Negative fractions - what's the difference?What's the difference between the following fractions:−4−54−5−45−45

The first one is 45. The other three are all −45.

Another way to think about this would be in terms of equivalence classes. If you are not familiar with this, it is pretty much how mathematicians say in the rationals that12=24=48.In fact one says that given two fractionsx=mn and y=ab,they are equal iff mb−na=0. So in your case for example −45 and −45 are equal because−45−((−1)45)=−45+45=−4+45=0recalling that −45=(−1)45. You can go on like this for all of them, e.g. for example the first and second are not equal because−4−5−4−5=−4−45≠0.

The first one is 45. The other three are all −45.

Another way to think about this would be in terms of equivalence classes. If you are not familiar with this, it is pretty much how mathematicians say in the rationals that12=24=48.In fact one says that given two fractionsx=mn and y=ab,they are equal iff mb−na=0. So in your case for example −45 and −45 are equal because−45−((−1)45)=−45+45=−4+45=0recalling that −45=(−1)45. You can go on like this for all of them, e.g. for example the first and second are not equal because−4−5−4−5=−4−45≠0.

Find out the answer to "Negative fractions - what's the difference?What's the difference..."

bacfrancaiso0j

Answered question

2022-04-23

Negative fractions - what's the difference?
What's the difference between the following fractions:

\frac{- 4}{- 5}

\frac{4}{- 5}

\frac{- 4}{5}

- \frac{4}{5}

Answer & Explanation

Ciara Melton

Beginner2022-04-24Added 12 answers

The first one is

\frac{4}{5}

. The other three are all

- \frac{4}{5}

ubafumene42h

Beginner2022-04-25Added 13 answers

Another way to think about this would be in terms of equivalence classes. If you are not familiar with this, it is pretty much how mathematicians say in the rationals that

\frac{1}{2} = \frac{2}{4} = \frac{4}{8} .

In fact one says that given two fractions

x = \frac{m}{n} and y = \frac{a}{b},

they are equal iff

m b - n a = 0

. So in your case for example

\frac{- 4}{5}

and

- \frac{4}{5}

are equal because

\frac{- 4}{5} - ((- 1) \frac{4}{5}) = \frac{- 4}{5} + \frac{4}{5} = \frac{- 4 + 4}{5} = 0

recalling that

- \frac{4}{5} = (- 1) \frac{4}{5}

. You can go on like this for all of them, e.g. for example the first and second are not equal because

\frac{- 4}{- 5} - \frac{4}{- 5} = \frac{- 4 - 4}{5} \neq 0 .

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