On a system where /bin/sh is Bash (Mac OS X 10.9.2 Mavericks), then I get:
$ cat math
A=5
B=10
let C=A+B
let D=B-A
let E=A*B
let F=A/B
echo $A $B $C $D $E $F
$ sh math
5 10 15 5 50 0
$ bash math
5 10 15 5 50 0
$ ksh math
5 10 15 5 50 0
$ dash math
math: 3: math: let: not found
math: 4: math: let: not found
math: 5: math: let: not found
math: 6: math: let: not found
5 10
$ hsh math
math: let: not found
math: let: not found
math: let: not found
math: let: not found
5 10
$
(hsh is the Heirloom Bourne Shell installed as another name.)
That means that both sh math and bash math do the arithmetic as you intended. Are you perhaps on a machine with a different shell as /bin/sh (perhaps it is dash in disguise and you're on Ubuntu)?
bash ./mathC=$((A+B)).letis a relic of a bygone age.dash. Can you show the output of:bash mathand thensh mathand thendash math? I expect the output ofsh mathto be identical to that ofdash math.