51 times 2 is 102, but what is the answer if both 51 and 2 are negative numbers? Here we will determine if the answer to negative 51 times negative 2 is positive 102 or negative 102.
There are many different ways to explain and determine if the answer to negative 51 times negative 2 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 51 times negative 2 equals negative 102, and then simplifying the equation to see if it is true.
(-51) (-2) = (-102)
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:
| (-51) = |
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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:
| (-51) = |
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A numerator of 102 and denominator of 2 on the right side is the same as 102 divided by 2 which is 51. Now we end up with this untrue equation:
(-51) = (51)
-51 is NOT equal to 51, thus we have proven that negative 51 times negative 2 is not equal to -102. The answer must therefore be 102:
-51 x -2 = 102
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 51 times negative 2 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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