72 times 3 is 216, but what is the answer if both 72 and 3 are negative numbers? Here we will determine if the answer to negative 72 times negative 3 is positive 216 or negative 216.
There are many different ways to explain and determine if the answer to negative 72 times negative 3 is -216 or +216 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 -216 is the correct answer using basic algebra.
We will test if -216 is correct by setting up the equation negative 72 times negative 3 equals negative 216, and then simplifying the equation to see if it is true.
(-72) (-3) = (-216)
Divide both sides of the equation by (-3) :
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| = |
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The numerator and denominator on the left side both have (-3) which even each other out and can be removed:
| (-72) = |
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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:
| (-72) = |
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A numerator of 216 and denominator of 3 on the right side is the same as 216 divided by 3 which is 72. Now we end up with this untrue equation:
(-72) = (72)
-72 is NOT equal to 72, thus we have proven that negative 72 times negative 3 is not equal to -216. The answer must therefore be 216:
-72 x -3 = 216
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 72 times negative 3 will always have a positive answer.
Negative Times Negative Calculator
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