17 times 3 is 51, but what is the answer if both 17 and 3 are negative numbers? Here we will determine if the answer to negative 17 times negative 3 is positive 51 or negative 51.
There are many different ways to explain and determine if the answer to negative 17 times negative 3 is -51 or +51 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 -51 is the correct answer using basic algebra.
We will test if -51 is correct by setting up the equation negative 17 times negative 3 equals negative 51, and then simplifying the equation to see if it is true.
(-17) (-3) = (-51)
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:
| (-17) = |
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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:
| (-17) = |
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A numerator of 51 and denominator of 3 on the right side is the same as 51 divided by 3 which is 17. Now we end up with this untrue equation:
(-17) = (17)
-17 is NOT equal to 17, thus we have proven that negative 17 times negative 3 is not equal to -51. The answer must therefore be 51:
-17 x -3 = 51
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 17 times negative 3 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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