Balance the following chemical equations:
$(a)$ $HNO_{3} + Ca(OH)_{2} \longrightarrow Ca(NO_{3})_{2} + H_{2}O$
$(b)$ $NaOH + H_{2}SO_{4} \longrightarrow Na_{2}SO_{4} + H_{2}O$
$(c)$ $NaCl + AgNO_{3} \longrightarrow AgCl + NaNO_{3}$
$(d)$ $BaCl_{2} + H_{2}SO_{4} \longrightarrow BaSO_{4} + HCl$

(A) To balance a chemical equation,the number of atoms of each element must be equal on both the reactant and product sides.
$(a)$ $2HNO_{3} + Ca(OH)_{2} \longrightarrow Ca(NO_{3})_{2} + 2H_{2}O$
Here,there are $2$ $N$ atoms,$8$ $O$ atoms,$4$ $H$ atoms,and $1$ $Ca$ atom on both sides.
$(b)$ $2NaOH + H_{2}SO_{4} \longrightarrow Na_{2}SO_{4} + 2H_{2}O$
Here,there are $2$ $Na$ atoms,$6$ $O$ atoms,$4$ $H$ atoms,and $1$ $S$ atom on both sides.
$(c)$ $NaCl + AgNO_{3} \longrightarrow AgCl + NaNO_{3}$
This equation is already balanced as the number of atoms of each element is equal on both sides.
$(d)$ $BaCl_{2} + H_{2}SO_{4} \longrightarrow BaSO_{4} + 2HCl$
Here,there is $1$ $Ba$ atom,$2$ $Cl$ atoms,$2$ $H$ atoms,$1$ $S$ atom,and $4$ $O$ atoms on both sides.