Question

OwlKid's intuition. Why is \(a \Large {b \over c} = {\Large ac + b \over c}?\)

First intuition: \(a {\Large{b \over c}} = a + \Large{b \over c}\)

Second intuition: \(a { \Large {b \over c}} = \Large{ac \over c} + \Large{b \over c}\). So, we may claim that we are multiplying \(c\) to \(a\) and getting a common denominator.

Third intuition: \(\Large {ac \over c} + \Large {b \over c} = \Large{ac + b \over c}\)

But if you remember, that is what we are doing! We are adding \(ac + b\) and then putting that little common denominator under! :)

Answer 1

good for students who are dealing with fractions..it is reallly helpful ..

Answer 2

students generally make mistakes .. like these

Answer 3

Thank you, both!

Answer 4

Generally we write it as:
A fraction we can represent it as:


\[Quotient \frac{Remainder}{Divisor}\]

Suppose:

8/3

\[2\frac{2}{3}\]

Answer 5

What's your question right there?

Answer 6

I am only showing that how a fraction is converted into the form: \(a \frac{b}{c}\)

Answer 7

Yep, but this tutorial is about something else :P

Answer 8

I believe that it's a prerequisite for people to know that actually.

Answer 9

On Dividing 8 by 3,

You get Divisor = 3, Quotient = 2 and Remainder = 2..

Just put these values..

Answer 10

It is obvious that:

\[Dividend = Divisor \times Quotient + Remainder\]

Answer 11

That is why \(a \frac{b}{c} = \frac{ac + b}{c}\)

Answer 12

That's a good explanation too.

Answer 13

there's one problem though... you're explaining the transformation of mixed number to improper fraction.....using algebra?

Answer 14

Yes.

Answer 15

People who are 13+ must know algeba