1. ## Fractions

Can anybody give me give me some idea how to tackle this:

1/ (2/5) - 1/ (2/3)

Can anybody give me give me some idea how to tackle this:

1/ (2/5) - 1/ (2/3)
is this $\frac 1{\frac 25} - \frac 1{ \frac 23}$?

if so, for starters, you can flip both fractions to get: $\frac 52 - \frac 32$

now can you continue?

3. Originally Posted by Jhevon
is this $\frac 1{\frac 25} - \frac 1{ \frac 23}$?

if so, for starters, you can flip both fractions to get: $\frac 52 - \frac 32$

now can you continue?
Fraid not. A bit more please...

4. When you have an expression like

$x=\frac a{\dfrac bc}$

it's the same if we say $x=a:\dfrac bc$

Does that make sense?

5. OK. These are completely new to me but here goes:

1/ (2/5) - 1/ (2/3)

= 1 : 2/5 - 1: 2/3

1/1 divide by 2/5 flip to get 1/1 multiply 5/2

1/1 divide by 2/3 flip to get 1/1 multiply 3/2

5/2 - 3/2 = 2/2 = 1

I have a feeling this is totally wrong....

6. It is correct!

OK. These are completely new to me but here goes:

1/ (2/5) - 1/ (2/3)

= 1 : 2/5 - 1: 2/3

1/1 divide by 2/5 flip to get 1/1 multiply 5/2

1/1 divide by 2/3 flip to get 1/1 multiply 3/2

5/2 - 3/2 = 2/2 = 1

I have a feeling this is totally wrong....
There is a way to avoid the ":" stuff. Consider the fraction:
$\frac{1}{\frac{2}{5}}$

We need to remove the fraction in the denominator of the "overall" fraction. How would you do this? Well, note that if we multiply $\frac{2}{5}$ by 5 the result is an integer: 2. But what we multiply in the denominator we must also multiply in the numerator. So:
$\frac{1}{\frac{2}{5}} = \frac{1}{\frac{2}{5}} \cdot \frac{5}{5} = \frac{1 \cdot 5}{\frac{2}{5} \cdot 5} = \frac{5}{2}$

(No offense Krizalid. I hate ratio notation with a passion. )

-Dan

8. Doesn't matter.

If it's necessary, I try to explain pedagogically so that the user understands the problem well.