Fractions Please!

Algebra Level 1

Find the natural number x x satisfying

x − 1 x = 38 38 39 . x - \dfrac1x = 38\dfrac{38}{39}.

29 24 39 44

Rajdeep Ghosh by Rajdeep Ghosh , 18, India

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2 solutions

Rajdeep Ghosh
Aug 24, 2016

Since x − 1 x = 38 ( 38 39 ) x-\frac{1}{x}=38(\frac{38}{39}) x − 1 x = 38 + ( 38 39 ) x-\frac{1}{x}=38+(\frac{38}{39}) x − 1 x = 38 + ( 39 − 1 39 ) x-\frac{1}{x}=38+(\frac{39-1}{39}) x − 1 x = 38 + 1 − ( 1 39 ) x-\frac{1}{x}=38+1-(\frac{1}{39}) x − 1 x = 39 − ( 1 39 ) x-\frac{1}{x}=39-(\frac{1}{39}) so, x − = 39 x-=39 I've checked it with a calculator. If you try to do it by Sreedharacharya's rule then you'll end up with something like ( − 39 + − 1524 ) / 2 (-39+-\sqrt{1524})/2

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If you write 38 38 39 38 \frac{38}{39} , it looks like you're multiplying 38 by the fraction; you may want to explicit that you're doing an addition.

Roberto Gallotta - 4 years, 9 months ago

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It's the commonest of the basics in mathematics that a mixed friction is an integer + a fraction.

Rajdeep Ghosh - 4 years, 9 months ago
Loo Soo Yong
Sep 15, 2016

Since this is a multiple choice question - you can just plug the possible answers and check whether the solution checks out.

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