53 times 13 is 689, but what is the answer if both 53 and 13 are negative numbers? Here we will determine if the answer to negative 53 times negative 13 is positive 689 or negative 689.
There are many different ways to explain and determine if the answer to negative 53 times negative 13 is -689 or +689 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 -689 is the correct answer using basic algebra.
We will test if -689 is correct by setting up the equation negative 53 times negative 13 equals negative 689, and then simplifying the equation to see if it is true.
(-53) (-13) = (-689)
Divide both sides of the equation by (-13) :
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| = |
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The numerator and denominator on the left side both have (-13) which even each other out and can be removed:
| (-53) = |
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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:
| (-53) = |
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A numerator of 689 and denominator of 13 on the right side is the same as 689 divided by 13 which is 53. Now we end up with this untrue equation:
(-53) = (53)
-53 is NOT equal to 53, thus we have proven that negative 53 times negative 13 is not equal to -689. The answer must therefore be 689:
-53 x -13 = 689
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 53 times negative 13 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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