Why does the growth rate of real GDP per capita equal the percentage change in real GDP minus the percentage change in population but not divide?

The growth rate of real GDP per capita reflects changes in economic output relative to the population size. It equals the percentage change in real GDP minus the percentage change in population because it accounts for how much of the economic growth can be attributed to each individual in the population. Dividing would not accurately represent the relationship since it would imply an average rather than a per-person growth adjustment, failing to capture the effect of population growth on individual economic well-being. This subtraction effectively isolates the impact of population changes on real GDP per capita.