Question

Suppose you have 0.500 M sucrose
stock solution. How do you prepare 250
mL of 0.348 M sucrose solution ?

Answer 1

you need to add water to x mL of stock sucrose so that

.5(x) = .348(.250)
x = .174

so, add 76mL of water to 174mL of .5M sucrose to get 250mL of .348M solution

check:
.5*.174 = .087
.348*.250 = .087

Answer 2

Technically, and this may be a very small point, but I disagree because it assumes that volumes are additive. While that may be true in a few instances it is not true universally, and not very often. In addition I think it is bad practice to leave students with that impression. A better answer, I think, is to take 174 mL of the stock solution AND ADD WATER TO MAKE A TOTAL VOLUME of 250 mL.
The reason I say that is that many a student of mine wanted to say they could add a mole of AgNO3 to 1000 mL water and it makes a 1 M solution. It does not BECAUSE the total volume will be greater than 1000 mL. If the density of water is 1.00 g/mL it will be a 1 m solution but not a 1 M solution. OK, I'm off my soap box. :-)