removed:
| (-83) = |
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A numerator of 166 and denominator of 2 on the right side is the same as 166 divided by 2 which is 83. Now we end up with this untrue equation:
(-83) = (83)
-83 is NOT equal to 83, thus we have proven that negative 83 times negative 2 is not equal to -166. The answer must therefore be 166:
-83 x -2 = 166
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 83 times negative 2 will always have a positive answer.
Negative Times Negative Calculator
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