21 times 22 is 462, but what is the answer if both 21 and 22 are negative numbers? Here we will determine if the answer to negative 21 times negative 22 is positive 462 or negative 462.
There are many different ways to explain and determine if the answer to negative 21 times negative 22 is -462 or +462 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 -462 is the correct answer using basic algebra.
We will test if -462 is correct by setting up the equation negative 21 times negative 22 equals negative 462, and then simplifying the equation to see if it is true.
(-21) (-22) = (-462)
Divide both sides of the equation by (-22) :
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| = |
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The numerator and denominator on the left side both have (-22) which even each other out and can be removed:
| (-21) = |
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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:
| (-21) = |
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A numerator of 462 and denominator of 22 on the right side is the same as 462 divided by 22 which is 21. Now we end up with this untrue equation:
(-21) = (21)
-21 is NOT equal to 21, thus we have proven that negative 21 times negative 22 is not equal to -462. The answer must therefore be 462:
-21 x -22 = 462
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 21 times negative 22 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 21 times negative 23?
Here is the next problem on our list that we have explained and calculated.
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