7 times 3 is 21, but what is the answer if both 7 and 3 are negative numbers? Here we will determine if the answer to negative 7 times negative 3 is positive 21 or negative 21.
There are many different ways to explain and determine if the answer to negative 7 times negative 3 is -21 or +21 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 -21 is the correct answer using basic algebra.
We will test if -21 is correct by setting up the equation negative 7 times negative 3 equals negative 21, and then simplifying the equation to see if it is true.
(-7) (-3) = (-21)
Divide both sides of the equation by (-3) :
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| = |
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The numerator and denominator on the left side both have (-3) which even each other out and can be removed:
| (-7) = |
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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:
| (-7) = |
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A numerator of 21 and denominator of 3 on the right side is the same as 21 divided by 3 which is 7. Now we end up with this untrue equation:
(-7) = (7)
-7 is NOT equal to 7, thus we have proven that negative 7 times negative 3 is not equal to -21. The answer must therefore be 21:
-7 x -3 = 21
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 7 times negative 3 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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