1. fraction cancellations

if you have a fraction, say (25*3*pi*h^3)/(25*pi*24*24*24*3), what would the reduction of this fraction be?

i thought that since they are all factors, you could change the 3s for 1s (3/3=1)and the 24s for 8s (since 24/3=8), the the 25s and pis would cancel and you're left with (h^3)/(8^3), but the book i have says the answer is (h^3)/(24^3). why is the way i was doing it wrong?

2. Originally Posted by ihateregistering
if you have a fraction, say (25*3*pi*h^3)/(25*pi*24*24*24*3), what would the reduction of this fraction be?

i thought that since they are all factors, you could change the 3s for 1s (3/3=1)and the 24s for 8s (since 24/3=8), the the 25s and pis would cancel and you're left with (h^3)/(8^3), but the book i have says the answer is (h^3)/(24^3). why is the way i was doing it wrong?

You have a 25 on top and bottom, so they cancel. The same goes for the 3 on top and the 3 on bottom and the $\pi$ on top and on bottom.

When you cancel all of those you are left with $\frac{h^3}{24^3}$

You cant change the 24s for 8s, you can only change 1 24 for 8 because there are 3 24's and only 1 3. If there were 3 3s on top then you could change all the 24s to 8s.