52 times 77 is 4004, but what is the answer if both 52 and 77 are negative numbers? Here we will determine if the answer to negative 52 times negative 77 is positive 4004 or negative 4004.
There are many different ways to explain and determine if the answer to negative 52 times negative 77 is -4004 or +4004 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 -4004 is the correct answer using basic algebra.
We will test if -4004 is correct by setting up the equation negative 52 times negative 77 equals negative 4004, and then simplifying the equation to see if it is true.
(-52) (-77) = (-4004)
Divide both sides of the equation by (-77) :
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| = |
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The numerator and denominator on the left side both have (-77) which even each other out and can be removed:
| (-52) = |
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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:
| (-52) = |
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A numerator of 4004 and denominator of 77 on the right side is the same as 4004 divided by 77 which is 52. Now we end up with this untrue equation:
(-52) = (52)
-52 is NOT equal to 52, thus we have proven that negative 52 times negative 77 is not equal to -4004. The answer must therefore be 4004:
-52 x -77 = 4004
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 52 times negative 77 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 52 times negative 78?
Here is the next problem on our list that we have explained and calculated.
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