Rational Number equations help

[Paige1]

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?

 

[kaliprasad]

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

 

[Paige1]

zero is the exception as it does not have inverse

Thank you!

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zero is the exception as it does not have inverse

however, what is the product of the rational number and it's inverse?

 

[MarkFL]

We could choose to let the rational number be:

\(\displaystyle \frac{m}{n}\) where \(\displaystyle m,n\in\mathbb{Z}\land m\ne0\) (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?

 

[CellCoree]

I can confirm that rational number equations are indeed very helpful in solving mathematical problems. In regards to your question, I would be happy to provide an explanation.

To show that the product of a rational number and its inverse is equal to 1, we can use the general form of a rational number: a/b, where a and b are integers and b ≠ 0. The inverse of this rational number would be b/a.

Now, when we multiply a rational number and its inverse, we get (a/b) * (b/a) = ab/ba. Since a and b are integers, we can simplify this to 1, making the product equal to 1.

However, there is one exception to this rule. The exception occurs when the rational number is 0. In this case, the inverse would be undefined, as we cannot divide by 0. Therefore, the product of 0 and its inverse would not be equal to 1.

I hope this explanation helps. If you need further assistance, please do not hesitate to ask for help. Remember, as scientists, we are always here to support and assist in any way we can.