The POSIX standard shell provides a mechanism for performing integer arithmetic on shell variables called arithmetic expansion. 

The format for arithmetic expansion is
$((expression))

Notice that the variable var doesn't have to be preceded by a dollar sign. 
That's because the shell knows that the only valid items that can appear in arithmetic expansions are operators, numbers, and variables. 

If the variable is not defined or contains a NULL string, its value is assumed to be zero. 
$ echo $((not_assign + 3))	#3

Parentheses may be used freely inside expressions to force grouping
$ echo $(( (zz-1)*3 ))		#-3