### Arithmetic Operations in Programming

Programmers make use of arithmetic operations in programming for a variety of reasons. Most of these operations will already be familiar to you from your Maths lessons and can be applied to your programs by knowing the syntax (spelling & grammar of a language). Arithmetic operators in programming refer to the mathematical operators in the language. These are

• –    (subtract)
• /    (divide)
• *   (multiply)
• DIV  (integer division)
• MOD (remainder after integer division)

Whilst some programs use obvious maths, such as outputting a times table program, others may have less obvious maths built in.

Consider program that needs to calculate the distance between two letters in the alphabet that the user has entered. Initially, this looks like it is a program that is only using string & char data types. But, in fact we are looking at the position (or index) of a letter in the alphabet.

In this example we would need to save a start and end variable and use an arithmetic comparrison to output the distance between the tow letterse. In pseudocode, this may look like:

alphabet = "abcdefghijklmnopqrstuvwxyz"user = ""OUTPUT "Please enter the first letter"startLetter = INPUTOUTPUT "Please enter the second letter"endLetter = INPUTdistance = alphabet.index(endLetter) - alphabet.index(startLetter)OUTPUT startLetter + "is" + distance + "places from" + endLette

If we were to translate this into Python 3, this would look like the code below. Try extending this code in the browser to output whether the start letter is before or after the end letter by checking for a negative number.

You can edit & run the code within your browser:

The final two operators in this section may not be as familiar to you at first, but they are actually something that you have been using since primary school!

DIV is used to create a calculation for integer division. Put simply, this will output how many times one number will go into another. eg.

10 DIV 2 = 5

Why? Because 2 goes into 10 5 times.

MOD is very similar, but instead of calculating the integer division, MOD gives the remainder after the division is completed. So, if we combined the two, we could have:

Hover over the image for the answer!

division = 10 DIV 2remainder = 10 MOD 2

DIV is particularly useful in programs where we don’t want a real number returned, or we want to round down.

MOD is often used to check if one number is divisible by another. For example, we could write  a program to check if a number is even using the following pseudocode:

OUTPUT "Enter an integer"myInt = INPUTIF myInt MOD 2 == 0 THEN   OUTPUT "Number is even"ELSE   OUTPUT "Number is odd"END IF