3 times 11 is 33, but what is the answer if both 3 and 11 are negative numbers? Here we will determine if the answer to negative 3 times negative 11 is positive 33 or negative 33.
There are many different ways to explain and determine if the answer to negative 3 times negative 11 is -33 or +33 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 -33 is the correct answer using basic algebra.
We will test if -33 is correct by setting up the equation negative 3 times negative 11 equals negative 33, and then simplifying the equation to see if it is true.
(-3) (-11) = (-33)
Divide both sides of the equation by (-11) :
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| = |
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The numerator and denominator on the left side both have (-11) 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 33 and denominator of 11 on the right side is the same as 33 divided by 11 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 11 is not equal to -33. The answer must therefore be 33:
-3 x -11 = 33
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 3 times negative 11 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 12?
Here is the next problem on our list that we have explained and calculated.
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