51 times 67 is 3417, but what is the answer if both 51 and 67 are negative numbers? Here we will determine if the answer to negative 51 times negative 67 is positive 3417 or negative 3417.
There are many different ways to explain and determine if the answer to negative 51 times negative 67 is -3417 or +3417 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 -3417 is the correct answer using basic algebra.
We will test if -3417 is correct by setting up the equation negative 51 times negative 67 equals negative 3417, and then simplifying the equation to see if it is true.
(-51) (-67) = (-3417)
Divide both sides of the equation by (-67) :
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| = |
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The numerator and denominator on the left side both have (-67) 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 3417 and denominator of 67 on the right side is the same as 3417 divided by 67 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 67 is not equal to -3417. The answer must therefore be 3417:
-51 x -67 = 3417
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 51 times negative 67 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 68?
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