1. ## Fractions

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

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

2. Originally Posted by GAdams
Can anybody give me give me some idea how to tackle this:

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

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

now can you continue?

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

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

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

4. When you have an expression like

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

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

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!

Trust in your answers, if you apply correctly the learnt, there's nothing to worry about.

7. Originally Posted by GAdams
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:
$\displaystyle \frac{1}{\frac{2}{5}}$

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

(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.