31 times 17 is 527, but what is the answer if both 31 and 17 are negative numbers? Here we will determine if the answer to negative 31 times negative 17 is positive 527 or negative 527.
There are many different ways to explain and determine if the answer to negative 31 times negative 17 is -527 or +527 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 -527 is the correct answer using basic algebra.
We will test if -527 is correct by setting up the equation negative 31 times negative 17 equals negative 527, and then simplifying the equation to see if it is true.
(-31) (-17) = (-527)
Divide both sides of the equation by (-17) :
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| = |
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The numerator and denominator on the left side both have (-17) 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 527 and denominator of 17 on the right side is the same as 527 divided by 17 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 17 is not equal to -527. The answer must therefore be 527:
-31 x -17 = 527
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 31 times negative 17 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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