How can variables be used in shell scripting to perform mathematical operations?

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Variables can be used in shell scripting to perform mathematical operations by assigning numerical values to variables and then using them in arithmetic expressions. For example:

#!/bin/bash
num1=4
num2=2
sum=$((num1 + num2))
echo "The sum of $num1 and $num2 is $sum"

# Output:
# The sum of 4 and 2 is 6

In this script, the variables num1 and num2 are assigned the values 4 and 2 respectively. The arithmetic expression sum=$((num1 + num2)) uses these variables to calculate their sum and store the result in the variable sum. Finally, the echo command is used to display the output of the script, which prints the sum of the two numbers.

Similarly, variables can be used for other arithmetic operations like subtraction (-), multiplication (*), division (/), and modulus (%). For example:

#!/bin/bash
num1=6
num2=3
diff=$((num1 - num2))
prod=$((num1 * num2))
div=$((num1 / num2))
mod=$((num1 % num2))
echo "The difference between $num1 and $num2 is $diff"
echo "The product of $num1 and $num2 is $prod"
echo "$num1 divided by $num2 is $div, with a remainder of $mod"

# Output:
# The difference between 6 and 3 is 3
# The product of 6 and 3 is 18
# 6 divided by 3 is 2, with a remainder of 0

In this script, the variables num1 and num2 are assigned the values 6 and 3 respectively. Arithmetic expressions are used with these variables to calculate the difference, product, quotient, and remainder of the two numbers. Finally, echo commands are used to display the output of the script.