67 times 71 is 4757, but what is the answer if both 67 and 71 are negative numbers? Here we will determine if the answer to negative 67 times negative 71 is positive 4757 or negative 4757.
There are many different ways to explain and determine if the answer to negative 67 times negative 71 is -4757 or +4757 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 -4757 is the correct answer using basic algebra.
We will test if -4757 is correct by setting up the equation negative 67 times negative 71 equals negative 4757, and then simplifying the equation to see if it is true.
(-67) (-71) = (-4757)
Divide both sides of the equation by (-71) :
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| = |
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The numerator and denominator on the left side both have (-71) which even each other out and can be removed:
| (-67) = |
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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:
| (-67) = |
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A numerator of 4757 and denominator of 71 on the right side is the same as 4757 divided by 71 which is 67. Now we end up with this untrue equation:
(-67) = (67)
-67 is NOT equal to 67, thus we have proven that negative 67 times negative 71 is not equal to -4757. The answer must therefore be 4757:
-67 x -71 = 4757
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 67 times negative 71 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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Here is the next problem on our list that we have explained and calculated.
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