Two exchange rates
A balance weighs grams. Chemistry reacts in whole numbers of particles. The mole is the bridge, and crossing it costs one multiplication in each direction.
— read aloud n equals m over M. is the amount of substance in moles, is the mass you weighed in grams, and is the molar mass in grams per mole, a property of the substance that you look up rather than measure. The unit does the arguing for you: grams divided by grams per mole leaves moles, and nothing else on the page divides that way.
The second rate is — N equals n times N-A. is the number of particles, a bare count, and is the Avogadro constant, particles per mole, fixed by definition since 2019. Note the direction: multiplies a number of moles. It has never multiplied a mass, and a mass fed into it comes back meaningless by a factor of the molar mass.
Scale is the point of this chapter, so get a feel for it. A 25 kg sack of caustic soda is 625 moles, and it is also about formula units. Nobody counts the second number, and every dosing calculation on the plant runs on the first.
The nugget worth carrying: a mole is a count, not a mass. A mole of caustic soda is 40 g and a mole of limestone is 100 g, and they contain exactly the same number of formula units. That is the whole reason stoichiometry works in moles and never in kilograms.