Write 3.75(vinculum above 75) as a reduced fraction

Question

anonymous · Answer

hi
Can you help?

phi · Answer

The bar over the 75 means it repeats forever

anonymous · Answer

yes

anonymous · Answer

So if that is, how do you write it as reduced fraction?

anonymous · Answer

one second, so laggy, stay please

anonymous · Answer

ok

valpey · Answer

3.75757575757 = x
375.7575757575 = 100x
372 = 99x
372/99 = x

phi · Answer

let x= 3.75

phi · Answer

I see valpey did it.

anonymous · Answer

Not sure what he means...

anonymous · Answer

how did it get from 375 to 372

valpey · Answer

$$= 3 \frac{75}{99}$$

phi · Answer

x is the original number 
100x = 375.75 with 75 repeating

valpey · Answer

375.75757-3.75757

anonymous · Answer

ohh

phi · Answer

when you subtract 100x-x, the repeating 75 cancels

anonymous · Answer

Wait..

anonymous · Answer

I remember something about my teacher using x/99, but i dont remember all of it

valpey · Answer

$$5.123123123123123... = 5 \frac{123}{999}$$

anonymous · Answer

right, that i understand

anonymous · Answer

because 99 or 999 will keep it repeating

anonymous · Answer

But how would it relate to mine?Like how to use that with my question

anonymous · Answer

What kind of answer is it looking for?

anonymous · Answer

How would it be 372/99? What exactly is the answer?

phi · Answer

They would want you to divide it out, to get a mixed number

phi · Answer

Do you understand how to get to 372/99 ?

anonymous · Answer

no, sorry i dont understand..

anonymous · Answer

3.75 with line over it is 3 75/99

anonymous · Answer

But where does the 372 come from?

phi · Answer

To get to your answer, you would do what valpey showed.
It's a trick to get rid of the repeating part...
let x= 3.75
let 100x= 375.75  (in both cases the .75 is repeating)
subtract the 2 equations. solve for x

valpey · Answer

$$375.7575757...-3.757575... = 372$$

anonymous · Answer

Phi what do you mean subtract the 2 equations? 
Valpey why is it subtract?

phi · Answer

100x  = 375.7575...
   -  x  = -  3.7575....
------------------
    99 x=  372  (the nasty .7575... goes away)

anonymous · Answer

Oh, i think i see it

valpey · Answer

Terrific!

anonymous · Answer

But it asks as a reduced fraction. Shouldnt it be like a fraction answer?

valpey · Answer

$$\frac{372}{99} = 3\frac{75}{99}$$

anonymous · Answer

And so the final answer would be 372/99?

phi · Answer

I think they would want a mixed number. See http://www.webmath.com/redfract.html

valpey · Answer

$$3\frac{75}{99} = 3\frac{25}{33}$$

anonymous · Answer

Oh, because it's more simplified?

valpey · Answer

Yes, 3 & 25/33 would be the best answer.

anonymous · Answer

Okay, thank you very much guys, i think i get it

anonymous · Answer

If you want, can you help me with one quick one?

valpey · Answer

Just start a new question. It helps other people too.

anonymous · Answer

ok ok, thanks