82 times 51 is 4182, but what is the answer if both 82 and 51 are negative numbers? Here we will determine if the answer to negative 82 times negative 51 is positive 4182 or negative 4182.
There are many different ways to explain and determine if the answer to negative 82 times negative 51 is -4182 or +4182 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 -4182 is the correct answer using basic algebra.
We will test if -4182 is correct by setting up the equation negative 82 times negative 51 equals negative 4182, and then simplifying the equation to see if it is true.
(-82) (-51) = (-4182)
Divide both sides of the equation by (-51) :
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| = |
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The numerator and denominator on the left side both have (-51) 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 4182 and denominator of 51 on the right side is the same as 4182 divided by 51 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 51 is not equal to -4182. The answer must therefore be 4182:
-82 x -51 = 4182
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 82 times negative 51 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 82 times negative 52?
Here is the next problem on our list that we have explained and calculated.
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