81 times 5 is 405, but what is the answer if both 81 and 5 are negative numbers? Here we will determine if the answer to negative 81 times negative 5 is positive 405 or negative 405.
There are many different ways to explain and determine if the answer to negative 81 times negative 5 is -405 or +405 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 -405 is the correct answer using basic algebra.
We will test if -405 is correct by setting up the equation negative 81 times negative 5 equals negative 405, and then simplifying the equation to see if it is true.
(-81) (-5) = (-405)
Divide both sides of the equation by (-5) :
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| = |
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The numerator and denominator on the left side both have (-5) which even each other out and can be removed:
| (-81) = |
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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:
| (-81) = |
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A numerator of 405 and denominator of 5 on the right side is the same as 405 divided by 5 which is 81. Now we end up with this untrue equation:
(-81) = (81)
-81 is NOT equal to 81, thus we have proven that negative 81 times negative 5 is not equal to -405. The answer must therefore be 405:
-81 x -5 = 405
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 81 times negative 5 will always have a positive answer.
Negative Times Negative Calculator
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