5 times 21 is 105, but what is the answer if both 5 and 21 are negative numbers? Here we will determine if the answer to negative 5 times negative 21 is positive 105 or negative 105.
There are many different ways to explain and determine if the answer to negative 5 times negative 21 is -105 or +105 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 -105 is the correct answer using basic algebra.
We will test if -105 is correct by setting up the equation negative 5 times negative 21 equals negative 105, and then simplifying the equation to see if it is true.
(-5) (-21) = (-105)
Divide both sides of the equation by (-21) :
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| = |
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The numerator and denominator on the left side both have (-21) which even each other out and can be removed:
| (-5) = |
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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:
| (-5) = |
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A numerator of 105 and denominator of 21 on the right side is the same as 105 divided by 21 which is 5. Now we end up with this untrue equation:
(-5) = (5)
-5 is NOT equal to 5, thus we have proven that negative 5 times negative 21 is not equal to -105. The answer must therefore be 105:
-5 x -21 = 105
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 5 times negative 21 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 5 times negative 22?
Here is the next problem on our list that we have explained and calculated.
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