Would you like to inspect the original subtitles? These are the user uploaded subtitles that are being translated: 1 00:00:00,670 --> 00:00:05,670 In the previous lesson we saw how we could use the plus sign either to 2 00:00:05,770 --> 00:00:10,770 concatenate strings together or as a mathematical operation where we add two 3 00:00:11,710 --> 00:00:15,370 integers or two floats, basically two numbers together. 4 00:00:16,390 --> 00:00:20,230 In this lesson I want to show you some of the other mathematical operators that 5 00:00:20,230 --> 00:00:21,220 you have access to 6 00:00:21,670 --> 00:00:25,810 in addition to adding. The next obvious one is subtraction. 7 00:00:25,840 --> 00:00:29,080 So 7 - 3 , you would just use the minus sign, 8 00:00:29,590 --> 00:00:33,130 but then when you get to multiplication it's a little bit weird. Um, 9 00:00:33,160 --> 00:00:37,060 instead of using the x or some sort of time symbol, 10 00:00:37,390 --> 00:00:38,950 you actually use the asterix. 11 00:00:39,070 --> 00:00:43,630 So you would say something like 3 * 2 and that would be 3 12 00:00:43,630 --> 00:00:44,470 times 2. 13 00:00:45,160 --> 00:00:50,160 Now the final one is division and that's done using the forward-slash, so 6 14 00:00:50,800 --> 00:00:54,820 / 3 and when that prints out, 15 00:00:54,850 --> 00:00:56,020 it'll give you 2. 16 00:00:56,830 --> 00:01:00,550 Now one thing to notice here is that whenever you're dividing things, 17 00:01:01,030 --> 00:01:04,360 you actually always end up with a floating point number. 18 00:01:04,450 --> 00:01:07,420 So you can see even though six divides into three cleanly, 19 00:01:07,630 --> 00:01:12,630 we're still getting 2.0. And in fact if I put a type check around this division, 20 00:01:14,890 --> 00:01:18,520 you'll see that it will print float instead of integer. 21 00:01:19,210 --> 00:01:21,880 And this is just something that happens with division in Python. 22 00:01:22,420 --> 00:01:26,200 But at the end of the day, you get the result that you need and it doesn't really 23 00:01:26,200 --> 00:01:29,350 matter whether if it's a float or if it's a integer. 24 00:01:30,220 --> 00:01:35,220 Now the last one that's really useful is two asterisk signs and this gives you 25 00:01:35,500 --> 00:01:39,760 access to the exponents or when you want to raise the number to a power. 26 00:01:40,210 --> 00:01:40,930 So for example, 27 00:01:40,930 --> 00:01:45,930 if you wanted to get a hold of 2 to the power of 2, then you would write it 28 00:01:46,270 --> 00:01:51,270 like this and 2 to the power of 2 is of course basically just 2 times 2 29 00:01:52,210 --> 00:01:54,040 which is going to be equal to 4. 30 00:01:55,600 --> 00:01:58,660 Now if I change this to 2 to the power of 3, 31 00:01:58,660 --> 00:02:03,660 then that's going to be 2 times 2 times 2. So that should be 8 and so 32 00:02:04,360 --> 00:02:05,260 on and so forth. 33 00:02:05,890 --> 00:02:09,610 Having the exponent being built into the language is one of the reasons why 34 00:02:09,610 --> 00:02:14,610 Python is really loved by a lot of data scientists and mathematicians because 35 00:02:14,800 --> 00:02:19,300 it's really optimized towards manipulating and handling numbers. Now, 36 00:02:19,300 --> 00:02:22,510 one of the things that you have to be careful about when you are doing these 37 00:02:22,510 --> 00:02:27,280 mathematical operations is when you have more than one operation on the same 38 00:02:27,280 --> 00:02:32,020 line of code, then there's a certain level of priority. 39 00:02:32,710 --> 00:02:37,710 So some of these operations like division or multiplication are going to be 40 00:02:37,900 --> 00:02:38,740 first class, 41 00:02:38,770 --> 00:02:42,460 whereas other ones are going to be more economy like the plus and minus. 42 00:02:42,940 --> 00:02:47,140 And the rule that you might've remember from high school is something called 43 00:02:47,170 --> 00:02:48,003 PEMDAS. 44 00:02:48,250 --> 00:02:52,750 It basically states the order of priority is parentheses, 45 00:02:52,780 --> 00:02:56,290 exponents, multiplication, division, addition and subtraction. 46 00:02:56,800 --> 00:03:01,180 So the things that happen first are the things inside brackets, then it's our exponents, 47 00:03:01,630 --> 00:03:05,320 then it's our multiplication and division. 48 00:03:05,680 --> 00:03:10,680 And finally, the lowest priority is our addition and subtraction. 49 00:03:11,530 --> 00:03:14,740 Now it's a little bit deceiving because of this order. 50 00:03:14,830 --> 00:03:18,400 It makes it seem like as if multiplication happens before division, 51 00:03:18,850 --> 00:03:21,580 but actually they are equally important. 52 00:03:22,150 --> 00:03:24,640 And when it actually comes to your calculations, 53 00:03:24,850 --> 00:03:28,360 the calculation that's most to the left is the one that will be prioritized 54 00:03:28,390 --> 00:03:30,280 between multiplication and division. 55 00:03:30,850 --> 00:03:34,120 So let me give you a real-life example to make this more clear. 56 00:03:34,540 --> 00:03:39,540 Let's say we had a line of code where we wanted to multiply 3 * 3 + 57 00:03:39,940 --> 00:03:43,150 3 / 3 - 3. 58 00:03:44,500 --> 00:03:49,500 If I was to execute this entire line of code and print it out into the console, 59 00:03:50,170 --> 00:03:54,670 here's the time where you play computer again and guess using what you've 60 00:03:54,670 --> 00:03:56,350 learned here, um, 61 00:03:56,470 --> 00:04:00,190 what exactly will be printed because you will get a number printed, 62 00:04:00,190 --> 00:04:04,990 it will calculate this entire line of code for you. But the order matters. 63 00:04:05,260 --> 00:04:10,260 Is it going to first add 3 to 3 then multiply the result by 3 or is 64 00:04:11,710 --> 00:04:15,610 it first going to divide through by 3 and then add 3 to it? 65 00:04:15,910 --> 00:04:17,050 What is the order? 66 00:04:17,260 --> 00:04:21,760 And I want you to really pause the video and have a little play with it on pen 67 00:04:21,760 --> 00:04:25,450 and paper before you come back and we'll show you the result. 68 00:04:28,660 --> 00:04:30,400 Using our rule, PEMDAS, 69 00:04:30,430 --> 00:04:34,210 we can see the first thing that happens is what's in the parentheses, 70 00:04:34,270 --> 00:04:37,480 so that doesn't matter. The next thing, our exponents, 71 00:04:37,510 --> 00:04:39,040 we don't actually have an exponent here. 72 00:04:39,040 --> 00:04:42,790 We don't have 2 to the power of 3 or something to the power of anything. 73 00:04:42,880 --> 00:04:44,140 So we can ignore that as well. 74 00:04:44,740 --> 00:04:48,700 So the next level is the multiplication and division. 75 00:04:48,940 --> 00:04:52,120 And as I mentioned, they are all equal importance. 76 00:04:52,450 --> 00:04:57,450 So this 3 * 3 and 3 / 3 are both equally important, 77 00:04:58,120 --> 00:05:01,540 but the calculation goes from left to right. 78 00:05:01,720 --> 00:05:06,220 So the first thing we see is actually the multiplication. So if it helps you, 79 00:05:06,310 --> 00:05:10,690 you might want to add LR to the end of this mnemonic. 80 00:05:10,780 --> 00:05:15,130 So it becomes PEMDASLR, or at least that's the way I would think about it. 81 00:05:15,730 --> 00:05:20,080 So even if this was division and this was multiplication, 82 00:05:20,500 --> 00:05:23,320 this calculation will always get executed first. 83 00:05:24,190 --> 00:05:28,420 Coming back to the question I asked you, what do you think this number would be? 84 00:05:28,900 --> 00:05:33,900 Let's go ahead and comment out all the other code and run this line of code and 85 00:05:34,840 --> 00:05:38,890 it will give us 7.0. Now if math is not your strong point, don't worry, 86 00:05:38,890 --> 00:05:42,130 it's not mine either and you're the sort of person who would prefer to see it 87 00:05:42,130 --> 00:05:46,180 visualize. Then I recommend again putting this line of code in Thonny, 88 00:05:46,660 --> 00:05:51,220 and then go ahead and clicking on the debugging symbol and then just step into, 89 00:05:51,220 --> 00:05:56,220 so press F7 or this button multiple times and you'll see it evaluate 90 00:05:56,290 --> 00:05:57,680 this line of code step-by-step. 91 00:05:57,830 --> 00:06:01,520 So first it looks at the entire thing and then it goes from left to right. 92 00:06:02,120 --> 00:06:07,120 And the first calculation is 3 * 3 and that is the one that's going 93 00:06:07,130 --> 00:06:09,260 to execute first and it becomes 9. 94 00:06:09,950 --> 00:06:13,670 Next it's going to look along this line of code and see that the next most 95 00:06:13,670 --> 00:06:17,120 important thing is this division here, 3 divided by 3. 96 00:06:17,660 --> 00:06:20,690 So it's going to carry out that next and that becomes 1. 97 00:06:21,200 --> 00:06:26,200 So now 9 + 1 is going to be the next thing because it's the most to the 98 00:06:26,330 --> 00:06:31,330 left and then it becomes 10 - 3 and we finally get the result of 7. 99 00:06:32,630 --> 00:06:34,700 So now here's another challenge for you. 100 00:06:35,240 --> 00:06:39,980 How can you change this code so that instead of getting 7, 101 00:06:40,340 --> 00:06:41,570 we get 3? 102 00:06:41,990 --> 00:06:46,170 How can you change this line of code given what you know about PEMDASLR? 103 00:06:46,170 --> 00:06:49,520 See if you can figure it out. Pause the video now. 104 00:06:54,110 --> 00:06:57,290 Alright, so this will involve a little bit of trial and error. 105 00:06:57,890 --> 00:07:02,890 And the most important tool we have access to is the parentheses or the 106 00:07:04,400 --> 00:07:08,600 brackets. This means that we can actually isolate bits of our code, 107 00:07:08,630 --> 00:07:12,800 which normally have very low priority and turn them into higher priority 108 00:07:12,800 --> 00:07:15,020 operations. So in this case, 109 00:07:15,050 --> 00:07:17,810 we know that 3 * 3 is going to happen first, 110 00:07:18,170 --> 00:07:20,930 and then the multiplication, and then the addition on the left, 111 00:07:20,990 --> 00:07:22,310 and then the subtraction. 112 00:07:22,940 --> 00:07:27,940 But if we added a set of parentheses around our 3 + 3, 113 00:07:29,450 --> 00:07:31,760 then out of all of these calculations, 114 00:07:32,180 --> 00:07:36,440 this particular one suddenly becomes the highest priority and it will happen 115 00:07:36,440 --> 00:07:37,273 first. 116 00:07:37,640 --> 00:07:42,640 So if I change what I've got in Thonny to our new version and go ahead and debug 117 00:07:43,100 --> 00:07:43,820 through it, 118 00:07:43,820 --> 00:07:48,020 the very first calculation it's going to perform is this 3 + 3 inside 119 00:07:48,020 --> 00:07:50,720 the brackets and we end up with 6. 120 00:07:51,170 --> 00:07:53,690 So then it's going to go again from left to right, 121 00:07:53,690 --> 00:07:55,910 prioritizing multiplication and division. 122 00:07:56,240 --> 00:08:01,240 So then it's 3 * 6 is 18. 18 / 3 is 6. 6 - 3 is 123 00:08:02,630 --> 00:08:06,500 3. Just by isolating certain calculations, 124 00:08:06,890 --> 00:08:11,890 you can elevate it to right at the top of the priority list and you will be able 125 00:08:11,900 --> 00:08:14,300 to perform the calculation that you need. 126 00:08:15,530 --> 00:08:19,250 Now that you've learned a lot about calculations and performing mathematical 127 00:08:19,250 --> 00:08:23,060 operations using Python, I've got another code challenge for you. 128 00:08:23,180 --> 00:08:26,060 So head up to the next lesson and you'll be able to discover it there. 12671