30 times 67 is 2010, but what is the answer if both 30 and 67 are negative numbers? Here we will determine if the answer to negative 30 times negative 67 is positive 2010 or negative 2010.
There are many different ways to explain and determine if the answer to negative 30 times negative 67 is -2010 or +2010 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 -2010 is the correct answer using basic algebra.
We will test if -2010 is correct by setting up the equation negative 30 times negative 67 equals negative 2010, and then simplifying the equation to see if it is true.
(-30) (-67) = (-2010)
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:
| (-30) = |
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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:
| (-30) = |
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A numerator of 2010 and denominator of 67 on the right side is the same as 2010 divided by 67 which is 30. Now we end up with this untrue equation:
(-30) = (30)
-30 is NOT equal to 30, thus we have proven that negative 30 times negative 67 is not equal to -2010. The answer must therefore be 2010:
-30 x -67 = 2010
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 30 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 30 times negative 68?
Here is the next problem on our list that we have explained and calculated.
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