10 times 40 is 400, but what is the answer if both 10 and 40 are negative numbers? Here we will determine if the answer to negative 10 times negative 40 is positive 400 or negative 400.
There are many different ways to explain and determine if the answer to negative 10 times negative 40 is -400 or +400 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 -400 is the correct answer using basic algebra.
We will test if -400 is correct by setting up the equation negative 10 times negative 40 equals negative 400, and then simplifying the equation to see if it is true.
(-10) (-40) = (-400)
Divide both sides of the equation by (-40) :
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| = |
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The numerator and denominator on the left side both have (-40) which even each other out and can be removed:
| (-10) = |
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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:
| (-10) = |
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A numerator of 400 and denominator of 40 on the right side is the same as 400 divided by 40 which is 10. Now we end up with this untrue equation:
(-10) = (10)
-10 is NOT equal to 10, thus we have proven that negative 10 times negative 40 is not equal to -400. The answer must therefore be 400:
-10 x -40 = 400
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 10 times negative 40 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 10 times negative 41?
Here is the next problem on our list that we have explained and calculated.
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