0:00:01.140,0:00:05.771 Today we're going to go over the[br]President Rules of arithmetic, 0:00:05.771,0:00:09.139 which allow us to workout[br]calculations involving brackets, 0:00:09.139,0:00:11.665 powers, division and[br]multiplication, addition and 0:00:11.665,0:00:15.875 Subtraction, and let us all[br]arrive at the same answer. 0:00:16.500,0:00:20.200 Then afterwards, we're going to[br]go on and do calculations 0:00:20.200,0:00:21.680 involving positive and negative 0:00:21.680,0:00:25.828 numbers. And use rules for[br]addition, subtraction, 0:00:25.828,0:00:27.442 multiplication and division. 0:00:28.480,0:00:30.895 But first, let us look at this 0:00:30.895,0:00:36.688 expression. It's 2 + 4 * 3 - 1[br]and let us work at night. 0:00:37.650,0:00:42.655 Well, we can work it out first[br]by moving from left to right, 0:00:42.655,0:00:47.660 and if we do that then we will[br]add, then multiply and then 0:00:47.660,0:00:54.188 subtract. If we do that, we get[br]2 + 4, which is 6 times by 0:00:54.188,0:00:58.555 three. Is it T minus one gives[br]us the answer 17. 0:00:59.150,0:01:06.002 But if we change the order, the[br]calculation and we use add 0:01:06.002,0:01:08.857 first, then subtract and then 0:01:08.857,0:01:15.236 multiply. What answer do we get?[br]Well, 2 + 4 is 6. Do they 0:01:15.236,0:01:21.116 subtract next 3 - 1 which is 2[br]so 6 * 2's answer is 12. 0:01:21.800,0:01:29.690 Or we could multiply first,[br]then add followed by subtract. 0:01:30.300,0:01:34.188 Well, if we multiply first,[br]that's 4 * 3, which is 12. 0:01:34.860,0:01:37.776 Do the add 2 + 12 which is 14. 0:01:38.290,0:01:41.350 Then subtract the answer is 13. 0:01:41.870,0:01:42.998 And so on. 0:01:43.840,0:01:47.855 And as you can see, we get[br]different answers according to 0:01:47.855,0:01:52.235 the order in which we do the[br]operations, so that's not very 0:01:52.235,0:01:56.980 good. So we need to have a[br]presidents in which we know the 0:01:56.980,0:01:59.170 order in which we do the 0:01:59.170,0:02:02.819 calculation. The order that most[br]people use is. 0:02:03.680,0:02:05.348 We do brackets first. 0:02:06.300,0:02:07.998 Followed by powers. 0:02:08.670,0:02:10.206 And then multiplication 0:02:10.206,0:02:13.490 Indovision. Then finally[br]addition and Subtraction. 0:02:14.040,0:02:15.858 And that's a lot to remember. 0:02:16.400,0:02:20.100 So there's an acronym to allow[br]you to remember it. 0:02:20.650,0:02:23.806 And that acronym[br]is barred maths. 0:02:27.400,0:02:35.830 BODMAS.[br]Be for brackets. 0:02:38.210,0:02:40.880 Oh for powers. 0:02:40.880,0:02:43.820 Date for 0:02:43.820,0:02:49.650 division. An multiplication[br]for the M. 0:02:49.650,0:02:56.800 And these two go together 'cause[br]they have the same priority 0:02:56.800,0:03:02.378 Avery Edition. And[br]As for subtraction. 0:03:04.660,0:03:07.690 And these two go together[br]because they have the same 0:03:07.690,0:03:10.515 priority. So if you remember Bob 0:03:10.515,0:03:15.773 Maths. FIFA brackets and[br]Overpowers followed by division 0:03:15.773,0:03:20.036 and multiplication, and then[br]finally addition and 0:03:20.036,0:03:24.856 Subtraction. If you want to[br]calculate any expression, use 0:03:24.856,0:03:27.508 that order and you won't go 0:03:27.508,0:03:32.264 wrong. So why don't we[br]look at some examples? 0:03:33.510,0:03:39.362 Take for example, the first one[br]that we started off with 2 + 4 0:03:39.362,0:03:45.214 times by 3 - 1. Now using board[br]maths we should have no problem 0:03:45.214,0:03:50.230 working night this expression we[br]do the Times first, so it's two 0:03:50.230,0:03:55.246 add 12 - 1 night. The addition[br]and subtraction of the same 0:03:55.246,0:04:00.680 order of priority. So we work[br]from left to right. That's 2 + 0:04:00.680,0:04:04.442 12 which is 14 - 1 which is 13. 0:04:05.610,0:04:07.790 Look at this next example. 0:04:08.340,0:04:12.870 Here we've got brackets and[br]using board mass brackets are 0:04:12.870,0:04:18.759 done first, so 3 + 5 is it,[br]so our expression becomes two 0:04:18.759,0:04:21.930 times it, which is 16. Can be 0:04:21.930,0:04:29.032 easier. What about the next one[br]9 - 6? But I've got to add the 0:04:29.032,0:04:34.466 plus one now in this case we've[br]got the subtract and the ad 0:04:34.466,0:04:39.418 together. So we've got the same[br]priority. The rule is work from 0:04:39.418,0:04:45.504 left to right, so we say 9 - 6[br]which is 3 add 1 which is 4. 0:04:46.680,0:04:49.210 The last two involving powers. 0:04:49.760,0:04:55.818 3 + 2 squared while using board[br]Mars again, we do the squares, 0:04:55.818,0:05:02.342 the powers first 2 squared is 4,[br]so our expression becomes 3 + 4 0:05:02.342,0:05:05.138 and 3 + 4 is 7. 0:05:06.370,0:05:08.738 And finally this expression. 0:05:09.350,0:05:14.534 3 + 2 all squared. Now we've got[br]powers, an brackets. But 0:05:14.534,0:05:18.854 remember using board Mads we do[br]what's inside the brackets 0:05:18.854,0:05:22.742 first, so it's 3 + 2 which is 5. 0:05:22.760,0:05:26.676 And then we have to square the[br]five which is 25. 0:05:27.560,0:05:32.012 Now in these two last examples[br]with the got the same numbers. 0:05:32.870,0:05:36.740 And we've got a square, but[br]you've got two totally 0:05:36.740,0:05:40.997 different answers. And the[br]reason why is in this one the 0:05:40.997,0:05:45.641 square is for the things[br]inside the bracket. The 3 + 2, 0:05:45.641,0:05:49.511 whereas in this one this[br]square relates to just the 0:05:49.511,0:05:49.898 two. 0:05:51.140,0:05:55.721 So remember when you're doing[br]any calculations which involve 0:05:55.721,0:05:58.775 operations such as brackets,[br]powers, division, 0:05:58.775,0:06:02.847 multiplication, subtraction and[br]addition, use board baths and 0:06:02.847,0:06:04.883 you won't go wrong. 0:06:05.770,0:06:07.009 What math means? 0:06:07.740,0:06:12.628 Brackets first, then powers[br]followed by multiplication and 0:06:12.628,0:06:15.292 division. And then addition to 0:06:15.292,0:06:19.955 Subtraction. And when you have[br]operations of the same priority. 0:06:20.530,0:06:22.630 He just work from left to right. 0:06:23.420,0:06:24.668 Nothing could be easier. 0:06:26.200,0:06:30.330 And now I will move on to[br]calculations involving positive 0:06:30.330,0:06:34.047 and negative numbers. Now what[br]are positive and negative 0:06:34.047,0:06:38.590 numbers? Well, if we take all[br]the real numbers except 0. 0:06:39.100,0:06:40.519 All real numbers. 0:06:41.070,0:06:43.758 Can be. Either[br]positive or 0:06:43.758,0:06:46.434 negative, and of[br]course except 0. 0:06:47.710,0:06:50.806 Now, where are those[br]numbers? Well, if we 0:06:50.806,0:06:52.741 look on a number line. 0:06:53.810,0:07:00.223 And position 0 all the positive[br]numbers are to the right. 0:07:00.830,0:07:04.538 And all the negative numbers are[br]to the left. 0:07:05.440,0:07:12.139 And we represent the numbers on[br]the number line like this 0:07:12.139,0:07:17.011 positive one, positive 2[br]positive 3 positive for. 0:07:17.650,0:07:19.810 Positive 5 and so on. 0:07:21.400,0:07:27.000 Negative one negative, two[br]negative, three negative, 0:07:27.000,0:07:29.400 four negative 5. 0:07:30.540,0:07:35.022 Notice how we've written in[br]numbers, the positive numbers 0:07:35.022,0:07:40.002 and the negative numbers. We[br]write positive three like this 0:07:40.002,0:07:46.476 and negative for like this. The[br]sign of the number is written as 0:07:46.476,0:07:49.220 a superscript. Now we do this. 0:07:50.080,0:07:54.722 To help our understanding so[br]that we don't confuse the sign 0:07:54.722,0:07:57.254 of the number with addition and 0:07:57.254,0:07:59.726 Subtraction. But of course with 0:07:59.726,0:08:04.620 practice. We drop this and we[br]just use the normal standard 0:08:04.620,0:08:08.404 notation. But for this[br]session I'm going to use the 0:08:08.404,0:08:10.240 superscripts just to help[br]our understanding. 0:08:12.580,0:08:16.308 But what about calculations[br]involving positive and negative 0:08:16.308,0:08:19.570 numbers? What about addition,[br]subtraction, multiplication and 0:08:19.570,0:08:25.450 division? Well, I would take[br]some examples. If I take these 0:08:25.450,0:08:27.760 two examples, negative four at 0:08:27.760,0:08:30.020 positive 5. And. 0:08:31.450,0:08:34.463 Positive for. Subtract 0:08:34.463,0:08:40.560 positive 9. If I have[br]those two calculations, what do 0:08:40.560,0:08:43.380 they work out to be well? 0:08:43.890,0:08:47.621 In the first instance, we can[br]use a number line to help us 0:08:47.621,0:08:52.930 evaluate them. And we have to[br]remember that using a number 0:08:52.930,0:08:57.530 line addition means you kind on[br]in that direction, and 0:08:57.530,0:09:01.210 subtraction means you kind back[br]in that direction. 0:09:01.880,0:09:07.710 So using those two little rules[br]will calculate this expression 0:09:07.710,0:09:09.459 and then this. 0:09:10.130,0:09:15.278 So take this one to begin with[br]negative 4. Add positive five. 0:09:15.278,0:09:17.852 Start at negative, 4 on the 0:09:17.852,0:09:25.104 number line. And kind on[br]five 12345, so it negative 0:09:25.104,0:09:32.284 4 add positive 5 gives[br]me the answer positive one. 0:09:33.970,0:09:39.107 For the other example, we've got[br]a subtraction, so we started 0:09:39.107,0:09:41.442 positive four, and we subtract 0:09:41.442,0:09:44.470 positive 9. To start a positive 0:09:44.470,0:09:47.820 for. And kind 0:09:47.820,0:09:53.968 back 91234.[br]56789 so 0:09:53.968,0:09:56.756 positive for 0:09:56.756,0:10:02.128 subtract. Positive 9 gives[br]you negative 5. 0:10:03.430,0:10:04.458 It could be simpler. 0:10:04.990,0:10:09.324 Now, to simplify matters a[br]little bit further, it really is 0:10:09.324,0:10:12.082 a fast to keep writing all these 0:10:12.082,0:10:16.425 signs. And because positive[br]numbers are the numbers that we 0:10:16.425,0:10:20.330 usually use in calculations, we[br]drop them. We dropped the sign. 0:10:20.940,0:10:27.544 So positive 5 can be written is[br]just five, and we know that 0:10:27.544,0:10:33.132 positive one is equal to 1 and[br]positive 9 has 9. 0:10:34.870,0:10:39.655 And it's understood by everyone[br]that where you have numbers with 0:10:39.655,0:10:43.570 no sign written there then they[br]are positive numbers. 0:10:44.170,0:10:45.916 And I'm going to use that. 0:10:46.480,0:10:48.945 In all my calculations following 0:10:48.945,0:10:55.320 on. But if you notice in[br]this calculation and in this 0:10:55.320,0:11:00.030 one. We've added and[br]subtracted positive numbers. 0:11:01.640,0:11:05.224 But how do we add and subtract 0:11:05.224,0:11:12.120 negative numbers? Well, try and[br]generate an easy route. 0:11:12.120,0:11:16.542 Going to look at some patterns[br]of both addition and Subtraction 0:11:16.542,0:11:18.552 and will start with addition. 0:11:19.140,0:11:21.860 And we'll start with something[br]that we know. 0:11:22.540,0:11:28.960 If we start with 5 + 2,[br]we know that is 7. 0:11:29.690,0:11:33.716 And then I'm going to write a[br]sequence of calculations which 0:11:33.716,0:11:35.180 follow on from this. 0:11:35.540,0:11:37.568 5 at one. 0:11:38.110,0:11:44.150 Is equal to 65. Add zero[br]is equal to 5. 0:11:45.440,0:11:50.516 Notice in this sequence of[br]addition the answers decreased 0:11:50.516,0:11:56.027 by one. As the numbers that we[br]add decreased by one. 0:11:56.610,0:12:00.558 So if we follow the pattern. 0:12:01.470,0:12:07.311 We take 5 add negative one[br]because negative one is 0. 0:12:07.311,0:12:14.214 Subtract 1 is one less than[br]zero, then it must equal for. If 0:12:14.214,0:12:16.869 we continue the pattern on. 0:12:17.870,0:12:24.690 And five add negative, two must[br]equal 3 and five ad. 0:12:25.500,0:12:31.044 Negative three must equal[br]two and five add negative. 0:12:31.044,0:12:33.508 Four must equal 1. 0:12:34.760,0:12:36.968 Not if we look at these 0:12:36.968,0:12:41.688 additions. These additions of[br]negative numbers we can actually 0:12:41.688,0:12:45.055 write these calculations as[br]subtractions of positive 0:12:45.055,0:12:50.827 numbers, so 5 add negative, one[br]would be the same as five 0:12:50.827,0:12:54.194 subtract 1 and you get the same 0:12:54.194,0:13:00.664 answer for. Similarly, 5 add[br]negative two can be written as 0:13:00.664,0:13:07.216 five subtract 2 and you get the[br]answer 35 add negative. Three 0:13:07.216,0:13:10.492 can be written as five, subtract 0:13:10.492,0:13:14.178 3. Give me the answer 2 and 0:13:14.178,0:13:19.859 then 5. Add negative four is[br]the same as five. Subtract 0:13:19.859,0:13:21.623 4, which is one. 0:13:22.790,0:13:27.020 So when we have the addition[br]of negative numbers. 0:13:28.330,0:13:31.340 That's the same as[br]the subtraction of 0:13:31.340,0:13:32.630 the positive number. 0:13:33.860,0:13:36.776 So I had these two examples. 0:13:37.580,0:13:40.980 It at negative 10. 0:13:42.180,0:13:45.572 And negative 9 at 0:13:45.572,0:13:49.212 negative 5. Using that 0:13:49.212,0:13:52.652 room. Hi, we calculate 0:13:52.652,0:13:59.532 the answer. Now we take it add[br]negative 10. That's the same as 0:13:59.532,0:14:01.008 it subtract 10. 0:14:01.800,0:14:06.276 I'm thinking about the number[br]line. He started it and you go 0:14:06.276,0:14:11.326 back 10. So you go back to 0[br]and then another two you get 0:14:11.326,0:14:12.866 to the answer negative 2. 0:14:14.000,0:14:16.648 And with this example. 0:14:17.200,0:14:22.810 Negative nine and negative five.[br]We can rewrite that as negative 0:14:22.810,0:14:28.930 9 subtract 5 again. Visualizing[br]it on the number line start at 0:14:28.930,0:14:36.500 negative 9. And you go[br]back five, go back five so your 0:14:36.500,0:14:38.760 land at negative 14. 0:14:40.320,0:14:45.952 So when we have the addition of[br]negative numbers, it's always 0:14:45.952,0:14:50.560 easier to change them into[br]subtraction of positive numbers. 0:14:51.420,0:14:57.569 But the one thing that we[br]haven't done is the subtraction 0:14:57.569,0:14:59.246 of negative numbers. 0:15:00.030,0:15:04.905 So again, I'd like to use a[br]pattern to help us workout the 0:15:04.905,0:15:07.155 rule that we're going to use. 0:15:07.890,0:15:10.669 If we start off with what we 0:15:10.669,0:15:13.950 know. 4 subtract 2 is 2. 0:15:14.590,0:15:22.240 So 4 subtract 1 is[br]3 and four subtract 0 0:15:22.240,0:15:23.770 is for. 0:15:24.890,0:15:29.219 Notice in this sequence of[br]Subtractions, the answers are 0:15:29.219,0:15:31.143 going up by one. 0:15:32.060,0:15:36.065 As the numbers that we're[br]subtracting decreased by one. 0:15:36.860,0:15:42.030 So if we continue the pattern in[br]the calculations, the next 0:15:42.030,0:15:47.200 calculation would be 4. Subtract[br]negative one and the answer will 0:15:47.200,0:15:53.780 be 5. You add one on to the[br]four to make 5, and four 0:15:53.780,0:15:55.190 subtract negative 2. 0:15:55.880,0:16:02.722 Will be 6 and four. Subtract[br]negative. Three would be 7. 0:16:03.250,0:16:07.898 And four subtract[br]negative four is it? 0:16:09.900,0:16:16.060 Now again. If we look[br]at these subtractions 0:16:16.060,0:16:18.235 of negative numbers. 0:16:20.160,0:16:23.922 What calculation would be easier[br]to do using the numbers but 0:16:23.922,0:16:27.684 still arriving at the same[br]answer when I think it's quite 0:16:27.684,0:16:31.145 obvious. For this one, it's for 0:16:31.145,0:16:36.383 AD one. And that gives us the[br]answer 5. The numbers of the 0:16:36.383,0:16:39.047 same, but the operation and[br]assign are different. 0:16:40.460,0:16:44.880 For this one it before add 2 and[br]that will give us 6. 0:16:45.450,0:16:49.948 For this one it before at three,[br]and that will give us 7. 0:16:50.590,0:16:54.690 And finally, for ad for which[br]will give us it. 0:16:56.280,0:16:56.960 So. 0:16:58.000,0:17:03.600 If we look at our pattern, we[br]can see that when you've got the 0:17:03.600,0:17:07.600 subtraction of a negative[br]number, that's the same as the 0:17:07.600,0:17:09.600 addition of a positive number. 0:17:11.540,0:17:17.271 So we'll use that room to[br]workout these calculations if we 0:17:17.271,0:17:19.876 take it, subtract negative 10. 0:17:20.720,0:17:24.244 And negative 6 subtract 0:17:24.244,0:17:31.663 negative 13. What answers do[br]we get if we use our room where 0:17:31.663,0:17:36.093 we change the subtraction to[br]addition of a positive number? 0:17:36.093,0:17:40.966 So is it plus 10? What could be[br]easier? That's 18. 0:17:41.820,0:17:48.012 This one you've got negative 6[br]add 13 slightly harder, but not 0:17:48.012,0:17:53.172 too difficult. They give[br]negative 6 and the number line 0:17:53.172,0:17:59.880 and go forward kind on 13. He[br]kind on 6 and then another 0:17:59.880,0:18:05.040 Seven. So the answer is positive[br]7 written like that. 0:18:07.020,0:18:13.299 So how can we combine all these[br]rooms together in a nice, easy 0:18:13.299,0:18:18.129 way for you to remember? Well,[br]this is one way. 0:18:18.870,0:18:24.788 If the operation in the sign are[br]the same like this. 0:18:25.920,0:18:26.790 Sam 0:18:28.170,0:18:31.980 The calculation works like[br]an addition. 0:18:33.450,0:18:36.550 Off a positive number. 0:18:40.960,0:18:46.252 If the operation and assign are[br]different like this. 0:18:48.350,0:18:50.999 Then the operation. 0:18:51.750,0:18:55.718 Works like this subtraction. 0:18:55.940,0:18:59.808 Off a positive number. 0:19:00.920,0:19:05.683 Now, if you remember those two[br]Golden rules, then the addition 0:19:05.683,0:19:10.013 and subtraction of positive and[br]negative numbers is dead easy. 0:19:10.830,0:19:14.950 Now we've talked about addition[br]and subtraction of positive and 0:19:14.950,0:19:17.010 negative numbers, but wanna bite 0:19:17.010,0:19:22.532 multiplication Indovision. Well,[br]we start with what we know. We 0:19:22.532,0:19:28.131 know how to multiply and divide[br]positive numbers. We know that 0:19:28.131,0:19:31.185 five times by 5 is 25. 0:19:32.060,0:19:35.972 An 5 / 5 is one 0:19:35.972,0:19:41.060 dead easy. But what about[br]the multiplication division 0:19:41.060,0:19:42.515 of negative numbers? 0:19:43.540,0:19:48.204 Well, I'll use patterns the way[br]I did before. In addition, 0:19:48.204,0:19:53.288 Subtraction. And I'll start off[br]with this calculation and 0:19:53.288,0:19:57.056 continue doing a sequence of[br]multiplications that involve 0:19:57.056,0:20:03.179 negative numbers, and we'll see[br]if we can get a rule coming out 0:20:03.179,0:20:05.534 from the pattern in the 0:20:05.534,0:20:09.904 calculations. For the next[br]calculation here, I'll say this 0:20:09.904,0:20:11.994 is 5 times by 4. 0:20:12.780,0:20:14.688 And we know that is 20. 0:20:15.420,0:20:22.756 Five times by 3:15,[br]five times two is 0:20:22.756,0:20:28.892 10. 5 * 1[br]is 5 and 5 0:20:28.892,0:20:31.556 * 0 is not. 0:20:32.850,0:20:37.729 I notice in these[br]multiplications the answers. 0:20:38.300,0:20:43.184 Are going down by 5 as the[br]number that we times by 0:20:43.184,0:20:44.405 decreases by one. 0:20:45.220,0:20:50.620 So the next calculation in the[br]sequence would be 5 times by 0:20:50.620,0:20:54.740 negative one. And if we use the[br]pattern that have just stated. 0:20:55.430,0:21:00.916 We subtract 5 from zero as we[br]subtract 5 from zero, we get 0:21:00.916,0:21:05.980 negative 5. The next calculation[br]would be 5 times by negative 2. 0:21:07.270,0:21:11.477 Negative 5 subtract[br]5 is negative 10. 0:21:12.720,0:21:15.070 Five times by negative 3. 0:21:15.920,0:21:19.685 Negative 10 subtract 5 negative 0:21:19.685,0:21:26.504 15. Will do just one more just[br]to see if we can spot the 0:21:26.504,0:21:30.784 pattern and the pattern is[br]working five times negative 4. 0:21:31.550,0:21:35.528 Take negative 15 and subtract 5.[br]That's negative 20. 0:21:37.170,0:21:39.108 So look at. 0:21:39.740,0:21:41.864 Our multiplications by a 0:21:41.864,0:21:48.818 negative number. We get[br]a negative number answer. 0:21:49.490,0:21:54.350 So when we multiply a negative[br]sorry, a negative by a positive. 0:21:56.040,0:21:58.800 Will always get a[br]negative answer. 0:21:59.940,0:22:04.857 And vice versa if we multiply a[br]negative by a positive. 0:22:05.810,0:22:07.278 Will get a negative. 0:22:08.290,0:22:11.174 So if I give you these two 0:22:11.174,0:22:15.770 examples. 6 times by[br]negative 5. 0:22:17.120,0:22:21.432 Steady, easy to workout. The[br]answer you just multiply the six 0:22:21.432,0:22:26.528 by the five to get 30. The signs[br]are different. Remember this is 0:22:26.528,0:22:31.232 positive 6 times by negative 5[br]the two signs are different, so 0:22:31.232,0:22:33.584 the answer is a negative number 0:22:33.584,0:22:40.694 negative 30. If we take[br]negative four times by three. 0:22:41.260,0:22:44.570 Multipliers normal 3/4 or 12. 0:22:45.500,0:22:48.900 And then take into account[br]the signs. This is a 0:22:48.900,0:22:51.620 negative. This is a[br]positive. 2 signs different. 0:22:51.620,0:22:53.320 So the answer is negative. 0:22:54.610,0:22:56.650 And the same goes for division. 0:22:58.020,0:23:04.380 And we can just double check[br]that by looking at these two 0:23:04.380,0:23:08.620 calculations. Negative 30[br]divided by positive six must 0:23:08.620,0:23:10.210 equal negative 5. 0:23:11.490,0:23:16.638 And negative 12 divided by[br]positive three must equal 0:23:16.638,0:23:17.782 negative 4. 0:23:19.700,0:23:24.364 So when the signs are different[br]and you multiply positive and 0:23:24.364,0:23:28.604 negative numbers together in[br]pairs, the answer will always be 0:23:28.604,0:23:29.876 a negative number. 0:23:31.010,0:23:37.544 But we haven't finished just[br]yet. What if you multiply and 0:23:37.544,0:23:39.920 divide by negative numbers? 0:23:40.480,0:23:41.878 What happens there? 0:23:42.680,0:23:46.200 Well, again, I'm going to use[br]patterns. I like using patterns 0:23:46.200,0:23:50.040 because it gives me a bit of[br]confidence that I'm doing things 0:23:50.040,0:23:54.520 correctly and I always start off[br]with things that I know. So if I 0:23:54.520,0:23:57.400 start off with negative five[br]times by positive 4. 0:23:58.140,0:24:02.412 I know the answer is negative 20[br]because the signs are different 0:24:02.412,0:24:04.548 and 5 * 4 is 20. 0:24:05.080,0:24:10.820 Next one in the sequence[br]negative five times by three. 0:24:10.820,0:24:17.708 That will give us negative 15[br]negative 5 * 2 negative, ten 0:24:17.708,0:24:24.596 negative 5 * 1 is negative,[br]five negative 5 * 0 is 0:24:24.596,0:24:26.318 equal to 0. 0:24:27.940,0:24:29.100 Now look at the pattern. 0:24:30.620,0:24:35.573 Is a bit like a dejavu. We've[br]done this before. Look at the 0:24:35.573,0:24:40.145 answers. You can see that we[br]are increasing by 5 each time 0:24:40.145,0:24:44.717 as we multiply by one less[br]each time. That seems a bit 0:24:44.717,0:24:46.622 odd, but stay with Maine. 0:24:47.970,0:24:52.910 The next multiplication, if we[br]keep the pattern in the 0:24:52.910,0:24:57.850 calculations, the same would be[br]negative five times by negative 0:24:57.850,0:25:03.140 one. And according to our[br]pattern, that will equal 5 more 0:25:03.140,0:25:05.834 than zero, which is positive 5. 0:25:06.590,0:25:11.430 Negative five times negative 2,[br]which is the next calculation in 0:25:11.430,0:25:16.270 sequence. That would be five[br]more than five, which is 10. 0:25:16.800,0:25:19.600 Negative five times by negative 0:25:19.600,0:25:22.350 3. Is 15th. 0:25:23.040,0:25:27.674 Negative five times negative[br]four is 20. 0:25:29.880,0:25:35.801 So. It's really great. See that[br]when we multiply negative 0:25:35.801,0:25:37.917 numbers together in pairs. 0:25:38.420,0:25:40.620 We get a positive answer. 0:25:41.740,0:25:46.051 Negative by negative gives it a[br]positive negative negative 0:25:46.051,0:25:48.925 positive, negative negative[br]positive negative negative 0:25:48.925,0:25:54.194 positive is not great. Dead[br]easy. So if I had this 0:25:54.194,0:25:58.505 calculation negative 6 times by[br]negative three, you multipliers 0:25:58.505,0:26:04.732 normal. 6 * 3 is it teen? And[br]the answer is positive positive 0:26:04.732,0:26:09.043 via team because it's two[br]negatives makes the positive. 0:26:09.570,0:26:16.370 And the same goes with[br]this one. If we had 0:26:16.370,0:26:19.770 negative 9 times by negative 0:26:19.770,0:26:22.040 229382. Two negatives. 0:26:22.590,0:26:26.358 The answer is a positive, so[br]again we get the same answer 0:26:26.358,0:26:28.870 it team but different numbers[br]in the calculation. 0:26:29.910,0:26:33.620 But remember where else did we[br]get a positive answer? 0:26:34.600,0:26:37.055 When you multiplied 2 positive 0:26:37.055,0:26:41.440 numbers together. So if you[br]multiplied 6 by three, you'll 0:26:41.440,0:26:46.055 get it team and when you[br]multiplied 9 by two you get it 0:26:46.055,0:26:49.725 too. So when the signs of 0:26:49.725,0:26:54.935 the same. Then the answer will[br]be positive whether they are 0:26:54.935,0:26:58.095 two negatives be multiplied[br]together or two positive 0:26:58.095,0:26:59.675 numbers being multiplied[br]together. 0:27:00.790,0:27:07.450 And that's a lot to take[br]in for multiplication and 0:27:07.450,0:27:10.114 division of negative numbers. 0:27:10.120,0:27:16.060 I'd like to summarize that bit[br]by again using a diagram when 0:27:16.060,0:27:18.535 the signs of the sea. 0:27:19.480,0:27:27.328 A positive times by a positive[br]or a negative times by a 0:27:27.328,0:27:30.170 negative. The 0:27:30.170,0:27:33.810 answer. Is 0:27:33.810,0:27:40.856 positive. Is a[br]positive number when the signs 0:27:40.856,0:27:48.021 are different. I positive[br]times by a negative or 0:27:48.021,0:27:51.536 a negative times by a 0:27:51.536,0:27:54.270 positive. The answer. 0:27:55.760,0:27:57.460 Is negative. 0:28:00.400,0:28:07.154 And the same goes the same[br]rules go if you divide. 0:28:07.950,0:28:15.142 So if[br]I had 0:28:15.142,0:28:22.685 these examples.[br]Negative 6 divided 0:28:22.685,0:28:26.870 by. Negative[br]2. 0:28:28.730,0:28:34.666 My answer will be do the[br]division first 6 / 2, which is 3 0:28:34.666,0:28:38.906 and then think about the signs[br]negative negative signs saying 0:28:38.906,0:28:41.026 so. The answer is positive. 0:28:41.960,0:28:49.210 And if we had this[br]division negative 12 divided by 0:28:49.210,0:28:55.130 positive 3. Do the division is[br]normal 12 / 3 is for. 0:28:55.650,0:28:58.314 Think of the signs[br]signs, different 0:28:58.314,0:29:00.978 negative and a[br]positive. So the 0:29:00.978,0:29:02.310 answer is negative.