9 times 12 is 108, but what is the answer if both 9 and 12 are negative numbers? Here we will determine if the answer to negative 9 times negative 12 is positive 108 or negative 108.
There are many different ways to explain and determine if the answer to negative 9 times negative 12 is -108 or +108 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 -108 is the correct answer using basic algebra.
We will test if -108 is correct by setting up the equation negative 9 times negative 12 equals negative 108, and then simplifying the equation to see if it is true.
(-9) (-12) = (-108)
Divide both sides of the equation by (-12) :
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| = |
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The numerator and denominator on the left side both have (-12) which even each other out and can be removed:
| (-9) = |
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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:
| (-9) = |
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A numerator of 108 and denominator of 12 on the right side is the same as 108 divided by 12 which is 9. Now we end up with this untrue equation:
(-9) = (9)
-9 is NOT equal to 9, thus we have proven that negative 9 times negative 12 is not equal to -108. The answer must therefore be 108:
-9 x -12 = 108
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 9 times negative 12 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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Here is the next problem on our list that we have explained and calculated.
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