How to do math in Bash

Arithmetic Operator
Description
id++, id--
variable post-increment, post-decrement
++id, --id
variable pre-increment, pre-decrement
-, +
unary minus, plus
!, ~
logical and bitwise negation
**
exponentiation
*, /, %
multiplication, division, remainder (modulo)
+, -
addition, subtraction
<<, >>
left and right bitwise shifts
<=, >=, <, >
comparison
==, !=
equality, inequality
&
bitwise AND
^
bitwise XOR
|
bitwise OR
&&
logical AND
||
logical OR
expression ? expression : expression
conditional operator
=, *=, /=, %=, +=, -=, <<=, >>=, &=, ^=, |=
assignment
let sum=1+2+3+4
echo "Sum: $sum"
​
i=0
i=$((++i))
echo "i: $i"
​
let minus=sum-i
echo "minus: $minus"
​
let division=minus/3
echo "division: $division"
​
let exponentiation=$((2**division))
echo "exponentiation: $exponentiation"
​
true=1
false=0
echo "\!$true=$((! true))  \!$false=$((! false))"
echo "$true&&$true=$((true&&true))"
echo "$true&&$false=$((true&&false))"
​
echo "Result: $((true ? 1000 : 2000))"
​

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Arithmetic Operator	Description
id++, id--	variable post-increment, post-decrement
++id, --id	variable pre-increment, pre-decrement
-, +	unary minus, plus
!, ~	logical and bitwise negation
**	exponentiation
*, /, %	multiplication, division, remainder (modulo)
+, -	addition, subtraction
<<, >>	left and right bitwise shifts
<=, >=, <, >	comparison
==, !=	equality, inequality
&	bitwise AND
^	bitwise XOR
\|	bitwise OR
&&	logical AND
\|\|	logical OR
expression ? expression : expression	conditional operator
=, *=, /=, %=, +=, -=, <<=, >>=, &=, ^=, \|=	assignment