There are two things you need to be aware of. The first is that bc uses standard input for expressions so you would need to actually pipe your expression through it, or use the <<< redirection operator, one of:
c=$(echo "($a - $b) / 52" | bc) c=$(bc <<< "($a - $b) / 52")
The <<< method is specific to bash and ksh (an possibly others, but I'm not really au fait with them). The other method can be used in most shells.
Secondly, you should be careful when using big numbers for this since bc has the annoying habit of splitting them across lines:
pax$ x=999999999999999999999999999999999999999999999999999999999999999999999 pax$ echo "$x / 7" | bc 14285714285714285714285714285714285714285714285714285714285714285714\ 2
In order to avoid this, you need to change the line length:
pax$ echo "$x / 7" | BC_LINE_LENGTH=0 bc 142857142857142857142857142857142857142857142857142857142857142857142
bcyou create a subprocess (system call user -> kernel mode, fork, exec,... then it takes time with memory allocation, new entry in the processes table, more work for the process scheduler, cache misses and eventually page misses, dynamic library might be loaded bybc,...) so you lose many CPU cycles. This would not be the case if you were using the appropriate language for this!