82 times 2 is 164, but what is the answer if both 82 and 2 are negative numbers? Here we will determine if the answer to negative 82 times negative 2 is positive 164 or negative 164.
There are many different ways to explain and determine if the answer to negative 82 times negative 2 is -164 or +164 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 -164 is the correct answer using basic algebra.
We will test if -164 is correct by setting up the equation negative 82 times negative 2 equals negative 164, and then simplifying the equation to see if it is true.
(-82) (-2) = (-164)
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:
| (-82) = |
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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:
| (-82) = |
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A numerator of 164 and denominator of 2 on the right side is the same as 164 divided by 2 which is 82. Now we end up with this untrue equation:
(-82) = (82)
-82 is NOT equal to 82, thus we have proven that negative 82 times negative 2 is not equal to -164. The answer must therefore be 164:
-82 x -2 = 164
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 82 times negative 2 will always have a positive answer.
Negative Times Negative Calculator
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