31 times 7 is 217, but what is the answer if both 31 and 7 are negative numbers? Here we will determine if the answer to negative 31 times negative 7 is positive 217 or negative 217.
There are many different ways to explain and determine if the answer to negative 31 times negative 7 is -217 or +217 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 -217 is the correct answer using basic algebra.
We will test if -217 is correct by setting up the equation negative 31 times negative 7 equals negative 217, and then simplifying the equation to see if it is true.
(-31) (-7) = (-217)
Divide both sides of the equation by (-7) :
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| = |
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The numerator and denominator on the left side both have (-7) 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 217 and denominator of 7 on the right side is the same as 217 divided by 7 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 7 is not equal to -217. The answer must therefore be 217:
-31 x -7 = 217
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 31 times negative 7 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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