7 times 31 is 217, but what is the answer if both 7 and 31 are negative numbers? Here we will determine if the answer to negative 7 times negative 31 is positive 217 or negative 217.
There are many different ways to explain and determine if the answer to negative 7 times negative 31 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 7 times negative 31 equals negative 217, and then simplifying the equation to see if it is true.
(-7) (-31) = (-217)
Divide both sides of the equation by (-31) :
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| = |
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The numerator and denominator on the left side both have (-31) which even each other out and can be removed:
| (-7) = |
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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:
| (-7) = |
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A numerator of 217 and denominator of 31 on the right side is the same as 217 divided by 31 which is 7. Now we end up with this untrue equation:
(-7) = (7)
-7 is NOT equal to 7, thus we have proven that negative 7 times negative 31 is not equal to -217. The answer must therefore be 217:
-7 x -31 = 217
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 7 times negative 31 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 7 times negative 32?
Here is the next problem on our list that we have explained and calculated.
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