23 times 30 is 690, but what is the answer if both 23 and 30 are negative numbers? Here we will determine if the answer to negative 23 times negative 30 is positive 690 or negative 690.
There are many different ways to explain and determine if the answer to negative 23 times negative 30 is -690 or +690 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 -690 is the correct answer using basic algebra.
We will test if -690 is correct by setting up the equation negative 23 times negative 30 equals negative 690, and then simplifying the equation to see if it is true.
(-23) (-30) = (-690)
Divide both sides of the equation by (-30) :
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| = |
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The numerator and denominator on the left side both have (-30) which even each other out and can be removed:
| (-23) = |
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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:
| (-23) = |
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A numerator of 690 and denominator of 30 on the right side is the same as 690 divided by 30 which is 23. Now we end up with this untrue equation:
(-23) = (23)
-23 is NOT equal to 23, thus we have proven that negative 23 times negative 30 is not equal to -690. The answer must therefore be 690:
-23 x -30 = 690
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 23 times negative 30 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 23 times negative 31?
Here is the next problem on our list that we have explained and calculated.
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