3 times 5 is 15, but what is the answer if both 3 and 5 are negative numbers? Here we will determine if the answer to negative 3 times negative 5 is positive 15 or negative 15.
There are many different ways to explain and determine if the answer to negative 3 times negative 5 is -15 or +15 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 -15 is the correct answer using basic algebra.
We will test if -15 is correct by setting up the equation negative 3 times negative 5 equals negative 15, and then simplifying the equation to see if it is true.
(-3) (-5) = (-15)
Divide both sides of the equation by (-5) :
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| = |
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The numerator and denominator on the left side both have (-5) which even each other out and can be removed:
| (-3) = |
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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:
| (-3) = |
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A numerator of 15 and denominator of 5 on the right side is the same as 15 divided by 5 which is 3. Now we end up with this untrue equation:
(-3) = (3)
-3 is NOT equal to 3, thus we have proven that negative 3 times negative 5 is not equal to -15. The answer must therefore be 15:
-3 x -5 = 15
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 3 times negative 5 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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