Question

Can you explain the Reciprocals of Quotients Theorem?

Answer 1

I've done an Internet search and find no such phrase, "Reciprocals of Quotients Theorem." Looks as though you're going to have to explain the context from which you got this, along with some inkling of what you need / want to know.

Answer 2

It's something like if \[b/a \neq 0\] , then 1/(b/a) = a/b.

I'm gonna do a report about this so I'm gonna need lots of information and a good explanation about this theorem.

Answer 3

The point of this assignment, Danielle, is that it's to give you an opportunity to develop research skills whereby you can find your own research materials. Hope I'm wrong, but it sounds as though you're hoping that someone else is going to do your research for you and give you a good explanation. Not so.

Again I ask you to identify more clearly the CONTEXT from which this material came. If you know that context, then it's more likely that you'll be able to find useful material online through Internet searches. You've got to have appropriate search terms for that to be successful.

Answer 4

As I see it, the basic concept here is that we can't divide by zero. Then we focus on not being able to divide by a fraction that happens to be zero.

Answer 5

well
you have \[\frac{ 1 }{ \frac{ a }{ b } }\]
so multiply numerator and denominator by a
you get
\[\frac{ b }{ b \frac{ a }{ b }}\]
b gets canceled and you get
\[\frac{ b }{ a }\]

Answer 6

so multiply numerator and denominator by b*
typo there

Answer 7

are there any theorems or concepts used in proving that a/b is the reciprocal of b/a ?

Answer 8

i doubt that

Answer 9

ok thanks

Answer 10

welcome

Answer 11

The "reciprocal of b" is a definition. No need to "prove" it.