97 times 78 is 7566, but what is the answer if both 97 and 78 are negative numbers? Here we will determine if the answer to negative 97 times negative 78 is positive 7566 or negative 7566.
There are many different ways to explain and determine if the answer to negative 97 times negative 78 is -7566 or +7566 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 -7566 is the correct answer using basic algebra.
We will test if -7566 is correct by setting up the equation negative 97 times negative 78 equals negative 7566, and then simplifying the equation to see if it is true.
(-97) (-78) = (-7566)
Divide both sides of the equation by (-78) :
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| = |
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The numerator and denominator on the left side both have (-78) 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 7566 and denominator of 78 on the right side is the same as 7566 divided by 78 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 78 is not equal to -7566. The answer must therefore be 7566:
-97 x -78 = 7566
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 97 times negative 78 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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