Example #1:

We have 1 liter of a stock solution (5 moles/liter) of glucose.
We want to make a new solution (1 mole/liter) of glucose.

How much water do I have to add to the stock solution to make the desired concentration?

Vol _new x conc _new = vol _st x conc _st
Vol _new x 1 = 1 x 5

The volume of the new solution will be 5 liters. Of these 5 liters we will have 1 liter of stock solution which means that we need to add (5 liters- 1 liters) 4 liters of water to the stock solution to reach the desired concentration. This is a 1:4 dilution (1 volume stock solution, 4 volumes water).