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In this video, we're going to look at operator precedence.

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It's something you'll have learnt about in basic maths class, and we're going to see how it applies to expressions in Python.

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Before I start that though, I'm going to delete lines 16 through 21 in our program.

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I added those just to show you what the for loop was doing,

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but I don't want to leave it as an example of how you should code,

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and in fact I'll take this opportunity to delete the for loop as well.

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Alright, so our examples so far have been very simple expressions,

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but they can be much more complicated.

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So consider the following line as I type it, and see if you can work out what will be printed, before you run the program.

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So I'm going to type, on line 13, print and in parentheses I'm going to type a + b

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divided by 3 minus 4 multiplied by 12.
Then we've got our closing parenthesis.

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So if you can figure out what the answer will be, let's actually run the program and see what happens.

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You can see we've got the answer: -35.0.

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Now if you're surprised that the answer is -35.0 rather than 12,

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then maybe you weren't paying attention in school.

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Don't worry, your computer isn't broken

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and you can reliably perform arithmetic in Python, but like with all programming languages,

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you have to understand some basic rules of the arithmetic operators.

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Operator precedence is a fancy term for the relative importance given to each of the operators.

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If they were all equally important we could just read the expression on line 13 from left to right,

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and we would get the result 12: a is 12 + b which is 3, is 15, divided by 3 gives 5, minus 4 leaves 1 times 12 equals 12.

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However multiplication and division have
higher precedence than addition and subtraction,

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so those operations will be performed first.

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Now many programming languages work in the same way.

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This isn't just a peculiarity of Python.

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So b divided by 3 is 1.0, and 4 times 12 is 48

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So the expression, therefore, is evaluated as 12 plus 1.0 take 48, which is -35.0.

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Now if you want to make your expressions clear and unambiguous, you can use parenthesis freely,

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even when Python doesn't specifically require them.

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So, along those lines, we could revise our
example from line 13, and instead type

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print parentheses a + and another set of
parentheses and b divided by 3 in those parentheses,

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then a minus, then parentheses 4 times 12. Then we've got our two closing right parentheses.

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I'll just space that out a little bit so it's a little bit easier to read.

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So if you run this code again, we get the identical answer -35.0 printed twice.

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So in other words, both these expressions evaluate to the same value.

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Now, if we had intended the earlier expression to reduce the result 12,

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we'd write it a different way.

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We could do print parentheses,

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and we're going to add another three parentheses here, so we've got four in total to the left hand side.

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Then a + b, closing parenthesis, divided by 3, closing parenthesis,

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- 4 closing parenthesis, multiplied by 12, and there we've got our last closing parenthesis at the end of the line.

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And now if we run that, we correctly get the result of 12.0,

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or, we could revise that because dividing by 3 is higher precedence than subtracting 4.

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We can actually remove one set of parentheses.

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So what I could do is change that to print, and we want three left parenthesis this time,

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and it's going to be a + b, closing parenthesis, divided by 3 - 4,

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closing right parentheses, multiplied by 12, and the final closing parenthesis.

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If you run the program again now, we get the same answer, 12.0.

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Now we could also use variables to hold the intermediate values if we wanted to.

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So if I come down here to line 18, I could type c = a + b. On the next line,

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d = c / 3, and e =  d - 4,

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and we can do a print, in parentheses, e multiplied by 12.

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Now if we run that we,

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we also get the value 12 outputted.

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So there will be times when it makes sense to break up an expression into smaller parts, as we've done here.

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I think in this example, though, the code's harder to read, and difficult to work out what's going on.

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Compare the two previous examples and see which one you think's easier to read.

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Okay, so I mentioned learning about operator precedence at school.

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Unfortunately, many schools use acronyms to help you remember the order of evaluation,

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but the acronyms are ambiguous.

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So common acronyms are;

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So multiplication and division have equal precedence, which is higher than addition and subtraction,

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and addition and subtraction have equal
precedence.

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Because multiplication and division are equal, expressions using those operations are evaluated from left to right.

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So let's go ahead and on line 23, I'll do a print, left and right parentheses to give us a bit of space.

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Then on line 25 I'm going to type print parentheses

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and within the parentheses I'm going to top a divided by, then another set of parentheses, b multiplied by a,

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closing parenthesis and divided by b, closing parentheses.

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and if I run this program,

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we get the result 0.1111111111

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and that's 12 times 3 is 36, and 12 divided by 36 is 1/3 divided by 3 is 1/9.

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If you were taught using those acronyms, make sure you're interpreting them correctly.

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Alright, so in the next video we're going to look at the string datatype in more detail.

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See you in the next video.