Determine how much of the final solution you will need and what its dilution ratio should be. For example, you may require 100mL of a 1:8 dilution.
Divide the total volume of solution required by the second number in the dilution ratio. This second number tells you how many total parts are in the dilution, so the answer will tell you how big each part is. In the above example, 100mL divided by 8 is 12.5mL.
Multiply the above answer by the first number in the dilution ratio to find out how much of the concentrated solute you will need. It is common for the first number to be 1, as in the above case, so you will need 12.5mL of the solute.
Subtract the amount of solute from the total volume of the solution needed to find out how much of the solvent is required. In this case, you will need 100mL minus 12.5mL, or 87.5mL of solvent in the dilution.
Determine the concentration of the starting solution, abbreviated as C1. Most prepared solutions are labeled with their concentration either in weight per unit volume or in molarity, which is the number of moles per liter. For example, you may have a 0.4M solution of acid.
Look up what volume and concentration of the solution you will need. These are abbreviated V2 and C2. For example, you may need 350mL of 0.15M acid solution.
Plug all of the numbers into the formula C1 x V1 = C2 x V2 and solve algebraically to find V1, or the volume of starting solution needed to make the dilution. In this example, you would solve 0.4M x V1 = 0.015M x 350mL to find that V1 is 13.125mL.
Subtract V1 from V2 to find out how much water should be mixed with the portion of the starting solution. In the above example, 350mL minus 13.125mL leaves 336.875mL of water required to mix the dilution.