33 times 5 is 165, but what is the answer if both 33 and 5 are negative numbers? Here we will determine if the answer to negative 33 times negative 5 is positive 165 or negative 165.
There are many different ways to explain and determine if the answer to negative 33 times negative 5 is -165 or +165 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 -165 is the correct answer using basic algebra.
We will test if -165 is correct by setting up the equation negative 33 times negative 5 equals negative 165, and then simplifying the equation to see if it is true.
(-33) (-5) = (-165)
Divide both sides of the equation by (-5) :
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| = |
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The numerator and denominator on the left side both have (-5) which even each other out and can be removed:
| (-33) = |
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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:
| (-33) = |
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A numerator of 165 and denominator of 5 on the right side is the same as 165 divided by 5 which is 33. Now we end up with this untrue equation:
(-33) = (33)
-33 is NOT equal to 33, thus we have proven that negative 33 times negative 5 is not equal to -165. The answer must therefore be 165:
-33 x -5 = 165
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 33 times negative 5 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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