8 times 51 is 408, but what is the answer if both 8 and 51 are negative numbers? Here we will determine if the answer to negative 8 times negative 51 is positive 408 or negative 408.
There are many different ways to explain and determine if the answer to negative 8 times negative 51 is -408 or +408 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 -408 is the correct answer using basic algebra.
We will test if -408 is correct by setting up the equation negative 8 times negative 51 equals negative 408, and then simplifying the equation to see if it is true.
(-8) (-51) = (-408)
Divide both sides of the equation by (-51) :
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| = |
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The numerator and denominator on the left side both have (-51) which even each other out and can be removed:
| (-8) = |
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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:
| (-8) = |
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A numerator of 408 and denominator of 51 on the right side is the same as 408 divided by 51 which is 8. Now we end up with this untrue equation:
(-8) = (8)
-8 is NOT equal to 8, thus we have proven that negative 8 times negative 51 is not equal to -408. The answer must therefore be 408:
-8 x -51 = 408
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 8 times negative 51 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 8 times negative 52?
Here is the next problem on our list that we have explained and calculated.
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