52 times 61 is 3172, but what is the answer if both 52 and 61 are negative numbers? Here we will determine if the answer to negative 52 times negative 61 is positive 3172 or negative 3172.
There are many different ways to explain and determine if the answer to negative 52 times negative 61 is -3172 or +3172 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 -3172 is the correct answer using basic algebra.
We will test if -3172 is correct by setting up the equation negative 52 times negative 61 equals negative 3172, and then simplifying the equation to see if it is true.
(-52) (-61) = (-3172)
Divide both sides of the equation by (-61) :
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| = |
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The numerator and denominator on the left side both have (-61) 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 3172 and denominator of 61 on the right side is the same as 3172 divided by 61 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 61 is not equal to -3172. The answer must therefore be 3172:
-52 x -61 = 3172
The above applies to all math problems where you multiply two negative numbers. Multiplying two negative numbers such as negative 52 times negative 61 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 62?
Here is the next problem on our list that we have explained and calculated.
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