84 times 5 is 420, but what is the answer if both 84 and 5 are negative numbers? Here we will determine if the answer to negative 84 times negative 5 is positive 420 or negative 420.
There are many different ways to explain and determine if the answer to negative 84 times negative 5 is -420 or +420 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 -420 is the correct answer using basic algebra.
We will test if -420 is correct by setting up the equation negative 84 times negative 5 equals negative 420, and then simplifying the equation to see if it is true.
(-84) (-5) = (-420)
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:
| (-84) = |
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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:
| (-84) = |
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A numerator of 420 and denominator of 5 on the right side is the same as 420 divided by 5 which is 84. Now we end up with this untrue equation:
(-84) = (84)
-84 is NOT equal to 84, thus we have proven that negative 84 times negative 5 is not equal to -420. The answer must therefore be 420:
-84 x -5 = 420
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 84 times negative 5 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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