SOLUTION: I am havig difficulty determining the value of a determinant when there are fractions. Is there a short, easy way for me to evaluate? For example: |3/4 3/4| |1/16 -1/8|

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Question 616252: I am havig difficulty determining the value of a determinant when there are fractions. Is there a short, easy way for me to evaluate? For example:
|3/4 3/4|
|1/16 -1/8|
I know the following:
(3/4)(-1/8)-(1/16)(3/4) = -3/32-3/64 = -9/64

what I cant explain is the numberator. Where is the -9 coming from? Please help!
Answer by dragonwalker(73) (Show Source):
You can put this solution on YOUR website!
(3/4)(-1/8)-(1/16)(3/4) = -3/32-3/64 = -9/64
Look at the denominator of the final two parts.
Notice you have -3/32 but then -3/64 and the result is -9/64
If you just use -3 -3 to figure out the final numerator then you are not accounting for the size that each numerator represents.
Picture a fraction as pieces of pie fitting into a pie pan. The denominator tells you how many slices fit into the pan. The bigger the denominator the smaller each piece of pie is.
So if you have a fraction that has a denominator of 64 each unit of a numerator represents a smaller size than if the denominator is 32 (64 pieces of pie fitting in a pie pan rather than 32)
Before adding or subtracting the numerators you need to make the denominators the same size.
The easiest way is to see if the smaller denominator(s) fit in the largest denominator. In this case 32 fits into 64 twice.
However if you change 3/32's denominator to 64 you have to take into account that each numerator has to represent a smaller piece. In fact in this case they have to be half the size so that 64 pieces could fit into a whole pie (or a whole number). So if you cut three pieces of pie into half each you will get twice as many pieces so you would now have 6 pieces of pie.
The easiest way to remember this is if you are multiplying the denominator by a certain number, the numerator has to be multiplied by the same number to keep the fraction the same size.
So -3/32 becomes -6/64
Now if you type the formula again you get:
-6/64 - 3/64 = -9/64