7 times 12 is 84, but what is the answer if both 7 and 12 are negative numbers? Here we will determine if the answer to negative 7 times negative 12 is positive 84 or negative 84.
There are many different ways to explain and determine if the answer to negative 7 times negative 12 is -84 or +84 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 -84 is the correct answer using basic algebra.
We will test if -84 is correct by setting up the equation negative 7 times negative 12 equals negative 84, and then simplifying the equation to see if it is true.
(-7) (-12) = (-84)
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:
| (-7) = |
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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:
| (-7) = |
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A numerator of 84 and denominator of 12 on the right side is the same as 84 divided by 12 which is 7. Now we end up with this untrue equation:
(-7) = (7)
-7 is NOT equal to 7, thus we have proven that negative 7 times negative 12 is not equal to -84. The answer must therefore be 84:
-7 x -12 = 84
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 7 times negative 12 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 7 times negative 13?
Here is the next problem on our list that we have explained and calculated.
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