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First off, diluting a solution is essentially decreasing the concentration of its solute by adding solvent. It goes without saying that the final concentration of a dilute solution is less than the initial concentration of this solution.

The following formula is used when executing dilution calculations:
$$C_{1} • V_{1} = C_{2} • V_{2}$$
Legend:
• C1: initial concentration of the solution
• V1: initial volume of the solution
• C2: final concentration of the solution
• V2: final volume of solution

Several units can be used to describe the concentration and volume of a solution in the dilution formula. As long as the units are the same on both sides of the equation, the formula works.

Most dilution problems start off with 3 of the 4 variables in the equation. Algebraic manipulation subsequently allows to isolate the missing value:
$$C_{1} = \frac{C_{2} • V_{2}} {V_{1}}$$
$$V_{1} = \frac{C_{2} • V_{2}}{C_{1}}$$
$$C_{2} = \frac{C_{1} • V_{1}}{V_{2}}$$
$$V_{2} = \frac{C_{1} • V_{1}}{C_{2}}$$

Some problems require finding a volume of solution to add. In this case, you have to remember the following formula:
$$V_{final} = V_{initial} + V_{to_add}$$
Simply modifying the expression of the above equation allows to find the volume of solvent to add:
$$V_{to_add} = V_{final}− V_{initial}$$

There you go! Let us know if we can do anything else to help!