Arithmetic operators are simple calculations, like addition, subtraction, multiplication, and etc. This is simple and straightforward topic, I believe no need to explain here. Because we all did calculations in our school.
Your expression goes inside the 2 round brackets with the dollar prefix.

$( command )
means shell execution. 
$(( expression ))
means do some calculation.
Here are few examples for you to understand more.
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echo $(( expression )) # dummy expression
echo $(( 3 + 2 )) # simple expression, without variable
# calculation with variable
number=3
echo $((number += 2)) # addition
echo $((number = 2)) # subtract
echo $((number *= 2)) # multiplication
echo $((number /= 2)) # division
echo $((number %= 2)) # modulus or remainder
echo $((number++)) # increament
echo $((number)) # descrement