5 times 15 is 75, but what is the answer if both 5 and 15 are negative numbers? Here we will determine if the answer to negative 5 times negative 15 is positive 75 or negative 75.
There are many different ways to explain and determine if the answer to negative 5 times negative 15 is -75 or +75 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 -75 is the correct answer using basic algebra.
We will test if -75 is correct by setting up the equation negative 5 times negative 15 equals negative 75, and then simplifying the equation to see if it is true.
(-5) (-15) = (-75)
Divide both sides of the equation by (-15) :
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| = |
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The numerator and denominator on the left side both have (-15) 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 75 and denominator of 15 on the right side is the same as 75 divided by 15 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 15 is not equal to -75. The answer must therefore be 75:
-5 x -15 = 75
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 5 times negative 15 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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