Explain decarboxylation with examples. Or,provide the product obtained from the carboxylic acid method with examples.

(N/A) Sodium salts of carboxylic acids,when heated with soda lime (a mixture of sodium hydroxide and calcium oxide),yield alkanes containing one carbon atom less than the parent carboxylic acid. This process of eliminating carbon dioxide from a carboxylic acid is known as decarboxylation.
$RCOOH \xrightarrow{\text{Soda lime, } \Delta} RH + Na_2CO_3$
Soda lime is a mixture of sodium hydroxide $(NaOH)$ and calcium oxide $(CaO)$. The $NaOH$ in soda lime reacts with the carboxylic acid to form its sodium salt.
Example-$1$: Preparation of methane from ethanoic acid (acetic acid).
$CH_3COONa + NaOH \xrightarrow{CaO, \Delta} CH_4 + Na_2CO_3$
Example-$2$: Preparation of ethane from propanoic acid.
$CH_3CH_2COONa + NaOH \xrightarrow{CaO, \Delta} C_2H_6 + Na_2CO_3$