41 times 49 is 2009, but what is the answer if both 41 and 49 are negative numbers? Here we will determine if the answer to negative 41 times negative 49 is positive 2009 or negative 2009.
There are many different ways to explain and determine if the answer to negative 41 times negative 49 is -2009 or +2009 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 -2009 is the correct answer using basic algebra.
We will test if -2009 is correct by setting up the equation negative 41 times negative 49 equals negative 2009, and then simplifying the equation to see if it is true.
(-41) (-49) = (-2009)
Divide both sides of the equation by (-49) :
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| = |
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The numerator and denominator on the left side both have (-49) which even each other out and can be removed:
| (-41) = |
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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:
| (-41) = |
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A numerator of 2009 and denominator of 49 on the right side is the same as 2009 divided by 49 which is 41. Now we end up with this untrue equation:
(-41) = (41)
-41 is NOT equal to 41, thus we have proven that negative 41 times negative 49 is not equal to -2009. The answer must therefore be 2009:
-41 x -49 = 2009
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 41 times negative 49 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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