You have 47 mL of a 0.500 M stock solution that must be diluted to 0.100 M. Assuming the volumes are additive, how much water should you add?

188mL water must be added

To solve you need to use the equation: ##M_1V_1## = ##M_2V_2##

Solve for ##V_2## ##V_2## = ##M_1V_1##/##M_2##

Now substitute in your known values ##V_2## = 0.500M*47mL/0.100M

##V_2## = 235mL

Careful, that's not your final answer. To find the volume of water that must be added to the 47mL of stock solution, subtract 47 from the total volume of 0.100M solution produced after dilution.

235mL - 47mL = 188mL water must be added

BECAUSE 47mL stock + 188mL water = total volume of diluted solution

Here is another example of this type of calculation-

Hope this helps!