97 times 31 is 3007, but what is the answer if both 97 and 31 are negative numbers? Here we will determine if the answer to negative 97 times negative 31 is positive 3007 or negative 3007.
There are many different ways to explain and determine if the answer to negative 97 times negative 31 is -3007 or +3007 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 -3007 is the correct answer using basic algebra.
We will test if -3007 is correct by setting up the equation negative 97 times negative 31 equals negative 3007, and then simplifying the equation to see if it is true.
(-97) (-31) = (-3007)
Divide both sides of the equation by (-31) :
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| = |
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The numerator and denominator on the left side both have (-31) which even each other out and can be removed:
| (-97) = |
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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:
| (-97) = |
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A numerator of 3007 and denominator of 31 on the right side is the same as 3007 divided by 31 which is 97. Now we end up with this untrue equation:
(-97) = (97)
-97 is NOT equal to 97, thus we have proven that negative 97 times negative 31 is not equal to -3007. The answer must therefore be 3007:
-97 x -31 = 3007
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 97 times negative 31 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 97 times negative 32?
Here is the next problem on our list that we have explained and calculated.
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