82 times 5 is 410, but what is the answer if both 82 and 5 are negative numbers? Here we will determine if the answer to negative 82 times negative 5 is positive 410 or negative 410.
There are many different ways to explain and determine if the answer to negative 82 times negative 5 is -410 or +410 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 -410 is the correct answer using basic algebra.
We will test if -410 is correct by setting up the equation negative 82 times negative 5 equals negative 410, and then simplifying the equation to see if it is true.
(-82) (-5) = (-410)
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:
| (-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 410 and denominator of 5 on the right side is the same as 410 divided by 5 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 5 is not equal to -410. The answer must therefore be 410:
-82 x -5 = 410
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 82 times negative 5 will always have a positive answer.
Negative Times Negative Calculator
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