12 times 17 is 204, but what is the answer if both 12 and 17 are negative numbers? Here we will determine if the answer to negative 12 times negative 17 is positive 204 or negative 204.
There are many different ways to explain and determine if the answer to negative 12 times negative 17 is -204 or +204 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 -204 is the correct answer using basic algebra.
We will test if -204 is correct by setting up the equation negative 12 times negative 17 equals negative 204, and then simplifying the equation to see if it is true.
(-12) (-17) = (-204)
Divide both sides of the equation by (-17) :
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| = |
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The numerator and denominator on the left side both have (-17) which even each other out and can be removed:
| (-12) = |
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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:
| (-12) = |
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A numerator of 204 and denominator of 17 on the right side is the same as 204 divided by 17 which is 12. Now we end up with this untrue equation:
(-12) = (12)
-12 is NOT equal to 12, thus we have proven that negative 12 times negative 17 is not equal to -204. The answer must therefore be 204:
-12 x -17 = 204
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 12 times negative 17 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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