How do I convert fraction percentage into mixed fraction?

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I know how to convert a fraction into decimal but I want to make my calculation faster so I want to learn how to convert between fractions and percentage.

I found this on a book:

23/36= [(23/36)*100]% = [575/9]% = 63 8/9%

When I do the calculation on paper i get a decimal number 63.88. I really cant understand how to get 575/9 as an answer so that I can convert impropoer fraction to mixed fraction that is 63 8/9.

Im preparing for a competetive exam, so i need to save time, could you please help me in this, Thanks!

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Do division with remainder. $575=63\cdot 9 + 8$ so $\frac {575}9=63\frac 89$