31 times 84 is 2604, but what is the answer if both 31 and 84 are negative numbers? Here we will determine if the answer to negative 31 times negative 84 is positive 2604 or negative 2604.
There are many different ways to explain and determine if the answer to negative 31 times negative 84 is -2604 or +2604 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 -2604 is the correct answer using basic algebra.
We will test if -2604 is correct by setting up the equation negative 31 times negative 84 equals negative 2604, and then simplifying the equation to see if it is true.
(-31) (-84) = (-2604)
Divide both sides of the equation by (-84) :
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| = |
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The numerator and denominator on the left side both have (-84) which even each other out and can be removed:
| (-31) = |
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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:
| (-31) = |
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A numerator of 2604 and denominator of 84 on the right side is the same as 2604 divided by 84 which is 31. Now we end up with this untrue equation:
(-31) = (31)
-31 is NOT equal to 31, thus we have proven that negative 31 times negative 84 is not equal to -2604. The answer must therefore be 2604:
-31 x -84 = 2604
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 31 times negative 84 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 31 times negative 85?
Here is the next problem on our list that we have explained and calculated.
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