MHB Rational Number equations help

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The discussion focuses on demonstrating that the product of a rational number and its inverse equals 1, with the exception of zero, which lacks an inverse. Participants clarify that for a rational number expressed as m/n (where m and n are integers and m is not zero), its multiplicative inverse is n/m. The importance of zero is emphasized, as it cannot be used in this context due to the absence of an inverse. The conversation seeks to solidify understanding of rational numbers and their properties. Overall, the key takeaway is the relationship between rational numbers and their inverses, highlighting the unique case of zero.
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I have a question in math I need help with please:
Show that the product of a rational number and it's inverse is equal to 1, with one exception. what is the exception? can anyone help please?
 
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Paige said:
I have a question in math I need help with please:
Show that the product of a rational number and it's inverse is equal to 1, with one exception. what is the exception? can anyone help please?

zero is the exception as it does not have inverse
 
kaliprasad said:
zero is the exception as it does not have inverse

Thank you!

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kaliprasad said:
zero is the exception as it does not have inverse

however, what is the product of the rational number and it's inverse?
 
We could choose to let the rational number be:

$$\frac{m}{n}$$ where $$m,n\in\mathbb{Z}\land m\ne0$$ (This just means $m$ and $n$ are integers, with $m$ not equal to zero.)

So, what would the multiplicative inverse, or reciprocal, of $m$ be?
 

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