WEBVTT 0 00:00.410 --> 00:07.760 In the previous lesson, we saw how we could use the plus sign (+) either to concatenate strings together 1 00:07.760 --> 00:15.650 or as a mathematical operation where we add two integers or two floats, basically two numbers together. 2 00:16.100 --> 00:21.410 In this lesson, I want to show you some of the other mathematical operators that you have access to 3 00:21.410 --> 00:23.420 in addition to adding. 4 00:23.420 --> 00:25.760 The next obvious one is subtraction. 5 00:25.760 --> 00:29.270 So, 7 - 3, you would just use the minus sign. 6 00:29.270 --> 00:32.620 But then when you get to multiplication it's a little bit weird. 7 00:32.890 --> 00:38.890 Instead of using the X or some sort of times symbol, you actually use the asterisks. 8 00:38.890 --> 00:41.620 So you would say something like, 3 * 2, 9 00:41.620 --> 00:44.530 and that would be three times two. 10 00:45.040 --> 00:46.990 Now the final one is division. 11 00:46.990 --> 00:49.690 And that's done using the forward slash (/). 12 00:49.690 --> 00:52.330 So, 6 / 3, 13 00:52.600 --> 00:56.210 and when that prints out, it'll give you 2. 14 00:56.660 --> 01:02.630 Now, one thing to notice here is that whenever you're dividing things, you actually always end up 15 01:02.630 --> 01:04.340 with a floating point number. 16 01:04.340 --> 01:09.320 So you can see even though six divides into three cleanly, we're still getting 2.0. 17 01:09.920 --> 01:18.020 And in fact, if I put a type-check around this division, you'll see that it'll print float instead of 18 01:18.020 --> 01:18.800 integer. 19 01:19.150 --> 01:22.090 And this is just the default Python behavior. 20 01:22.090 --> 01:29.650 It's something called implicit typecasting, because Python is implicitly converting the result here 21 01:29.650 --> 01:32.170 into a floating point number. 22 01:32.200 --> 01:34.870 Now, sometimes you might not want that. 23 01:34.870 --> 01:41.260 So there is another Python division operator that might be worth knowing about. 24 01:41.260 --> 01:44.210 And it simply done with two forward slashes (//). 25 01:44.210 --> 01:49.070 So now when I run it, you can see what comes out is actually an integer. 26 01:49.070 --> 01:53.300 And I can do a type-check just to confirm that as well. 27 01:53.300 --> 01:55.850 Instead of float, it's coming out as an integer. 28 01:55.850 --> 02:02.810 But you have to be very careful with this second type of division operator, because what it's doing 29 02:02.810 --> 02:09.730 behind the scenes is it's actually doing this step first, and then it's simply just removing all of 30 02:09.730 --> 02:10.960 the decimal places. 31 02:10.960 --> 02:17.440 So what if instead of six divided by three, which we know divides cleanly into two, what if we divided 32 02:17.440 --> 02:19.390 five by three? 33 02:19.390 --> 02:21.280 What is the result of that? 34 02:21.280 --> 02:23.740 That's 1.6 recurring. 35 02:23.740 --> 02:30.760 So if I change this into, 5 //3, using the double forward slash, you'll see that it just 36 02:30.760 --> 02:37.590 gives me 1 and it wipes out all the rest of the numbers in this integer conversion, which can be 37 02:37.590 --> 02:42.960 quite dangerous if you're working with scientific numbers. But it can be useful when you know that 38 02:42.960 --> 02:46.860 you want an end result that has no decimal places. 39 02:47.640 --> 02:51.600 Now, the last one that's really useful is two asterisk signs (**), 40 02:51.600 --> 02:54.840 and this gives you access to the exponent. 41 02:54.840 --> 02:57.690 Or when you want to raise a number to a power. 42 02:57.690 --> 03:04.210 So for example, if you wanted to get hold of two to the power of two, then you would write it like 43 03:04.210 --> 03:10.810 this (2**2), and 2² is of course basically just 2 * 2, which is going to be equal 44 03:10.810 --> 03:11.920 to 4. 45 03:13.060 --> 03:18.940 Now if I change this to 2³, then that's going to be 2 * 2 * 2. 46 03:18.970 --> 03:21.130 So that should be 8. 47 03:21.280 --> 03:23.190 And so on and so forth. 48 03:23.610 --> 03:29.460 Having the exponent being built into the language is one of the reasons why Python is really loved by 49 03:29.460 --> 03:35.070 a lot of data scientists and mathematicians, because it's really optimized towards manipulating and 50 03:35.070 --> 03:36.240 handling numbers. 51 03:36.540 --> 03:41.790 Now, one of the things that you have to be careful about when you are doing these mathematical operations 52 03:41.790 --> 03:46.170 is when you have more than one operation on the same line of code. 53 03:46.170 --> 03:50.080 Then there's a certain level of priority. 54 03:50.110 --> 03:56.800 So some of these operations, like division or multiplication, are going to be first class, whereas 55 03:56.800 --> 04:00.370 other ones are going to be more economy like the plus and minus. 56 04:00.370 --> 04:05.590 And the rule that you might have remembered from high school is something called PEMDAS. 57 04:05.770 --> 04:13.080 It basically states the order of priority is Parentheses, Exponents, Multiplication, Division, Addition, 58 04:13.080 --> 04:14.250 and Subtraction. 59 04:14.250 --> 04:20.250 So the things that happen first are the things inside brackets ( ), then it's our exponents, then it's 60 04:20.250 --> 04:23.190 our multiplication * and division /. 61 04:23.190 --> 04:28.950 And finally, the lowest priority is our addition + and subtraction -. 62 04:28.950 --> 04:32.490 Now it's a little bit deceiving because of this order. 63 04:32.490 --> 04:39.590 It makes it seem like as if multiplication happens before division, but actually they are equally important. 64 04:39.590 --> 04:44.960 And when it actually comes to your calculations, the calculation that's most to the left is the one 65 04:44.960 --> 04:48.320 that will be prioritized between multiplication and division. 66 04:48.320 --> 04:51.980 So let me give you a real life example to make this more clear. 67 04:52.010 --> 04:59.930 Let's say we had a line of code where we wanted to multiply three by three, plus, three divided by three, 68 04:59.930 --> 05:01.010 minus three (3 * 3 + 3 -3). 69 05:01.980 --> 05:08.820 If I was to execute this entire line of code and print it out into the console, here's the time where 70 05:08.820 --> 05:13.500 you play computer again and guess using what you've learned here, 71 05:13.740 --> 05:16.170 what exactly will be printed? 72 05:16.170 --> 05:17.910 Because you will get a number printed. 73 05:17.910 --> 05:20.670 It will calculate this entire line of code for you. 74 05:20.670 --> 05:22.830 But the order matters. 75 05:22.830 --> 05:28.970 Is it going to first add 3 to 3, then multiply the result by 3? 76 05:28.970 --> 05:33.380 Or is it first going to divide 3 by 3 and then add 3 to it. 77 05:33.410 --> 05:34.820 What is the order? 78 05:34.820 --> 05:41.000 And I want you to really pause the video and have a little play with it on pen and paper before you 79 05:41.000 --> 05:43.310 come back, and will show you the result. 80 05:46.220 --> 05:52.270 Using our rule, PEMDAS, we can see the first thing that happens is what's in the parentheses, so 81 05:52.270 --> 05:53.260 that doesn't matter. 82 05:53.290 --> 05:55.180 The next thing are exponents. 83 05:55.180 --> 05:56.740 We don't actually have an exponent here. 84 05:56.740 --> 06:00.580 We don't have 2³ or something to the power of anything. 85 06:00.580 --> 06:02.170 So we can ignore that as well. 86 06:02.170 --> 06:06.490 So the next level is the multiplication and division, 87 06:06.490 --> 06:09.970 and as I mentioned they are of equal importance. 88 06:09.970 --> 06:15.610 So this 3 * 3 and 3 / 3 are both equally important, 89 06:15.620 --> 06:19.310 but the calculation goes from left to right. 90 06:19.310 --> 06:22.790 So the first thing we see is actually the multiplication. 91 06:22.790 --> 06:28.490 So if it helps you, you might want to add LR to the end of this mnemonic. 92 06:28.490 --> 06:29.990 So it becomes PEMDASLR 93 06:30.890 --> 06:33.050 Or at least that's the way I would think about it. 94 06:33.170 --> 06:40.640 So even if this was division and this was multiplication, this calculation will always get executed 95 06:40.640 --> 06:41.210 first. 96 06:41.830 --> 06:46.450 Coming back to the question I asked you, what do you think this number would be? 97 06:46.480 --> 06:51.970 Let's go ahead and comment out all the other code and run this line of code. 98 06:51.970 --> 06:54.070 And it will give us 7. 99 06:54.100 --> 06:57.670 Now if maths is not your strong point, don't worry, it's not mine either, 100 06:57.670 --> 06:59.860 and you're the sort of person who would prefer to see it 101 06:59.860 --> 07:00.610 visualised, 102 07:00.610 --> 07:06.230 then I recommend again putting this line of code in Thonny, and then go ahead and clicking on the debugging 103 07:06.230 --> 07:08.960 symbol, and then just step into. 104 07:08.960 --> 07:15.440 So press F7 or this button multiple times and you'll see it evaluate this line of code step by step. 105 07:15.440 --> 07:17.570 So first it looks at the entire thing, 106 07:17.570 --> 07:19.550 and then it goes from left to right. 107 07:19.550 --> 07:23.240 And the first calculation is 3 * 3. 108 07:23.240 --> 07:25.940 And that is the one that's going to execute first, 109 07:25.940 --> 07:27.350 and it becomes 9. 110 07:27.380 --> 07:33.190 Next, it's going to look along this line of code and see that the next most important thing is this division 111 07:33.190 --> 07:35.080 here, 3 / 3. 112 07:35.110 --> 07:37.330 So it's going to carry out that next, 113 07:37.330 --> 07:38.650 and that becomes 1. 114 07:38.650 --> 07:44.710 So now 9 + 1.0 is going to be the next thing because it's the most to the left. 115 07:44.710 --> 07:49.630 And then it becomes 10.0 - 3, and we finally get the result of 7.0. 116 07:50.170 --> 07:52.660 So now here's another challenge for you, 117 07:52.690 --> 07:59.490 "How can you change this code so that instead of getting 7, we get 3?" 118 07:59.520 --> 08:04.350 How can you change this line of code given what you know about PEMDASLR? 119 08:04.650 --> 08:06.270 See if you can figure it out. 120 08:06.270 --> 08:07.410 Pause the video now. 121 08:11.670 --> 08:15.270 All right, so this will involve a little bit of trial and error, 122 08:15.270 --> 08:22.930 and the most important tool we have access to us is the parentheses or the brackets. 123 08:22.960 --> 08:28.750 This means that we can actually isolate bits of our code, which normally have very low priority, and 124 08:28.750 --> 08:31.450 turn them into higher priority operations. 125 08:31.450 --> 08:40.030 If we added a set of parentheses around our 3 + 3, then out of all of these calculations, 126 08:40.030 --> 08:45.090 this particular one suddenly becomes the highest priority and it will happen first. 127 08:45.660 --> 08:52.380 So if I change what I've got in Thonny to our new version and go ahead and debug through it, the very 128 08:52.380 --> 08:56.850 first calculation it's going to perform is this 3 + 3 inside the brackets. 129 08:56.850 --> 08:58.980 And we end up with 6. 130 08:58.980 --> 09:04.050 So then it's going to go again from left to right prioritizing multiplication and division. 131 09:04.050 --> 09:07.230 So then it's 3 * 6 is 18. 132 09:07.230 --> 09:11.380 18 / 3 is 6. 6 - 3 is 3. 133 09:12.010 --> 09:18.850 Just by isolating certain calculations, you can elevate it to right at the top of the priority list, 134 09:18.850 --> 09:22.540 and you will be able to perform the calculations that you need. 135 09:23.350 --> 09:29.080 Now that you've learned a lot about calculations and performing mathematical operations using Python, 136 09:29.080 --> 09:31.150 I've got another code challenge for you. 137 09:31.150 --> 09:34.300 So head over to the next lesson and you'll be able to discover it there.