3 times 9 is 27, but what is the answer if both 3 and 9 are negative numbers? Here we will determine if the answer to negative 3 times negative 9 is positive 27 or negative 27.
There are many different ways to explain and determine if the answer to negative 3 times negative 9 is -27 or +27 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 -27 is the correct answer using basic algebra.
We will test if -27 is correct by setting up the equation negative 3 times negative 9 equals negative 27, and then simplifying the equation to see if it is true.
(-3) (-9) = (-27)
Divide both sides of the equation by (-9) :
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| = |
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The numerator and denominator on the left side both have (-9) which even each other out and can be removed:
| (-3) = |
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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:
| (-3) = |
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A numerator of 27 and denominator of 9 on the right side is the same as 27 divided by 9 which is 3. Now we end up with this untrue equation:
(-3) = (3)
-3 is NOT equal to 3, thus we have proven that negative 3 times negative 9 is not equal to -27. The answer must therefore be 27:
-3 x -9 = 27
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 3 times negative 9 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 3 times negative 10?
Here is the next problem on our list that we have explained and calculated.
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