# Arithmetic in Python: Understanding Expressions ## Introduction This is the second article in the Python programming beginner's series. In the previous one we got the environment ready; in this one we actually start writing Python code, beginning with the arithmetic everyone already knows — turning maths into something a computer understands. Besides the four basic operations, this article also introduces the idea of an *expression*. It sounds academic, but it's just the "sum" you've been writing since primary school, restated in programming terms. Once it clicks, variables and conditionals later on go down much more smoothly. ## Opening and Naming a Colab In the [previous article](../google-colaboratory/) we introduced Google Colaboratory (Colab), a handy online editor. It runs in the browser, so there's no need to install Python on your own machine — the lowest-friction starting point there is for a beginner. Before writing any Python code, create a new Colab file in your Drive and give it a recognisable name. Every piece of code from here on gets written and run inside a Colab cell. ## Basic Arithmetic Let's start with the simplest possible program: what is 123 + 456? A calculator answers that in a second, and in Python the code looks almost exactly like the maths: ```python 123 + 456 ``` Run that line in a Colab cell and you see the answer straight away. By the same token, if we want to work out 907 - 456, you can certainly write the program immediately: ```python 907 - 456 ``` For multiplication and division, note that the symbols differ from your maths textbook: multiplication uses an asterisk `*` and division a forward slash `/`, not `x` and `÷`. Here we compute 1445 x 404 and 1309 ÷ 56: ```python 1445 * 404 1309 / 56 ``` If you can write all of the above, you've already learned how to do arithmetic in Python. ## Understanding Expressions Now let's look at the concept of an expression. In fact, those lines of code we just wrote *are* expressions. {{< image src="expression.jpg" alt="A diagram breaking an expression into its parts, labelling the values and the operators within the sum." caption="The concept of an expression" >}} As the figure shows, an expression is made up of two kinds of thing: values and operators. Put more plainly, an expression is a mathematical "sum", containing a number of "values" and "operator symbols". What characterises an expression is that it can be *evaluated* — a long "sum" can be reduced to a single "value". For instance, 2 + 2 + 2 + 2 + 2 + 2 is an expression that evaluates to 12. So what the earlier code is doing is writing down one line of expression and handing it to the computer to evaluate: ```python 123 + 456 ``` One thing to watch: while evaluating, the computer follows the rules "multiplication and division before addition and subtraction" and "whatever is inside the parentheses first". That means `1 + 2 * 3` gives 7, not 9; if you really want the addition first, you have to add the parentheses yourself and write `(1 + 2) * 3`. Keep operator precedence in mind when writing expressions, or you'll get an answer you didn't expect. ## More Advanced Operators: `**`, `%` and `//` Beyond the basic four operations, Python has three somewhat more advanced operators. First is `**`, meaning "to the power of". For example, run the following code to compute "2 to the power of 3": ```python 2 ** 3 ``` `%` means "remainder". For example, 15 ÷ 4 = 3 (quotient 3) ⋯ 3 (remainder 3). If we want the remainder of 15 divided by 4 in a program, we use `%`: ```python 15 % 4 ``` Finally, `//` means "quotient". Taking 15 ÷ 4 again, if we want the quotient of 15 divided by 4 in a program, we use `//`: ```python 15 // 4 ``` Here's a point that's easy to mix up: `/` produces the ordinary division result, while `//` keeps only the integer part. The two look one slash apart, but their purposes are entirely different. ## Syntax Errors {{< image src="syntax-error.jpg" alt="A Colab screenshot showing a SyntaxError message raised after running an invalid line of code." caption="A common beginner mistake: SyntaxError" >}} "Syntax Error" is an error message you'll see often while programming. It means exactly what it says — the computer is telling us there's something wrong with the syntax of the code you wrote. In the figure above, we originally meant to compute: ```python 1 + 3 * 4 ``` but the 3 got left out, making it: ```python 1 + * 4 ``` A multiplication sign immediately following a plus sign can't be evaluated, of course, so the computer displayed a SyntaxError. Don't panic when you see this message — it usually means a character was missed or typed twice somewhere, and re-reading that line will find it. One more note: while writing code, we often put "spaces" between numbers and symbols. Those spaces don't cause a syntax error; they're purely there to make the code look tidier and cleaner. ## Conclusion In this article we learned Python's most basic syntax and the concept of an expression, and implemented a variety of mathematical operations in Python code — the four basic operations plus the three more advanced operators `**`, `%` and `//`. Along the way we also got to know what the SyntaxError that beginners hit most often actually is. In the [next article](../python-variable-data-type/) we'll introduce the concept of a "variable" in programming, so we can store a computed result and reuse it instead of rewriting the sum every time.