31 times 33 is 1023, but what is the answer if both 31 and 33 are negative numbers? Here we will determine if the answer to negative 31 times negative 33 is positive 1023 or negative 1023.
There are many different ways to explain and determine if the answer to negative 31 times negative 33 is -1023 or +1023 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 -1023 is the correct answer using basic algebra.
We will test if -1023 is correct by setting up the equation negative 31 times negative 33 equals negative 1023, and then simplifying the equation to see if it is true.
(-31) (-33) = (-1023)
Divide both sides of the equation by (-33) :
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| = |
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The numerator and denominator on the left side both have (-33) 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 1023 and denominator of 33 on the right side is the same as 1023 divided by 33 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 33 is not equal to -1023. The answer must therefore be 1023:
-31 x -33 = 1023
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 31 times negative 33 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 34?
Here is the next problem on our list that we have explained and calculated.
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