8 times 21 is 168, but what is the answer if both 8 and 21 are negative numbers? Here we will determine if the answer to negative 8 times negative 21 is positive 168 or negative 168.
There are many different ways to explain and determine if the answer to negative 8 times negative 21 is -168 or +168 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 -168 is the correct answer using basic algebra.
We will test if -168 is correct by setting up the equation negative 8 times negative 21 equals negative 168, and then simplifying the equation to see if it is true.
(-8) (-21) = (-168)
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:
| (-8) = |
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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:
| (-8) = |
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A numerator of 168 and denominator of 21 on the right side is the same as 168 divided by 21 which is 8. Now we end up with this untrue equation:
(-8) = (8)
-8 is NOT equal to 8, thus we have proven that negative 8 times negative 21 is not equal to -168. The answer must therefore be 168:
-8 x -21 = 168
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 8 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 8 times negative 22?
Here is the next problem on our list that we have explained and calculated.
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