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May 4th, 2008, 01:39 PM   #1
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Negetive number in fraction

What if the numerator or the denominator in a fraction is negative? Like -22 over 5? Can I turn it into a mixed fraction? Or if its -10 over 5 can I reduce it? Basically I need to now what I can do and not do with a negative in a fraction.
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May 4th, 2008, 03:11 PM   #2
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You can both mix it and reduce it. Let us look at your two examples and see how we can think of dealing with negative fractions.

-22/5
We know that 22/5 can be written at 4+2/5. Of course, it was negative before, so it should be negative now. So it can be written as -4 2/5 (or -4+- 2/5). We could think of this numerically. 22/5 = 4.4 . So -22/5 = -4.4 .
Well, -.4 is clearly -2/5, so -4.4=-4 + -.4 = -4+-2/5. Finally, we could think of -22/5 as -1*(22/5). We know we can rewrite 22/5 as 4 2/5, so we have -1*(4 2/5) = -4 2/5.

They all yield the same answer.

-10/5
Same ideas. -1*(10/5) = -1*2 = -2
10/5 = 2, so we take the negative --> -2
10/5 = 2, so -10/5 = -2

It's all on the same number line and they are all real numbers.
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May 17th, 2008, 10:32 PM   #3
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I thought I might interject to clarify what might be a future source of confusion for you that the previous post did not mention.

How do you think that you would handle 22/-5? What do you think that would mean?

Well, in terms of fractions you can do whatever you want with the negative. For example:

22 / -5 = ( 22 / -5 ) * ( -1 / -1 ) = -22 / 5

The lesson to be learned here is that anytime we have a negative in the denominator it really means the whole fraction is negative and we can just take it out in front.

The other possible case is when we have something like -22 / -5. In this case:

-22 / -5 = ( -1 * 22 ) / ( -1 * 5 ) = ( -1 / -1 ) * ( 22 / 5 ) = 22 / 5

Recall anything of the form c / c = 1. Also, although I am sure that you have had this beaten into you by now that, "A negative times a negative equals a positive."
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