5 times 7 is 35, but what is the answer if both 5 and 7 are negative numbers? Here we will determine if the answer to negative 5 times negative 7 is positive 35 or negative 35.
There are many different ways to explain and determine if the answer to negative 5 times negative 7 is -35 or +35 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 -35 is the correct answer using basic algebra.
We will test if -35 is correct by setting up the equation negative 5 times negative 7 equals negative 35, and then simplifying the equation to see if it is true.
(-5) (-7) = (-35)
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:
| (-5) = |
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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:
| (-5) = |
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A numerator of 35 and denominator of 7 on the right side is the same as 35 divided by 7 which is 5. Now we end up with this untrue equation:
(-5) = (5)
-5 is NOT equal to 5, thus we have proven that negative 5 times negative 7 is not equal to -35. The answer must therefore be 35:
-5 x -7 = 35
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 5 times negative 7 will always have a positive answer.
Negative Times Negative Calculator
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