78 times 7 is 546, but what is the answer if both 78 and 7 are negative numbers? Here we will determine if the answer to negative 78 times negative 7 is positive 546 or negative 546.
There are many different ways to explain and determine if the answer to negative 78 times negative 7 is -546 or +546 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 -546 is the correct answer using basic algebra.
We will test if -546 is correct by setting up the equation negative 78 times negative 7 equals negative 546, and then simplifying the equation to see if it is true.
(-78) (-7) = (-546)
Divide both sides of the equation by (-7) :
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| = |
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The numerator and denominator on the left side both have (-7) which even each other out and can be removed:
| (-78) = |
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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:
| (-78) = |
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A numerator of 546 and denominator of 7 on the right side is the same as 546 divided by 7 which is 78. Now we end up with this untrue equation:
(-78) = (78)
-78 is NOT equal to 78, thus we have proven that negative 78 times negative 7 is not equal to -546. The answer must therefore be 546:
-78 x -7 = 546
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 78 times negative 7 will always have a positive answer.
Negative Times Negative Calculator
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