52 times 65 is 3380, but what is the answer if both 52 and 65 are negative numbers? Here we will determine if the answer to negative 52 times negative 65 is positive 3380 or negative 3380.
There are many different ways to explain and determine if the answer to negative 52 times negative 65 is -3380 or +3380 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 -3380 is the correct answer using basic algebra.
We will test if -3380 is correct by setting up the equation negative 52 times negative 65 equals negative 3380, and then simplifying the equation to see if it is true.
(-52) (-65) = (-3380)
Divide both sides of the equation by (-65) :
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| = |
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The numerator and denominator on the left side both have (-65) which even each other out and can be removed:
| (-52) = |
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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:
| (-52) = |
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A numerator of 3380 and denominator of 65 on the right side is the same as 3380 divided by 65 which is 52. Now we end up with this untrue equation:
(-52) = (52)
-52 is NOT equal to 52, thus we have proven that negative 52 times negative 65 is not equal to -3380. The answer must therefore be 3380:
-52 x -65 = 3380
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 52 times negative 65 will always have a positive answer.
Negative Times Negative Calculator
Here you can multiply another two negative numbers together.
What is negative 52 times negative 66?
Here is the next problem on our list that we have explained and calculated.
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