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In the previous lesson we saw how we could use the plus sign either to

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concatenate strings together or as a mathematical operation where we add two

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integers or two floats, basically two numbers together.

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In this lesson I want to show you some of the other mathematical operators that

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you have access to

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in addition to adding. The next obvious one is subtraction.

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So 7 - 3 , you would just use the minus sign,

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but then when you get to multiplication it's a little bit weird. Um,

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instead of using the x or some sort of time symbol,

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you actually use the asterix.

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So you would say something like 3 * 2 and that would be 3

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times 2.

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Now the final one is division and that's done using the forward-slash, so 6

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/ 3 and when that prints out,

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it'll give you 2.

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Now one thing to notice here is that whenever you're dividing things,

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you actually always end up with a floating point number.

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So you can see even though six divides into three cleanly,

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we're still getting 2.0. And in fact if I put a type check around this division,

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you'll see that it will print float instead of integer.

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And this is just something that happens with division in Python.

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But at the end of the day, you get the result that you need and it doesn't really

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matter whether if it's a float or if it's a integer.

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Now the last one that's really useful is two asterisk signs and this gives you

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access to the exponents or when you want to raise the number to a power.

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So for example,

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if you wanted to get a hold of 2 to the power of 2, then you would write it

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like this and 2 to the power of 2 is of course basically just 2 times 2 

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which is going to be equal to 4.

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Now if I change this to 2 to the power of 3,

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then that's going to be 2 times 2 times 2. So that should be 8 and so

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on and so forth.

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Having the exponent being built into the language is one of the reasons why

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Python is really loved by a lot of data scientists and mathematicians because

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it's really optimized towards manipulating and handling numbers. Now,

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one of the things that you have to be careful about when you are doing these

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mathematical operations is when you have more than one operation on the same

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line of code, then there's a certain level of priority.

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So some of these operations like division or multiplication are going to be

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first class,

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whereas other ones are going to be more economy like the plus and minus.

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And the rule that you might've remember from high school is something called 

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PEMDAS.

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It basically states the order of priority is parentheses,

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exponents, multiplication, division, addition and subtraction.

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So the things that happen first are the things inside brackets, then it's our exponents,

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then it's our multiplication and division.

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And finally, the lowest priority is our addition and subtraction.

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Now it's a little bit deceiving because of this order.

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It makes it seem like as if multiplication happens before division,

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but actually they are equally important.

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And when it actually comes to your calculations,

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the calculation that's most to the left is the one that will be prioritized

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between multiplication and division.

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So let me give you a real-life example to make this more clear.

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Let's say we had a line of code where we wanted to multiply 3 * 3 +

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3 / 3 - 3.

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If I was to execute this entire line of code and print it out into the console,

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here's the time where you play computer again and guess using what you've

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learned here, um,

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what exactly will be printed because you will get a number printed,

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it will calculate this entire line of code for you. But the order matters.

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Is it going to first add 3 to 3 then multiply the result by 3 or is

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it first going to divide through by 3 and then add 3 to it?

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What is the order?

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And I want you to really pause the video and have a little play with it on pen

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and paper before you come back and we'll show you the result.

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Using our rule, PEMDAS,

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we can see the first thing that happens is what's in the parentheses,

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so that doesn't matter. The next thing, our exponents,

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we don't actually have an exponent here.

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We don't have 2 to the power of 3 or something to the power of anything.

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So we can ignore that as well.

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So the next level is the multiplication and division.

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And as I mentioned, they are all equal importance.

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So this 3 * 3 and 3 / 3 are both equally important,

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but the calculation goes from left to right.

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So the first thing we see is actually the multiplication. So if it helps you,

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you might want to add LR to the end of this mnemonic.

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So it becomes PEMDASLR, or at least that's the way I would think about it.

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So even if this was division and this was multiplication,

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this calculation will always get executed first.

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Coming back to the question I asked you, what do you think this number would be?

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Let's go ahead and comment out all the other code and run this line of code and

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it will give us 7.0. Now if math is not your strong point, don't worry,

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it's not mine either and you're the sort of person who would prefer to see it

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visualize. Then I recommend again putting this line of code in Thonny,

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and then go ahead and clicking on the debugging symbol and then just step into,

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so press F7 or this button multiple times and you'll see it evaluate

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this line of code step-by-step.

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So first it looks at the entire thing and then it goes from left to right.

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And the first calculation is 3 * 3 and that is the one that's going

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to execute first and it becomes 9.

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Next it's going to look along this line of code and see that the next most

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important thing is this division here, 3 divided by 3.

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So it's going to carry out that next and that becomes 1.

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So now 9 + 1 is going to be the next thing because it's the most to the

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left and then it becomes 10 - 3 and we finally get the result of 7.

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So now here's another challenge for you.

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How can you change this code so that instead of getting 7,

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we get 3?

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How can you change this line of code given what you know about PEMDASLR?

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See if you can figure it out. Pause the video now.

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Alright, so this will involve a little bit of trial and error.

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And the most important tool we have access to is the parentheses or the

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brackets. This means that we can actually isolate bits of our code,

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which normally have very low priority and turn them into higher priority

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operations. So in this case,

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we know that 3 * 3 is going to happen first,

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and then the multiplication, and then the addition on the left,

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and then the subtraction.

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But if we added a set of parentheses around our 3 + 3,

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then out of all of these calculations,

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this particular one suddenly becomes the highest priority and it will happen

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first.

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So if I change what I've got in Thonny to our new version and go ahead and debug

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through it,

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the very first calculation it's going to perform is this 3 + 3  inside

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the brackets and we end up with 6.

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So then it's going to go again from left to right,

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prioritizing multiplication and division.

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So then it's 3 * 6  is 18. 18 / 3 is 6. 6 - 3 is

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3. Just by isolating certain calculations,

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you can elevate it to right at the top of the priority list and you will be able

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to perform the calculation that you need.

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Now that you've learned a lot about calculations and performing mathematical

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operations using Python, I've got another code challenge for you.

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So head up to the next lesson and you'll be able to discover it there.