Question

We have a solution of C5H10O2 of concentration 4 M. Find out the volume we need to take from this solution to make a 250 mL solution of concentration 0.5 M.
Is my result right? I got 31.25 mL

Here's what I did:
M=moles solute / volume (L) solution (M=n/V)
First I calculate the moles of acid needed for a 0.5M, 0.25L solution.
n=M*V = 0.5*0.25 = 0.125 mol acid
Now knowing how many moles I need to take, I calculate the volume those moles occupy in the 4M solution.
V=n/M = 0.125/4 = 0.03125 L solution = 31.25 mL
So you need to take 31.25 mL of 4M acid solution and add 218.75 (250*31.25) of water to make a 0.5M, 250 mL solution.

Answer 1

You are right.

Here's an easier way to do it : 
We have an initial solution of concentration $C$.
We want to turn it into a $V$ mL solution of concentration $C_1$, and we want to know which volume $V_1$ of solution to take from the original to do that.
We know that $C_1=C\frac{V_1}V$ hence $V_1=\frac{C_1}CV=\frac{0.5}4250=\frac{250}8=31.25 mL$