9 times 45 is 405, but what is the answer if both 9 and 45 are negative numbers? Here we will determine if the answer to negative 9 times negative 45 is positive 405 or negative 405.
There are many different ways to explain and determine if the answer to negative 9 times negative 45 is -405 or +405 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 -405 is the correct answer using basic algebra.
We will test if -405 is correct by setting up the equation negative 9 times negative 45 equals negative 405, and then simplifying the equation to see if it is true.
(-9) (-45) = (-405)
Divide both sides of the equation by (-45) :
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| = |
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The numerator and denominator on the left side both have (-45) which even each other out and can be removed:
| (-9) = |
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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:
| (-9) = |
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A numerator of 405 and denominator of 45 on the right side is the same as 405 divided by 45 which is 9. Now we end up with this untrue equation:
(-9) = (9)
-9 is NOT equal to 9, thus we have proven that negative 9 times negative 45 is not equal to -405. The answer must therefore be 405:
-9 x -45 = 405
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 9 times negative 45 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 9 times negative 46?
Here is the next problem on our list that we have explained and calculated.
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