Moltiplicazione tra frazioni

[angela.russotto]

Salve,volevo chiedere,qual'è la definizione di moltiplicazione tra frazioni?
Inoltre,perchè per ottenere il risultato di tale operazione,si moltiplicano i numeratori e i denominatori delle due frazioni tra di loro? Cosa giustifica questo modo di procedere?

[Folpo13]

Moltiplicare un numero per $a/b$ è come moltiplicare per $a$ e poi dividere per $b$. Quindi se facciamo $n/m\cdota/b$ otteniamo $((n\cdota)/m)/b$

Notiamo che dividere prima per $m$ e poi per $b$ è come dividere per $m\cdotb$ quindi scriviamo direttamente $(n\cdota)/(m\cdotb)$

Non so bene se ho risposto ai tuoi dubbi

[pandistelle007]

In order to answer to your question, it is necessary to introduce some crucial and important algebraic structures and some tools, which are dealt in a course of Commutativa Algebra, in particolar the fractions' field of the domain $\mathbb{Z}$ (which is $\mathbb{Q}$).
Intuitively, we have to know that the moltiplication of two fractions is a function which attaches to these two fractions a third fractions, which is defined as you know.

[gio73]

Hi pandistelle007 and welcome to this room, which is dedicated to students from grade 6 to grade 8.
It means that the students will be from 11 to 14 years old.
Maybe your explanations are too much for them...



By the way, where are you from?

[pandistelle007]

Yes, sorry guys. I wanted to do just the idea that it is necessary to have some notions and knowledge of Commutative Algebra (we talk about university level) in order to giustify in a a sense the operations which we do every days.

P.S. I'm a PhD student in Maths in Italy

[gio73]

@pandistelle[ot]I mean are you Italian, American, Irish, Iranian ...?[/ot]

[pandistelle007]

@gio73
Yeah, I'm Italian for a certain percent

[angela.russotto]

"Folpo13":
Notiamo che dividere prima per $m$ e poi per $b$ è come dividere per $m\cdotb$

In base a cosa possiamo dirlo?

[angela.russotto]

"pandistelle007":In order to answer to your question, it is necessary to introduce some crucial and important algebraic structures and some tools, which are dealt in a course of Commutativa Algebra.

Do you mean to answer more clearly or to answer in general?

[pandistelle007]

"zaser123":[quote="pandistelle007"]In order to answer to your question, it is necessary to introduce some crucial and important algebraic structures and some tools, which are dealt in a course of Commutativa Algebra.

Do you mean to answer more clearly or to answer in general?[/quote]

Both of them. It is possible to generalize what happens in $mathbb{Q}$ and at the same time understand better everything