82 times 37 is 3034, but what is the answer if both 82 and 37 are negative numbers? Here we will determine if the answer to negative 82 times negative 37 is positive 3034 or negative 3034.
There are many different ways to explain and determine if the answer to negative 82 times negative 37 is -3034 or +3034 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 -3034 is the correct answer using basic algebra.
We will test if -3034 is correct by setting up the equation negative 82 times negative 37 equals negative 3034, and then simplifying the equation to see if it is true.
(-82) (-37) = (-3034)
Divide both sides of the equation by (-37) :
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| = |
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The numerator and denominator on the left side both have (-37) 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 3034 and denominator of 37 on the right side is the same as 3034 divided by 37 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 37 is not equal to -3034. The answer must therefore be 3034:
-82 x -37 = 3034
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 82 times negative 37 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 38?
Here is the next problem on our list that we have explained and calculated.
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