Derive the relation between molarity and molality

M = molarity = moles solute / Liter solution 

m = molality = moles solute / kg solvent 

ρ = density = g solution / mL solution = kg solution / L solution 

mw = molecular weight (molar mass) of solute in g/mole 

Equations:

(1) M = moles solute / L solution 

(2)m = moles solute / kg solvent 

(3) ρ = kg solution / L solution 

(4)mw = g solute / mole solute 

(5) kg solution = kg solvent + kg solute 

 multiplying (3) x 1/(1)