# 1.4. Integer Arithmetic¶

We start with the integers and integer arithmetic, not because arithmetic is exciting, but because the symbolism should be mostly familiar. Of course arithmetic is important in many cases, but Python is probably more often used to manipulate text and other sorts of data, as in the sample program in Running A Sample Program.

Python understands numbers and standard arithmetic. For the whole section on integer arithmetic, where you see a set-off line in typewriter font, type individual lines at the >>> prompt in the Python Shell. Press Enter after each line to get Python to respond:

77
2 + 3
5 - 7


Python should evaluate and print back the value of each expression. Of course the first one does not require any calculation. It appears that the shell just echoes back what you printed.

The Python Shell is an interactive interpreter. As you can see, after you press Enter, it is evaluating the expression you typed in, and then printing the result automatically. This is a very handy environment to check out simple Python syntax and get instant feedback. For more elaborate programs that you want to save, we will switch to an Editor Window later.

## 1.4.2. Multiplication, Parentheses, and Precedence¶

Try in the Shell:

2 x 3


You should get your first syntax error. The x should have become highlighted, indicating the location where the Python interpreter discovered that it cannot understand you: Python does not use x for multiplication as you may have done in grade school. The x can be confused with the use of x as a variable (more on that later).

Instead the symbol for multiplication is an asterisk *. Enter each of the following. You may include spaces or not. The Python interpreter can figure out what you mean either way. Try in the Shell:

2*5
2 + 3 * 4


If you expected the last answer to be 20, think again: Python uses the normal precedence of arithmetic operations: Multiplications and divisions are done before addition and subtraction, unless there are parentheses. Try

(2+3)*4
2 * (4 - 1)


Now try the following in the Shell, exactly as written, followed by Enter, with no closing parenthesis:

5 * (2 + 3


Look carefully. There is no answer given at the left margin of the next line and no prompt >>> to start a new expression. If you are using Idle, the cursor has gone to the next line and has only indented slightly. Python is waiting for you to finish your expression. It is smart enough to know that opening parentheses are always followed by the same number of closing parentheses. The cursor is on a continuation line. Type just the matching close-parenthesis and Enter,

)


and you should finally see the expression evaluated. (In some versions of the Python interpreter, the interpreter puts ‘...’ at the beginning of a continuation line, rather than just indenting.)

Negation also works. Try in the Shell:

-(2 + 3)


## 1.4.3. Division and Remainders¶

If you think about it, you learned several ways to do division. Eventually you learned how to do division resulting in a decimal. Try in the Shell:

5/2
14/4


As you saw in the previous section, numbers with decimal points in them are of type float in Python. They are discussed more in Floats, Division, Mixed Types.

In the earliest grades you would say “14 divided by 4 is 3 with a remainder of 2”. The problem here is that the answer is in two parts, the integer quotient 3 and the remainder 2, and neither of these results is the same as the decimal result. Python has separate operations to generate each part. Python uses the doubled division symbol // for the operation that produces just the integer quotient, and introduces the symbol % for the operation of finding the remainder. Try each in the Shell:

14/4
14//4
14%4


Now predict and then try each of

23//5
23%5
20%5
6//8
6%8
6/8


Finding remainders will prove more useful than you might think in the future!