45 times 4 is 180, but what is the answer if both 45 and 4 are negative numbers? Here we will determine if the answer to negative 45 times negative 4 is positive 180 or negative 180.
There are many different ways to explain and determine if the answer to negative 45 times negative 4 is -180 or +180 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 -180 is the correct answer using basic algebra.
We will test if -180 is correct by setting up the equation negative 45 times negative 4 equals negative 180, and then simplifying the equation to see if it is true.
(-45) (-4) = (-180)
Divide both sides of the equation by (-4) :
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| = |
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The numerator and denominator on the left side both have (-4) which even each other out and can be removed:
| (-45) = |
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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:
| (-45) = |
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A numerator of 180 and denominator of 4 on the right side is the same as 180 divided by 4 which is 45. Now we end up with this untrue equation:
(-45) = (45)
-45 is NOT equal to 45, thus we have proven that negative 45 times negative 4 is not equal to -180. The answer must therefore be 180:
-45 x -4 = 180
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 45 times negative 4 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
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