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# Take reciprocals in equations

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Intern
Joined: 04 Aug 2014
Posts: 2

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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?
Senior Manager
Joined: 13 Apr 2013
Posts: 352
Location: India
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)

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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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Joined: 26 Feb 2016
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GPA: 3.12
Re: Take reciprocals in equations [#permalink]

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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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