5 times 83 is 415, but what is the answer if both 5 and 83 are negative numbers? Here we will determine if the answer to negative 5 times negative 83 is positive 415 or negative 415.
There are many different ways to explain and determine if the answer to negative 5 times negative 83 is -415 or +415 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 -415 is the correct answer using basic algebra.
We will test if -415 is correct by setting up the equation negative 5 times negative 83 equals negative 415, and then simplifying the equation to see if it is true.
(-5) (-83) = (-415)
Divide both sides of the equation by (-83) :
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| = |
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The numerator and denominator on the left side both have (-83) 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 415 and denominator of 83 on the right side is the same as 415 divided by 83 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 83 is not equal to -415. The answer must therefore be 415:
-5 x -83 = 415
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 5 times negative 83 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 5 times negative 84?
Here is the next problem on our list that we have explained and calculated.
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