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Take reciprocals in equations

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Take reciprocals in equations  [#permalink]

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New post 06 Mar 2018, 00:47
Guys,

My mind is boiling here, so want to sense-check one super-basic thing with you.

Clearly, if I have a fractional expression like \(\frac{1}{2}\)=\(\frac{2}{4}\), I can invert it to reciprocals: \(\frac{2}{1}\)=\(\frac{4}{2}\).

Does that mean I can do this with any variables?

Meaning \(\frac{a}{b}\)=\(\frac{x}{y}\) can always become \(\frac{b}{a}\)=\(\frac{y}{x}\) if I find this second version more convenient to work with?
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Take reciprocals in equations  [#permalink]

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New post 06 Mar 2018, 01:18
grgsky wrote:
Guys,

My mind is boiling here, so want to sense-check one super-basic thing with you.

Clearly, if I have a fractional expression like \(\frac{1}{2}\)=\(\frac{2}{4}\), I can invert it to reciprocals: \(\frac{2}{1}\)=\(\frac{4}{2}\).

Does that mean I can do this with any variables?

Meaning \(\frac{a}{b}\)=\(\frac{x}{y}\) can always become \(\frac{b}{a}\)=\(\frac{y}{x}\) if I find this second version more convenient to work with?



IMO, you can go ahead with your version of variables. I hope I am not missing some exceptional values.


Firstly, try to reduce every fraction into its lowest form.

You can write a/b = x/y as b/a = y/x.

Thank you.
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Re: Take reciprocals in equations  [#permalink]

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New post 06 Mar 2018, 11:30
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Hey grgsky

We can simplify the ratio as follows

\(\frac{a}{b}\)=\(\frac{x}{y}\) -> \(\frac{ay}{bx} = 1\) -> \(\frac{y}{x} = \frac{b}{a}\)

Hope this helps you!
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Re: Take reciprocals in equations   [#permalink] 06 Mar 2018, 11:30
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