21 times 75 is 1575, but what is the answer if both 21 and 75 are negative numbers? Here we will determine if the answer to negative 21 times negative 75 is positive 1575 or negative 1575.
There are many different ways to explain and determine if the answer to negative 21 times negative 75 is -1575 or +1575 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 -1575 is the correct answer using basic algebra.
We will test if -1575 is correct by setting up the equation negative 21 times negative 75 equals negative 1575, and then simplifying the equation to see if it is true.
(-21) (-75) = (-1575)
Divide both sides of the equation by (-75) :
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| = |
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The numerator and denominator on the left side both have (-75) 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 1575 and denominator of 75 on the right side is the same as 1575 divided by 75 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 75 is not equal to -1575. The answer must therefore be 1575:
-21 x -75 = 1575
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 21 times negative 75 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 76?
Here is the next problem on our list that we have explained and calculated.
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