expr - evaluate a mathematical expression. 
  Outputs a result.

Taken from the man page with expanded descriptions.

ARG1 and ARG2 may be either constant strings or variables ($var)
Many of the expr operators have shell meanings,
  so the use of backslash will be necessary in many cases.


  ARG1 | ARG2 # OR
    ARG1 if it is neither null nor 0, otherwise ARG2
     # man incomplete
    Outputs 1st argument if neither 0, 
    Outputs non-zero argument if one is 0 or null.
    Outputs zero of both zero or null.

      Backslash required as | is the shell pipe. 

echo -n "Number 1 : "; read num1;
echo -n "Number 2 : "; read num2;
if expr "$num1" \| "$num2" > /dev/null
then 
   echo "At least one value > 0"
fi



  ARG1 & ARG2 # AND
    ARG1 if neither argument is null or 0, otherwise 0

      Backslash required as & is the background cmd-line separator.

echo -n "Number 1 : "; read num1;
echo -n "Number 2 : "; read num2;
if expr "$num1" \& "$num2" > /dev/null
then 
   echo "both values > 0"
fi


For the following comparisons,
  Conditional matches output a 1 and return a 0 (success) status.
  Failed matches output a 0 and return a 1 (fail) status.
 
  # backslash required for any use of < or > in the following.

  Accepts signed integers. e.g -7 +7

  If all characters in strings numeric,
    Evaluated numerically, zero padding OK. e.g  07 is equal to 7
  
  Strings evaluated using collating ASCII. e.g bob is greater than bill
     1a is greater than 02

# If run on command line, \, backquote, required in front of > and <  
  ARG1 < ARG2 # ARG1 is less than ARG2
    ARG1 is less than ARG2

  ARG1 <= ARG2
    ARG1 is less than or equal to ARG2
       
  ARG1 >= ARG2
    ARG1 is greater than or equal to ARG2

  ARG1 > ARG2
    ARG1 is greater than ARG2

  ARG1 = ARG2
    ARG1 is equal to ARG2

  ARG1 != ARG2
    ARG1 is unequal to ARG2
    # In a script, the ! does not need to be backslash escaped.
    # if issued on the command line, it will (history reference).


The following mathematical forms generate the result if input values valid.
  Input : signed integers.
  Results : signed integer.


  ARG1 + ARG2
    arithmetic sum of ARG1 and ARG2

  ARG1 - ARG2 
    arithmetic difference of ARG1 and ARG2

  ARG1 * ARG2
    arithmetic product of ARG1 and ARG2
    Will most likely need to be backslash escaped, filename wild card.

  ARG1 / ARG2
    arithmetic quotient of ARG1 divided by ARG2 gives integer dividend

  ARG1 % ARG2
    arithmetic remainder of ARG1 divided by ARG2

  ( ) 
    Used to group compound math statements.
    Use backslash to escape.

    expr \( $ARG1 + $ARG2 \) * 7 
    


The following do various string processing..
  STRING may be constant or variable reference.

  STRING : REGEXP
    anchored pattern match of REGEXP in STRING
    Uses regular expression to match STRING.
      Regular expression controls whether match exact or close.
    Returns count of matched characters.

    var=house
    expr "$var" : "\<hous\>"

    0

    expr "$var" : "hous"

    4

    expr "$var" : "[a-z]*"

    5

  match STRING REGEXP
    same as STRING : REGEXP 
    alternative to the :

    expr match "$var" "[a-z]*"

    5

  substr STRING POS LENGTH
    substring of STRING, POS counted from 1

    Outputs the substring of the larger STRING 
      starting at character POS, POS <= length of string value. 
      for LENGTH number of characters. LENGTH > 0

    var=house
    expr substr "$var" 2 3

    ous

  index STRING CHARS
    index in STRING where any CHARS is found, or 0
    CHARS is list of possible characters to match, order unimportant.
    Outputs index of 1st matched character
    STRING indexed from 1.

    var=house
    expr index "$var" uo
    2

  length STRING
    outputs length of STRING

  #+ TOKEN
  #  interpret TOKEN as a string, even if it is a
  #  keyword like 'match' or an operator like '/'



bc - interactive infix calculator.

dc - interactive post-fix or rpn calculator.
  However, it will also take input from a file or piping.

  echo 4 k 87 23 / p | dc
  3.7826