# Math Help - [SOLVED] How can the answer to this be 1 over 3?

1. ## [SOLVED] How can the answer to this be 1 over 3?

Can you guys/gals help me please? I'm studying for the GMAT exam and the book I have says that the answer to this:

I know it's blurry:

4 1
- -
5 8
--- ---
3 2
- -
5 3
--------------
3
-
4

The book says the answer is :

1
---
3

I keep coming up with:

3
---
100

$\frac {\frac{4}{5}}{\frac{3}{5}}$

So we're dividing fractions - we're dividing $\frac{4}{5}$ by $\frac{3}{5}$.

Remember that when we divide by a fraction, the way to do it is to actually multiply by the reciprocal, so that first set of parentheses turns into:

$\frac{4}{5} \times \frac{5}{3} = \frac{4}{3}$.

Similarly, the second set of parentheses in the numerator, changing division to multiplication again, turns into:

$\frac{1}{8} \times \frac{3}{2} = \frac{3}{16}$.

Now, our numerator is $\frac{4}{3} \times \frac{3}{16} = \frac{1}{4}$.

Our problem now looks like:

$\frac {\frac{1}{4}}{\frac{3}{4}}$.

Again, we're dividing by a fraction, so let's multiply by the reciprocal:

$\frac {1}{4} \times \frac{4}{3} = \frac{1}{3}$.

And that's it. With complicated problems like these, just deal with one thing at a time - simplify inside each set of parentheses first. Then, treat the numerator as if it is its own set of parentheses, so simplify that. Lastly, deal with combining the numerator and denominator appropriately.

3. $\frac{\frac{\frac{4}{5}\frac{1}{8}}{\frac{3}{5}\fr ac{2}{3}}}{\frac{3}{4}}=\frac{\frac{\frac{1}{10}}{ \frac{2}{5}}}{\frac{3}{4}}=\frac{\frac{1}{4}}{\fra c{3}{4}}=\frac{1}{3}$

4. Dividing!!! Aaagghhhh!!!!

I've been looking at this book for so long I've been multiplying!

Thanks all, seriously, thank you.