A chemical equation is balanced when it represents conservation of each element—and charge when relevant—using stoichiometric coefficients.

Consider propane combustion:

$$\mathrm{C_3H_8+O_2\rightarrow CO_2+H_2O}.$$

Balance one element at a time without changing any chemical subscripts.

First carbon: three carbon atoms in propane require

$$\mathrm{C_3H_8+O_2\rightarrow3CO_2+H_2O}.$$

Next hydrogen: eight hydrogen atoms require four water molecules:

$$\mathrm{C_3H_8+O_2\rightarrow3CO_2+4H_2O}.$$

The products now contain

$$3(2)+4(1)=10$$

oxygen atoms, so five $\mathrm{O_2}$ molecules are required:

$$\boxed{\mathrm{C_3H_8+5O_2\rightarrow3CO_2+4H_2O}}.$$

Finally, check every element on both sides.

If all coefficients share a common factor, divide by it so the equation is normally written with the smallest whole-number ratio. Fractional coefficients can be useful during intermediate algebra, but the conventional final form usually clears them.

Balancing changes how many units of each species participate, not what the species are. Altering a subscript such as turning $\mathrm{O_2}$ into $\mathrm{O_3}$ would change the chemical identity and would not be a legitimate balancing operation.