The first reaction is a single displacement type:
[tex]Mg+2HCl\to MgCl_2+H_2[/tex]
The second one is a decomposition reaction:
[tex]2Al_2O_3\to4Al+3O_2[/tex]
The third one is a double displacement reaction:
[tex]\begin{gathered} Ba(NO_3)_2+K_2CO_3\to2KNO_3+BaCO_3 \\ 1-Ba-1 \\ 2-N-2 \\ 9-O-9 \\ 2-K-2 \\ 1-C-1 \end{gathered}[/tex]
The fourth one is a combustion reaction:
[tex]2C_3H_6+9O_2\to6CO_2+6H_2O[/tex]
The last one is also a simple displacement reaction:
[tex]\begin{gathered} 3Ca+2Fe(OH)_3\to3Ca(OH)_2+2Fe \\ 3-Ca-3 \\ 2-Fe-2 \\ 6-O-6 \\ 6-H-6 \end{gathered}[/tex]
