30 times 7 is 210, but what is the answer if both 30 and 7 are negative numbers? Here we will determine if the answer to negative 30 times negative 7 is positive 210 or negative 210.
There are many different ways to explain and determine if the answer to negative 30 times negative 7 is -210 or +210 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 -210 is the correct answer using basic algebra.
We will test if -210 is correct by setting up the equation negative 30 times negative 7 equals negative 210, and then simplifying the equation to see if it is true.
(-30) (-7) = (-210)
Divide both sides of the equation by (-7) :
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| = |
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The numerator and denominator on the left side both have (-7) 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 210 and denominator of 7 on the right side is the same as 210 divided by 7 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 7 is not equal to -210. The answer must therefore be 210:
-30 x -7 = 210
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 30 times negative 7 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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