10 times 12 is 120, but what is the answer if both 10 and 12 are negative numbers? Here we will determine if the answer to negative 10 times negative 12 is positive 120 or negative 120.
There are many different ways to explain and determine if the answer to negative 10 times negative 12 is -120 or +120 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 -120 is the correct answer using basic algebra.
We will test if -120 is correct by setting up the equation negative 10 times negative 12 equals negative 120, and then simplifying the equation to see if it is true.
(-10) (-12) = (-120)
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:
| (-10) = |
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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:
| (-10) = |
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A numerator of 120 and denominator of 12 on the right side is the same as 120 divided by 12 which is 10. Now we end up with this untrue equation:
(-10) = (10)
-10 is NOT equal to 10, thus we have proven that negative 10 times negative 12 is not equal to -120. The answer must therefore be 120:
-10 x -12 = 120
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 10 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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