51 times 33 is 1683, but what is the answer if both 51 and 33 are negative numbers? Here we will determine if the answer to negative 51 times negative 33 is positive 1683 or negative 1683.
There are many different ways to explain and determine if the answer to negative 51 times negative 33 is -1683 or +1683 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 -1683 is the correct answer using basic algebra.
We will test if -1683 is correct by setting up the equation negative 51 times negative 33 equals negative 1683, and then simplifying the equation to see if it is true.
(-51) (-33) = (-1683)
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:
| (-51) = |
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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:
| (-51) = |
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A numerator of 1683 and denominator of 33 on the right side is the same as 1683 divided by 33 which is 51. Now we end up with this untrue equation:
(-51) = (51)
-51 is NOT equal to 51, thus we have proven that negative 51 times negative 33 is not equal to -1683. The answer must therefore be 1683:
-51 x -33 = 1683
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 51 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 51 times negative 34?
Here is the next problem on our list that we have explained and calculated.
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