Well, if you look at the physical definitions of the terms, molarity contains the amount of substance in mol while normality doesn't. Since the amount of substance is directly reflected by the stoichiometry, you cannot have an operation involve molarity without stoichiometry. For calculating a solution normality, all you need are the mass and the volume, so some calculations can be performed without getting the stoichiometry involved, although it certainly helps to know what you are doing.

Molarity measures moles of solute per liter and requires stoichiometry because it deals with mole ratios in a reaction. Normality measures equivalents per liter, reflecting the reactive capacity of a substance (like protons in acids or electrons in redox reactions), and doesn’t need stoichiometry for calculations. The number of equivalents shows how many reactive units a molecule can contribute, making normality a multiple of molarity based on the reaction type.