67 times 21 is 1407, but what is the answer if both 67 and 21 are negative numbers? Here we will determine if the answer to negative 67 times negative 21 is positive 1407 or negative 1407.
There are many different ways to explain and determine if the answer to negative 67 times negative 21 is -1407 or +1407 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 -1407 is the correct answer using basic algebra.
We will test if -1407 is correct by setting up the equation negative 67 times negative 21 equals negative 1407, and then simplifying the equation to see if it is true.
(-67) (-21) = (-1407)
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:
| (-67) = |
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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:
| (-67) = |
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A numerator of 1407 and denominator of 21 on the right side is the same as 1407 divided by 21 which is 67. Now we end up with this untrue equation:
(-67) = (67)
-67 is NOT equal to 67, thus we have proven that negative 67 times negative 21 is not equal to -1407. The answer must therefore be 1407:
-67 x -21 = 1407
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 67 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 67 times negative 22?
Here is the next problem on our list that we have explained and calculated.
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