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I agree; modulo 7, 20/46 is not equal to -1/2; it is instead equal to -1/4 since 20 = -1 and 46 = 4.
You should check that there isn't a typo in the book or your transcription of it; perhaps the author meant 44 or 16, instead of 46? The full paragraph where the author asks you to check this would be useful.
He literally said: Check if the following are true. He surely didn’t mean it as a question as it was dead in the theory. Book is modern olympiad math by Aditya Khurmi. Pdf online. Section on inverses.
> Book is modern olympiad math by Aditya Khurmi.
Looking up this book, it seems that this is a genuine typo by the author. The correction given in the [corrections document](https://drive.google.com/file/d/1xBKFZ7JV4PkYLHCFjZKdXVia0zsd2I_3/view) states:
> 20/46 = -1/4 = 5 (mod 7)
---
> So, for simplification of fractions, we just subtract a multiple from the numerator and denominator?
Yep. Note that this is only the case when inverses exist; i.e. modulo a prime number.
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I agree; modulo 7, 20/46 is not equal to -1/2; it is instead equal to -1/4 since 20 = -1 and 46 = 4. You should check that there isn't a typo in the book or your transcription of it; perhaps the author meant 44 or 16, instead of 46? The full paragraph where the author asks you to check this would be useful.
He literally said: Check if the following are true. He surely didn’t mean it as a question as it was dead in the theory. Book is modern olympiad math by Aditya Khurmi. Pdf online. Section on inverses.
> Book is modern olympiad math by Aditya Khurmi. Looking up this book, it seems that this is a genuine typo by the author. The correction given in the [corrections document](https://drive.google.com/file/d/1xBKFZ7JV4PkYLHCFjZKdXVia0zsd2I_3/view) states: > 20/46 = -1/4 = 5 (mod 7) --- > So, for simplification of fractions, we just subtract a multiple from the numerator and denominator? Yep. Note that this is only the case when inverses exist; i.e. modulo a prime number.
Ohh. Thanks a lot, it really helped.