4 times 21 is 84, but what is the answer if both 4 and 21 are negative numbers? Here we will determine if the answer to negative 4 times negative 21 is positive 84 or negative 84.
There are many different ways to explain and determine if the answer to negative 4 times negative 21 is -84 or +84 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 -84 is the correct answer using basic algebra.
We will test if -84 is correct by setting up the equation negative 4 times negative 21 equals negative 84, and then simplifying the equation to see if it is true.
(-4) (-21) = (-84)
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:
| (-4) = |
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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:
| (-4) = |
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A numerator of 84 and denominator of 21 on the right side is the same as 84 divided by 21 which is 4. Now we end up with this untrue equation:
(-4) = (4)
-4 is NOT equal to 4, thus we have proven that negative 4 times negative 21 is not equal to -84. The answer must therefore be 84:
-4 x -21 = 84
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 4 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 4 times negative 22?
Here is the next problem on our list that we have explained and calculated.
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