[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.14,0:00:05.77,Default,,0000,0000,0000,,Today we're going to go over the\NPresident Rules of arithmetic,
Dialogue: 0,0:00:05.77,0:00:09.14,Default,,0000,0000,0000,,which allow us to workout\Ncalculations involving brackets,
Dialogue: 0,0:00:09.14,0:00:11.66,Default,,0000,0000,0000,,powers, division and\Nmultiplication, addition and
Dialogue: 0,0:00:11.66,0:00:15.88,Default,,0000,0000,0000,,Subtraction, and let us all\Narrive at the same answer.
Dialogue: 0,0:00:16.50,0:00:20.20,Default,,0000,0000,0000,,Then afterwards, we're going to\Ngo on and do calculations
Dialogue: 0,0:00:20.20,0:00:21.68,Default,,0000,0000,0000,,involving positive and negative
Dialogue: 0,0:00:21.68,0:00:25.83,Default,,0000,0000,0000,,numbers. And use rules for\Naddition, subtraction,
Dialogue: 0,0:00:25.83,0:00:27.44,Default,,0000,0000,0000,,multiplication and division.
Dialogue: 0,0:00:28.48,0:00:30.90,Default,,0000,0000,0000,,But first, let us look at this
Dialogue: 0,0:00:30.90,0:00:36.69,Default,,0000,0000,0000,,expression. It's 2 + 4 * 3 - 1\Nand let us work at night.
Dialogue: 0,0:00:37.65,0:00:42.66,Default,,0000,0000,0000,,Well, we can work it out first\Nby moving from left to right,
Dialogue: 0,0:00:42.66,0:00:47.66,Default,,0000,0000,0000,,and if we do that then we will\Nadd, then multiply and then
Dialogue: 0,0:00:47.66,0:00:54.19,Default,,0000,0000,0000,,subtract. If we do that, we get\N2 + 4, which is 6 times by
Dialogue: 0,0:00:54.19,0:00:58.56,Default,,0000,0000,0000,,three. Is it T minus one gives\Nus the answer 17.
Dialogue: 0,0:00:59.15,0:01:06.00,Default,,0000,0000,0000,,But if we change the order, the\Ncalculation and we use add
Dialogue: 0,0:01:06.00,0:01:08.86,Default,,0000,0000,0000,,first, then subtract and then
Dialogue: 0,0:01:08.86,0:01:15.24,Default,,0000,0000,0000,,multiply. What answer do we get?\NWell, 2 + 4 is 6. Do they
Dialogue: 0,0:01:15.24,0:01:21.12,Default,,0000,0000,0000,,subtract next 3 - 1 which is 2\Nso 6 * 2's answer is 12.
Dialogue: 0,0:01:21.80,0:01:29.69,Default,,0000,0000,0000,,Or we could multiply first,\Nthen add followed by subtract.
Dialogue: 0,0:01:30.30,0:01:34.19,Default,,0000,0000,0000,,Well, if we multiply first,\Nthat's 4 * 3, which is 12.
Dialogue: 0,0:01:34.86,0:01:37.78,Default,,0000,0000,0000,,Do the add 2 + 12 which is 14.
Dialogue: 0,0:01:38.29,0:01:41.35,Default,,0000,0000,0000,,Then subtract the answer is 13.
Dialogue: 0,0:01:41.87,0:01:42.100,Default,,0000,0000,0000,,And so on.
Dialogue: 0,0:01:43.84,0:01:47.86,Default,,0000,0000,0000,,And as you can see, we get\Ndifferent answers according to
Dialogue: 0,0:01:47.86,0:01:52.24,Default,,0000,0000,0000,,the order in which we do the\Noperations, so that's not very
Dialogue: 0,0:01:52.24,0:01:56.98,Default,,0000,0000,0000,,good. So we need to have a\Npresidents in which we know the
Dialogue: 0,0:01:56.98,0:01:59.17,Default,,0000,0000,0000,,order in which we do the
Dialogue: 0,0:01:59.17,0:02:02.82,Default,,0000,0000,0000,,calculation. The order that most\Npeople use is.
Dialogue: 0,0:02:03.68,0:02:05.35,Default,,0000,0000,0000,,We do brackets first.
Dialogue: 0,0:02:06.30,0:02:07.100,Default,,0000,0000,0000,,Followed by powers.
Dialogue: 0,0:02:08.67,0:02:10.21,Default,,0000,0000,0000,,And then multiplication
Dialogue: 0,0:02:10.21,0:02:13.49,Default,,0000,0000,0000,,Indovision. Then finally\Naddition and Subtraction.
Dialogue: 0,0:02:14.04,0:02:15.86,Default,,0000,0000,0000,,And that's a lot to remember.
Dialogue: 0,0:02:16.40,0:02:20.10,Default,,0000,0000,0000,,So there's an acronym to allow\Nyou to remember it.
Dialogue: 0,0:02:20.65,0:02:23.81,Default,,0000,0000,0000,,And that acronym\Nis barred maths.
Dialogue: 0,0:02:27.40,0:02:35.83,Default,,0000,0000,0000,,BODMAS.\NBe for brackets.
Dialogue: 0,0:02:38.21,0:02:40.88,Default,,0000,0000,0000,,Oh for powers.
Dialogue: 0,0:02:40.88,0:02:43.82,Default,,0000,0000,0000,,Date for
Dialogue: 0,0:02:43.82,0:02:49.65,Default,,0000,0000,0000,,division. An multiplication\Nfor the M.
Dialogue: 0,0:02:49.65,0:02:56.80,Default,,0000,0000,0000,,And these two go together 'cause\Nthey have the same priority
Dialogue: 0,0:02:56.80,0:03:02.38,Default,,0000,0000,0000,,Avery Edition. And\NAs for subtraction.
Dialogue: 0,0:03:04.66,0:03:07.69,Default,,0000,0000,0000,,And these two go together\Nbecause they have the same
Dialogue: 0,0:03:07.69,0:03:10.52,Default,,0000,0000,0000,,priority. So if you remember Bob
Dialogue: 0,0:03:10.52,0:03:15.77,Default,,0000,0000,0000,,Maths. FIFA brackets and\NOverpowers followed by division
Dialogue: 0,0:03:15.77,0:03:20.04,Default,,0000,0000,0000,,and multiplication, and then\Nfinally addition and
Dialogue: 0,0:03:20.04,0:03:24.86,Default,,0000,0000,0000,,Subtraction. If you want to\Ncalculate any expression, use
Dialogue: 0,0:03:24.86,0:03:27.51,Default,,0000,0000,0000,,that order and you won't go
Dialogue: 0,0:03:27.51,0:03:32.26,Default,,0000,0000,0000,,wrong. So why don't we\Nlook at some examples?
Dialogue: 0,0:03:33.51,0:03:39.36,Default,,0000,0000,0000,,Take for example, the first one\Nthat we started off with 2 + 4
Dialogue: 0,0:03:39.36,0:03:45.21,Default,,0000,0000,0000,,times by 3 - 1. Now using board\Nmaths we should have no problem
Dialogue: 0,0:03:45.21,0:03:50.23,Default,,0000,0000,0000,,working night this expression we\Ndo the Times first, so it's two
Dialogue: 0,0:03:50.23,0:03:55.25,Default,,0000,0000,0000,,add 12 - 1 night. The addition\Nand subtraction of the same
Dialogue: 0,0:03:55.25,0:04:00.68,Default,,0000,0000,0000,,order of priority. So we work\Nfrom left to right. That's 2 +
Dialogue: 0,0:04:00.68,0:04:04.44,Default,,0000,0000,0000,,12 which is 14 - 1 which is 13.
Dialogue: 0,0:04:05.61,0:04:07.79,Default,,0000,0000,0000,,Look at this next example.
Dialogue: 0,0:04:08.34,0:04:12.87,Default,,0000,0000,0000,,Here we've got brackets and\Nusing board mass brackets are
Dialogue: 0,0:04:12.87,0:04:18.76,Default,,0000,0000,0000,,done first, so 3 + 5 is it,\Nso our expression becomes two
Dialogue: 0,0:04:18.76,0:04:21.93,Default,,0000,0000,0000,,times it, which is 16. Can be
Dialogue: 0,0:04:21.93,0:04:29.03,Default,,0000,0000,0000,,easier. What about the next one\N9 - 6? But I've got to add the
Dialogue: 0,0:04:29.03,0:04:34.47,Default,,0000,0000,0000,,plus one now in this case we've\Ngot the subtract and the ad
Dialogue: 0,0:04:34.47,0:04:39.42,Default,,0000,0000,0000,,together. So we've got the same\Npriority. The rule is work from
Dialogue: 0,0:04:39.42,0:04:45.50,Default,,0000,0000,0000,,left to right, so we say 9 - 6\Nwhich is 3 add 1 which is 4.
Dialogue: 0,0:04:46.68,0:04:49.21,Default,,0000,0000,0000,,The last two involving powers.
Dialogue: 0,0:04:49.76,0:04:55.82,Default,,0000,0000,0000,,3 + 2 squared while using board\NMars again, we do the squares,
Dialogue: 0,0:04:55.82,0:05:02.34,Default,,0000,0000,0000,,the powers first 2 squared is 4,\Nso our expression becomes 3 + 4
Dialogue: 0,0:05:02.34,0:05:05.14,Default,,0000,0000,0000,,and 3 + 4 is 7.
Dialogue: 0,0:05:06.37,0:05:08.74,Default,,0000,0000,0000,,And finally this expression.
Dialogue: 0,0:05:09.35,0:05:14.53,Default,,0000,0000,0000,,3 + 2 all squared. Now we've got\Npowers, an brackets. But
Dialogue: 0,0:05:14.53,0:05:18.85,Default,,0000,0000,0000,,remember using board Mads we do\Nwhat's inside the brackets
Dialogue: 0,0:05:18.85,0:05:22.74,Default,,0000,0000,0000,,first, so it's 3 + 2 which is 5.
Dialogue: 0,0:05:22.76,0:05:26.68,Default,,0000,0000,0000,,And then we have to square the\Nfive which is 25.
Dialogue: 0,0:05:27.56,0:05:32.01,Default,,0000,0000,0000,,Now in these two last examples\Nwith the got the same numbers.
Dialogue: 0,0:05:32.87,0:05:36.74,Default,,0000,0000,0000,,And we've got a square, but\Nyou've got two totally
Dialogue: 0,0:05:36.74,0:05:40.100,Default,,0000,0000,0000,,different answers. And the\Nreason why is in this one the
Dialogue: 0,0:05:40.100,0:05:45.64,Default,,0000,0000,0000,,square is for the things\Ninside the bracket. The 3 + 2,
Dialogue: 0,0:05:45.64,0:05:49.51,Default,,0000,0000,0000,,whereas in this one this\Nsquare relates to just the
Dialogue: 0,0:05:49.51,0:05:49.90,Default,,0000,0000,0000,,two.
Dialogue: 0,0:05:51.14,0:05:55.72,Default,,0000,0000,0000,,So remember when you're doing\Nany calculations which involve
Dialogue: 0,0:05:55.72,0:05:58.78,Default,,0000,0000,0000,,operations such as brackets,\Npowers, division,
Dialogue: 0,0:05:58.78,0:06:02.85,Default,,0000,0000,0000,,multiplication, subtraction and\Naddition, use board baths and
Dialogue: 0,0:06:02.85,0:06:04.88,Default,,0000,0000,0000,,you won't go wrong.
Dialogue: 0,0:06:05.77,0:06:07.01,Default,,0000,0000,0000,,What math means?
Dialogue: 0,0:06:07.74,0:06:12.63,Default,,0000,0000,0000,,Brackets first, then powers\Nfollowed by multiplication and
Dialogue: 0,0:06:12.63,0:06:15.29,Default,,0000,0000,0000,,division. And then addition to
Dialogue: 0,0:06:15.29,0:06:19.96,Default,,0000,0000,0000,,Subtraction. And when you have\Noperations of the same priority.
Dialogue: 0,0:06:20.53,0:06:22.63,Default,,0000,0000,0000,,He just work from left to right.
Dialogue: 0,0:06:23.42,0:06:24.67,Default,,0000,0000,0000,,Nothing could be easier.
Dialogue: 0,0:06:26.20,0:06:30.33,Default,,0000,0000,0000,,And now I will move on to\Ncalculations involving positive
Dialogue: 0,0:06:30.33,0:06:34.05,Default,,0000,0000,0000,,and negative numbers. Now what\Nare positive and negative
Dialogue: 0,0:06:34.05,0:06:38.59,Default,,0000,0000,0000,,numbers? Well, if we take all\Nthe real numbers except 0.
Dialogue: 0,0:06:39.10,0:06:40.52,Default,,0000,0000,0000,,All real numbers.
Dialogue: 0,0:06:41.07,0:06:43.76,Default,,0000,0000,0000,,Can be. Either\Npositive or
Dialogue: 0,0:06:43.76,0:06:46.43,Default,,0000,0000,0000,,negative, and of\Ncourse except 0.
Dialogue: 0,0:06:47.71,0:06:50.81,Default,,0000,0000,0000,,Now, where are those\Nnumbers? Well, if we
Dialogue: 0,0:06:50.81,0:06:52.74,Default,,0000,0000,0000,,look on a number line.
Dialogue: 0,0:06:53.81,0:07:00.22,Default,,0000,0000,0000,,And position 0 all the positive\Nnumbers are to the right.
Dialogue: 0,0:07:00.83,0:07:04.54,Default,,0000,0000,0000,,And all the negative numbers are\Nto the left.
Dialogue: 0,0:07:05.44,0:07:12.14,Default,,0000,0000,0000,,And we represent the numbers on\Nthe number line like this
Dialogue: 0,0:07:12.14,0:07:17.01,Default,,0000,0000,0000,,positive one, positive 2\Npositive 3 positive for.
Dialogue: 0,0:07:17.65,0:07:19.81,Default,,0000,0000,0000,,Positive 5 and so on.
Dialogue: 0,0:07:21.40,0:07:27.00,Default,,0000,0000,0000,,Negative one negative, two\Nnegative, three negative,
Dialogue: 0,0:07:27.00,0:07:29.40,Default,,0000,0000,0000,,four negative 5.
Dialogue: 0,0:07:30.54,0:07:35.02,Default,,0000,0000,0000,,Notice how we've written in\Nnumbers, the positive numbers
Dialogue: 0,0:07:35.02,0:07:40.00,Default,,0000,0000,0000,,and the negative numbers. We\Nwrite positive three like this
Dialogue: 0,0:07:40.00,0:07:46.48,Default,,0000,0000,0000,,and negative for like this. The\Nsign of the number is written as
Dialogue: 0,0:07:46.48,0:07:49.22,Default,,0000,0000,0000,,a superscript. Now we do this.
Dialogue: 0,0:07:50.08,0:07:54.72,Default,,0000,0000,0000,,To help our understanding so\Nthat we don't confuse the sign
Dialogue: 0,0:07:54.72,0:07:57.25,Default,,0000,0000,0000,,of the number with addition and
Dialogue: 0,0:07:57.25,0:07:59.73,Default,,0000,0000,0000,,Subtraction. But of course with
Dialogue: 0,0:07:59.73,0:08:04.62,Default,,0000,0000,0000,,practice. We drop this and we\Njust use the normal standard
Dialogue: 0,0:08:04.62,0:08:08.40,Default,,0000,0000,0000,,notation. But for this\Nsession I'm going to use the
Dialogue: 0,0:08:08.40,0:08:10.24,Default,,0000,0000,0000,,superscripts just to help\Nour understanding.
Dialogue: 0,0:08:12.58,0:08:16.31,Default,,0000,0000,0000,,But what about calculations\Ninvolving positive and negative
Dialogue: 0,0:08:16.31,0:08:19.57,Default,,0000,0000,0000,,numbers? What about addition,\Nsubtraction, multiplication and
Dialogue: 0,0:08:19.57,0:08:25.45,Default,,0000,0000,0000,,division? Well, I would take\Nsome examples. If I take these
Dialogue: 0,0:08:25.45,0:08:27.76,Default,,0000,0000,0000,,two examples, negative four at
Dialogue: 0,0:08:27.76,0:08:30.02,Default,,0000,0000,0000,,positive 5. And.
Dialogue: 0,0:08:31.45,0:08:34.46,Default,,0000,0000,0000,,Positive for. Subtract
Dialogue: 0,0:08:34.46,0:08:40.56,Default,,0000,0000,0000,,positive 9. If I have\Nthose two calculations, what do
Dialogue: 0,0:08:40.56,0:08:43.38,Default,,0000,0000,0000,,they work out to be well?
Dialogue: 0,0:08:43.89,0:08:47.62,Default,,0000,0000,0000,,In the first instance, we can\Nuse a number line to help us
Dialogue: 0,0:08:47.62,0:08:52.93,Default,,0000,0000,0000,,evaluate them. And we have to\Nremember that using a number
Dialogue: 0,0:08:52.93,0:08:57.53,Default,,0000,0000,0000,,line addition means you kind on\Nin that direction, and
Dialogue: 0,0:08:57.53,0:09:01.21,Default,,0000,0000,0000,,subtraction means you kind back\Nin that direction.
Dialogue: 0,0:09:01.88,0:09:07.71,Default,,0000,0000,0000,,So using those two little rules\Nwill calculate this expression
Dialogue: 0,0:09:07.71,0:09:09.46,Default,,0000,0000,0000,,and then this.
Dialogue: 0,0:09:10.13,0:09:15.28,Default,,0000,0000,0000,,So take this one to begin with\Nnegative 4. Add positive five.
Dialogue: 0,0:09:15.28,0:09:17.85,Default,,0000,0000,0000,,Start at negative, 4 on the
Dialogue: 0,0:09:17.85,0:09:25.10,Default,,0000,0000,0000,,number line. And kind on\Nfive 12345, so it negative
Dialogue: 0,0:09:25.10,0:09:32.28,Default,,0000,0000,0000,,4 add positive 5 gives\Nme the answer positive one.
Dialogue: 0,0:09:33.97,0:09:39.11,Default,,0000,0000,0000,,For the other example, we've got\Na subtraction, so we started
Dialogue: 0,0:09:39.11,0:09:41.44,Default,,0000,0000,0000,,positive four, and we subtract
Dialogue: 0,0:09:41.44,0:09:44.47,Default,,0000,0000,0000,,positive 9. To start a positive
Dialogue: 0,0:09:44.47,0:09:47.82,Default,,0000,0000,0000,,for. And kind
Dialogue: 0,0:09:47.82,0:09:53.97,Default,,0000,0000,0000,,back 91234.\N56789 so
Dialogue: 0,0:09:53.97,0:09:56.76,Default,,0000,0000,0000,,positive for
Dialogue: 0,0:09:56.76,0:10:02.13,Default,,0000,0000,0000,,subtract. Positive 9 gives\Nyou negative 5.
Dialogue: 0,0:10:03.43,0:10:04.46,Default,,0000,0000,0000,,It could be simpler.
Dialogue: 0,0:10:04.99,0:10:09.32,Default,,0000,0000,0000,,Now, to simplify matters a\Nlittle bit further, it really is
Dialogue: 0,0:10:09.32,0:10:12.08,Default,,0000,0000,0000,,a fast to keep writing all these
Dialogue: 0,0:10:12.08,0:10:16.42,Default,,0000,0000,0000,,signs. And because positive\Nnumbers are the numbers that we
Dialogue: 0,0:10:16.42,0:10:20.33,Default,,0000,0000,0000,,usually use in calculations, we\Ndrop them. We dropped the sign.
Dialogue: 0,0:10:20.94,0:10:27.54,Default,,0000,0000,0000,,So positive 5 can be written is\Njust five, and we know that
Dialogue: 0,0:10:27.54,0:10:33.13,Default,,0000,0000,0000,,positive one is equal to 1 and\Npositive 9 has 9.
Dialogue: 0,0:10:34.87,0:10:39.66,Default,,0000,0000,0000,,And it's understood by everyone\Nthat where you have numbers with
Dialogue: 0,0:10:39.66,0:10:43.57,Default,,0000,0000,0000,,no sign written there then they\Nare positive numbers.
Dialogue: 0,0:10:44.17,0:10:45.92,Default,,0000,0000,0000,,And I'm going to use that.
Dialogue: 0,0:10:46.48,0:10:48.94,Default,,0000,0000,0000,,In all my calculations following
Dialogue: 0,0:10:48.94,0:10:55.32,Default,,0000,0000,0000,,on. But if you notice in\Nthis calculation and in this
Dialogue: 0,0:10:55.32,0:11:00.03,Default,,0000,0000,0000,,one. We've added and\Nsubtracted positive numbers.
Dialogue: 0,0:11:01.64,0:11:05.22,Default,,0000,0000,0000,,But how do we add and subtract
Dialogue: 0,0:11:05.22,0:11:12.12,Default,,0000,0000,0000,,negative numbers? Well, try and\Ngenerate an easy route.
Dialogue: 0,0:11:12.12,0:11:16.54,Default,,0000,0000,0000,,Going to look at some patterns\Nof both addition and Subtraction
Dialogue: 0,0:11:16.54,0:11:18.55,Default,,0000,0000,0000,,and will start with addition.
Dialogue: 0,0:11:19.14,0:11:21.86,Default,,0000,0000,0000,,And we'll start with something\Nthat we know.
Dialogue: 0,0:11:22.54,0:11:28.96,Default,,0000,0000,0000,,If we start with 5 + 2,\Nwe know that is 7.
Dialogue: 0,0:11:29.69,0:11:33.72,Default,,0000,0000,0000,,And then I'm going to write a\Nsequence of calculations which
Dialogue: 0,0:11:33.72,0:11:35.18,Default,,0000,0000,0000,,follow on from this.
Dialogue: 0,0:11:35.54,0:11:37.57,Default,,0000,0000,0000,,5 at one.
Dialogue: 0,0:11:38.11,0:11:44.15,Default,,0000,0000,0000,,Is equal to 65. Add zero\Nis equal to 5.
Dialogue: 0,0:11:45.44,0:11:50.52,Default,,0000,0000,0000,,Notice in this sequence of\Naddition the answers decreased
Dialogue: 0,0:11:50.52,0:11:56.03,Default,,0000,0000,0000,,by one. As the numbers that we\Nadd decreased by one.
Dialogue: 0,0:11:56.61,0:12:00.56,Default,,0000,0000,0000,,So if we follow the pattern.
Dialogue: 0,0:12:01.47,0:12:07.31,Default,,0000,0000,0000,,We take 5 add negative one\Nbecause negative one is 0.
Dialogue: 0,0:12:07.31,0:12:14.21,Default,,0000,0000,0000,,Subtract 1 is one less than\Nzero, then it must equal for. If
Dialogue: 0,0:12:14.21,0:12:16.87,Default,,0000,0000,0000,,we continue the pattern on.
Dialogue: 0,0:12:17.87,0:12:24.69,Default,,0000,0000,0000,,And five add negative, two must\Nequal 3 and five ad.
Dialogue: 0,0:12:25.50,0:12:31.04,Default,,0000,0000,0000,,Negative three must equal\Ntwo and five add negative.
Dialogue: 0,0:12:31.04,0:12:33.51,Default,,0000,0000,0000,,Four must equal 1.
Dialogue: 0,0:12:34.76,0:12:36.97,Default,,0000,0000,0000,,Not if we look at these
Dialogue: 0,0:12:36.97,0:12:41.69,Default,,0000,0000,0000,,additions. These additions of\Nnegative numbers we can actually
Dialogue: 0,0:12:41.69,0:12:45.06,Default,,0000,0000,0000,,write these calculations as\Nsubtractions of positive
Dialogue: 0,0:12:45.06,0:12:50.83,Default,,0000,0000,0000,,numbers, so 5 add negative, one\Nwould be the same as five
Dialogue: 0,0:12:50.83,0:12:54.19,Default,,0000,0000,0000,,subtract 1 and you get the same
Dialogue: 0,0:12:54.19,0:13:00.66,Default,,0000,0000,0000,,answer for. Similarly, 5 add\Nnegative two can be written as
Dialogue: 0,0:13:00.66,0:13:07.22,Default,,0000,0000,0000,,five subtract 2 and you get the\Nanswer 35 add negative. Three
Dialogue: 0,0:13:07.22,0:13:10.49,Default,,0000,0000,0000,,can be written as five, subtract
Dialogue: 0,0:13:10.49,0:13:14.18,Default,,0000,0000,0000,,3. Give me the answer 2 and
Dialogue: 0,0:13:14.18,0:13:19.86,Default,,0000,0000,0000,,then 5. Add negative four is\Nthe same as five. Subtract
Dialogue: 0,0:13:19.86,0:13:21.62,Default,,0000,0000,0000,,4, which is one.
Dialogue: 0,0:13:22.79,0:13:27.02,Default,,0000,0000,0000,,So when we have the addition\Nof negative numbers.
Dialogue: 0,0:13:28.33,0:13:31.34,Default,,0000,0000,0000,,That's the same as\Nthe subtraction of
Dialogue: 0,0:13:31.34,0:13:32.63,Default,,0000,0000,0000,,the positive number.
Dialogue: 0,0:13:33.86,0:13:36.78,Default,,0000,0000,0000,,So I had these two examples.
Dialogue: 0,0:13:37.58,0:13:40.98,Default,,0000,0000,0000,,It at negative 10.
Dialogue: 0,0:13:42.18,0:13:45.57,Default,,0000,0000,0000,,And negative 9 at
Dialogue: 0,0:13:45.57,0:13:49.21,Default,,0000,0000,0000,,negative 5. Using that
Dialogue: 0,0:13:49.21,0:13:52.65,Default,,0000,0000,0000,,room. Hi, we calculate
Dialogue: 0,0:13:52.65,0:13:59.53,Default,,0000,0000,0000,,the answer. Now we take it add\Nnegative 10. That's the same as
Dialogue: 0,0:13:59.53,0:14:01.01,Default,,0000,0000,0000,,it subtract 10.
Dialogue: 0,0:14:01.80,0:14:06.28,Default,,0000,0000,0000,,I'm thinking about the number\Nline. He started it and you go
Dialogue: 0,0:14:06.28,0:14:11.33,Default,,0000,0000,0000,,back 10. So you go back to 0\Nand then another two you get
Dialogue: 0,0:14:11.33,0:14:12.87,Default,,0000,0000,0000,,to the answer negative 2.
Dialogue: 0,0:14:14.00,0:14:16.65,Default,,0000,0000,0000,,And with this example.
Dialogue: 0,0:14:17.20,0:14:22.81,Default,,0000,0000,0000,,Negative nine and negative five.\NWe can rewrite that as negative
Dialogue: 0,0:14:22.81,0:14:28.93,Default,,0000,0000,0000,,9 subtract 5 again. Visualizing\Nit on the number line start at
Dialogue: 0,0:14:28.93,0:14:36.50,Default,,0000,0000,0000,,negative 9. And you go\Nback five, go back five so your
Dialogue: 0,0:14:36.50,0:14:38.76,Default,,0000,0000,0000,,land at negative 14.
Dialogue: 0,0:14:40.32,0:14:45.95,Default,,0000,0000,0000,,So when we have the addition of\Nnegative numbers, it's always
Dialogue: 0,0:14:45.95,0:14:50.56,Default,,0000,0000,0000,,easier to change them into\Nsubtraction of positive numbers.
Dialogue: 0,0:14:51.42,0:14:57.57,Default,,0000,0000,0000,,But the one thing that we\Nhaven't done is the subtraction
Dialogue: 0,0:14:57.57,0:14:59.25,Default,,0000,0000,0000,,of negative numbers.
Dialogue: 0,0:15:00.03,0:15:04.90,Default,,0000,0000,0000,,So again, I'd like to use a\Npattern to help us workout the
Dialogue: 0,0:15:04.90,0:15:07.16,Default,,0000,0000,0000,,rule that we're going to use.
Dialogue: 0,0:15:07.89,0:15:10.67,Default,,0000,0000,0000,,If we start off with what we
Dialogue: 0,0:15:10.67,0:15:13.95,Default,,0000,0000,0000,,know. 4 subtract 2 is 2.
Dialogue: 0,0:15:14.59,0:15:22.24,Default,,0000,0000,0000,,So 4 subtract 1 is\N3 and four subtract 0
Dialogue: 0,0:15:22.24,0:15:23.77,Default,,0000,0000,0000,,is for.
Dialogue: 0,0:15:24.89,0:15:29.22,Default,,0000,0000,0000,,Notice in this sequence of\NSubtractions, the answers are
Dialogue: 0,0:15:29.22,0:15:31.14,Default,,0000,0000,0000,,going up by one.
Dialogue: 0,0:15:32.06,0:15:36.06,Default,,0000,0000,0000,,As the numbers that we're\Nsubtracting decreased by one.
Dialogue: 0,0:15:36.86,0:15:42.03,Default,,0000,0000,0000,,So if we continue the pattern in\Nthe calculations, the next
Dialogue: 0,0:15:42.03,0:15:47.20,Default,,0000,0000,0000,,calculation would be 4. Subtract\Nnegative one and the answer will
Dialogue: 0,0:15:47.20,0:15:53.78,Default,,0000,0000,0000,,be 5. You add one on to the\Nfour to make 5, and four
Dialogue: 0,0:15:53.78,0:15:55.19,Default,,0000,0000,0000,,subtract negative 2.
Dialogue: 0,0:15:55.88,0:16:02.72,Default,,0000,0000,0000,,Will be 6 and four. Subtract\Nnegative. Three would be 7.
Dialogue: 0,0:16:03.25,0:16:07.90,Default,,0000,0000,0000,,And four subtract\Nnegative four is it?
Dialogue: 0,0:16:09.90,0:16:16.06,Default,,0000,0000,0000,,Now again. If we look\Nat these subtractions
Dialogue: 0,0:16:16.06,0:16:18.24,Default,,0000,0000,0000,,of negative numbers.
Dialogue: 0,0:16:20.16,0:16:23.92,Default,,0000,0000,0000,,What calculation would be easier\Nto do using the numbers but
Dialogue: 0,0:16:23.92,0:16:27.68,Default,,0000,0000,0000,,still arriving at the same\Nanswer when I think it's quite
Dialogue: 0,0:16:27.68,0:16:31.14,Default,,0000,0000,0000,,obvious. For this one, it's for
Dialogue: 0,0:16:31.14,0:16:36.38,Default,,0000,0000,0000,,AD one. And that gives us the\Nanswer 5. The numbers of the
Dialogue: 0,0:16:36.38,0:16:39.05,Default,,0000,0000,0000,,same, but the operation and\Nassign are different.
Dialogue: 0,0:16:40.46,0:16:44.88,Default,,0000,0000,0000,,For this one it before add 2 and\Nthat will give us 6.
Dialogue: 0,0:16:45.45,0:16:49.95,Default,,0000,0000,0000,,For this one it before at three,\Nand that will give us 7.
Dialogue: 0,0:16:50.59,0:16:54.69,Default,,0000,0000,0000,,And finally, for ad for which\Nwill give us it.
Dialogue: 0,0:16:56.28,0:16:56.96,Default,,0000,0000,0000,,So.
Dialogue: 0,0:16:58.00,0:17:03.60,Default,,0000,0000,0000,,If we look at our pattern, we\Ncan see that when you've got the
Dialogue: 0,0:17:03.60,0:17:07.60,Default,,0000,0000,0000,,subtraction of a negative\Nnumber, that's the same as the
Dialogue: 0,0:17:07.60,0:17:09.60,Default,,0000,0000,0000,,addition of a positive number.
Dialogue: 0,0:17:11.54,0:17:17.27,Default,,0000,0000,0000,,So we'll use that room to\Nworkout these calculations if we
Dialogue: 0,0:17:17.27,0:17:19.88,Default,,0000,0000,0000,,take it, subtract negative 10.
Dialogue: 0,0:17:20.72,0:17:24.24,Default,,0000,0000,0000,,And negative 6 subtract
Dialogue: 0,0:17:24.24,0:17:31.66,Default,,0000,0000,0000,,negative 13. What answers do\Nwe get if we use our room where
Dialogue: 0,0:17:31.66,0:17:36.09,Default,,0000,0000,0000,,we change the subtraction to\Naddition of a positive number?
Dialogue: 0,0:17:36.09,0:17:40.97,Default,,0000,0000,0000,,So is it plus 10? What could be\Neasier? That's 18.
Dialogue: 0,0:17:41.82,0:17:48.01,Default,,0000,0000,0000,,This one you've got negative 6\Nadd 13 slightly harder, but not
Dialogue: 0,0:17:48.01,0:17:53.17,Default,,0000,0000,0000,,too difficult. They give\Nnegative 6 and the number line
Dialogue: 0,0:17:53.17,0:17:59.88,Default,,0000,0000,0000,,and go forward kind on 13. He\Nkind on 6 and then another
Dialogue: 0,0:17:59.88,0:18:05.04,Default,,0000,0000,0000,,Seven. So the answer is positive\N7 written like that.
Dialogue: 0,0:18:07.02,0:18:13.30,Default,,0000,0000,0000,,So how can we combine all these\Nrooms together in a nice, easy
Dialogue: 0,0:18:13.30,0:18:18.13,Default,,0000,0000,0000,,way for you to remember? Well,\Nthis is one way.
Dialogue: 0,0:18:18.87,0:18:24.79,Default,,0000,0000,0000,,If the operation in the sign are\Nthe same like this.
Dialogue: 0,0:18:25.92,0:18:26.79,Default,,0000,0000,0000,,Sam
Dialogue: 0,0:18:28.17,0:18:31.98,Default,,0000,0000,0000,,The calculation works like\Nan addition.
Dialogue: 0,0:18:33.45,0:18:36.55,Default,,0000,0000,0000,,Off a positive number.
Dialogue: 0,0:18:40.96,0:18:46.25,Default,,0000,0000,0000,,If the operation and assign are\Ndifferent like this.
Dialogue: 0,0:18:48.35,0:18:50.100,Default,,0000,0000,0000,,Then the operation.
Dialogue: 0,0:18:51.75,0:18:55.72,Default,,0000,0000,0000,,Works like this subtraction.
Dialogue: 0,0:18:55.94,0:18:59.81,Default,,0000,0000,0000,,Off a positive number.
Dialogue: 0,0:19:00.92,0:19:05.68,Default,,0000,0000,0000,,Now, if you remember those two\NGolden rules, then the addition
Dialogue: 0,0:19:05.68,0:19:10.01,Default,,0000,0000,0000,,and subtraction of positive and\Nnegative numbers is dead easy.
Dialogue: 0,0:19:10.83,0:19:14.95,Default,,0000,0000,0000,,Now we've talked about addition\Nand subtraction of positive and
Dialogue: 0,0:19:14.95,0:19:17.01,Default,,0000,0000,0000,,negative numbers, but wanna bite
Dialogue: 0,0:19:17.01,0:19:22.53,Default,,0000,0000,0000,,multiplication Indovision. Well,\Nwe start with what we know. We
Dialogue: 0,0:19:22.53,0:19:28.13,Default,,0000,0000,0000,,know how to multiply and divide\Npositive numbers. We know that
Dialogue: 0,0:19:28.13,0:19:31.18,Default,,0000,0000,0000,,five times by 5 is 25.
Dialogue: 0,0:19:32.06,0:19:35.97,Default,,0000,0000,0000,,An 5 / 5 is one
Dialogue: 0,0:19:35.97,0:19:41.06,Default,,0000,0000,0000,,dead easy. But what about\Nthe multiplication division
Dialogue: 0,0:19:41.06,0:19:42.52,Default,,0000,0000,0000,,of negative numbers?
Dialogue: 0,0:19:43.54,0:19:48.20,Default,,0000,0000,0000,,Well, I'll use patterns the way\NI did before. In addition,
Dialogue: 0,0:19:48.20,0:19:53.29,Default,,0000,0000,0000,,Subtraction. And I'll start off\Nwith this calculation and
Dialogue: 0,0:19:53.29,0:19:57.06,Default,,0000,0000,0000,,continue doing a sequence of\Nmultiplications that involve
Dialogue: 0,0:19:57.06,0:20:03.18,Default,,0000,0000,0000,,negative numbers, and we'll see\Nif we can get a rule coming out
Dialogue: 0,0:20:03.18,0:20:05.53,Default,,0000,0000,0000,,from the pattern in the
Dialogue: 0,0:20:05.53,0:20:09.90,Default,,0000,0000,0000,,calculations. For the next\Ncalculation here, I'll say this
Dialogue: 0,0:20:09.90,0:20:11.99,Default,,0000,0000,0000,,is 5 times by 4.
Dialogue: 0,0:20:12.78,0:20:14.69,Default,,0000,0000,0000,,And we know that is 20.
Dialogue: 0,0:20:15.42,0:20:22.76,Default,,0000,0000,0000,,Five times by 3:15,\Nfive times two is
Dialogue: 0,0:20:22.76,0:20:28.89,Default,,0000,0000,0000,,10. 5 * 1\Nis 5 and 5
Dialogue: 0,0:20:28.89,0:20:31.56,Default,,0000,0000,0000,,* 0 is not.
Dialogue: 0,0:20:32.85,0:20:37.73,Default,,0000,0000,0000,,I notice in these\Nmultiplications the answers.
Dialogue: 0,0:20:38.30,0:20:43.18,Default,,0000,0000,0000,,Are going down by 5 as the\Nnumber that we times by
Dialogue: 0,0:20:43.18,0:20:44.40,Default,,0000,0000,0000,,decreases by one.
Dialogue: 0,0:20:45.22,0:20:50.62,Default,,0000,0000,0000,,So the next calculation in the\Nsequence would be 5 times by
Dialogue: 0,0:20:50.62,0:20:54.74,Default,,0000,0000,0000,,negative one. And if we use the\Npattern that have just stated.
Dialogue: 0,0:20:55.43,0:21:00.92,Default,,0000,0000,0000,,We subtract 5 from zero as we\Nsubtract 5 from zero, we get
Dialogue: 0,0:21:00.92,0:21:05.98,Default,,0000,0000,0000,,negative 5. The next calculation\Nwould be 5 times by negative 2.
Dialogue: 0,0:21:07.27,0:21:11.48,Default,,0000,0000,0000,,Negative 5 subtract\N5 is negative 10.
Dialogue: 0,0:21:12.72,0:21:15.07,Default,,0000,0000,0000,,Five times by negative 3.
Dialogue: 0,0:21:15.92,0:21:19.68,Default,,0000,0000,0000,,Negative 10 subtract 5 negative
Dialogue: 0,0:21:19.68,0:21:26.50,Default,,0000,0000,0000,,15. Will do just one more just\Nto see if we can spot the
Dialogue: 0,0:21:26.50,0:21:30.78,Default,,0000,0000,0000,,pattern and the pattern is\Nworking five times negative 4.
Dialogue: 0,0:21:31.55,0:21:35.53,Default,,0000,0000,0000,,Take negative 15 and subtract 5.\NThat's negative 20.
Dialogue: 0,0:21:37.17,0:21:39.11,Default,,0000,0000,0000,,So look at.
Dialogue: 0,0:21:39.74,0:21:41.86,Default,,0000,0000,0000,,Our multiplications by a
Dialogue: 0,0:21:41.86,0:21:48.82,Default,,0000,0000,0000,,negative number. We get\Na negative number answer.
Dialogue: 0,0:21:49.49,0:21:54.35,Default,,0000,0000,0000,,So when we multiply a negative\Nsorry, a negative by a positive.
Dialogue: 0,0:21:56.04,0:21:58.80,Default,,0000,0000,0000,,Will always get a\Nnegative answer.
Dialogue: 0,0:21:59.94,0:22:04.86,Default,,0000,0000,0000,,And vice versa if we multiply a\Nnegative by a positive.
Dialogue: 0,0:22:05.81,0:22:07.28,Default,,0000,0000,0000,,Will get a negative.
Dialogue: 0,0:22:08.29,0:22:11.17,Default,,0000,0000,0000,,So if I give you these two
Dialogue: 0,0:22:11.17,0:22:15.77,Default,,0000,0000,0000,,examples. 6 times by\Nnegative 5.
Dialogue: 0,0:22:17.12,0:22:21.43,Default,,0000,0000,0000,,Steady, easy to workout. The\Nanswer you just multiply the six
Dialogue: 0,0:22:21.43,0:22:26.53,Default,,0000,0000,0000,,by the five to get 30. The signs\Nare different. Remember this is
Dialogue: 0,0:22:26.53,0:22:31.23,Default,,0000,0000,0000,,positive 6 times by negative 5\Nthe two signs are different, so
Dialogue: 0,0:22:31.23,0:22:33.58,Default,,0000,0000,0000,,the answer is a negative number
Dialogue: 0,0:22:33.58,0:22:40.69,Default,,0000,0000,0000,,negative 30. If we take\Nnegative four times by three.
Dialogue: 0,0:22:41.26,0:22:44.57,Default,,0000,0000,0000,,Multipliers normal 3/4 or 12.
Dialogue: 0,0:22:45.50,0:22:48.90,Default,,0000,0000,0000,,And then take into account\Nthe signs. This is a
Dialogue: 0,0:22:48.90,0:22:51.62,Default,,0000,0000,0000,,negative. This is a\Npositive. 2 signs different.
Dialogue: 0,0:22:51.62,0:22:53.32,Default,,0000,0000,0000,,So the answer is negative.
Dialogue: 0,0:22:54.61,0:22:56.65,Default,,0000,0000,0000,,And the same goes for division.
Dialogue: 0,0:22:58.02,0:23:04.38,Default,,0000,0000,0000,,And we can just double check\Nthat by looking at these two
Dialogue: 0,0:23:04.38,0:23:08.62,Default,,0000,0000,0000,,calculations. Negative 30\Ndivided by positive six must
Dialogue: 0,0:23:08.62,0:23:10.21,Default,,0000,0000,0000,,equal negative 5.
Dialogue: 0,0:23:11.49,0:23:16.64,Default,,0000,0000,0000,,And negative 12 divided by\Npositive three must equal
Dialogue: 0,0:23:16.64,0:23:17.78,Default,,0000,0000,0000,,negative 4.
Dialogue: 0,0:23:19.70,0:23:24.36,Default,,0000,0000,0000,,So when the signs are different\Nand you multiply positive and
Dialogue: 0,0:23:24.36,0:23:28.60,Default,,0000,0000,0000,,negative numbers together in\Npairs, the answer will always be
Dialogue: 0,0:23:28.60,0:23:29.88,Default,,0000,0000,0000,,a negative number.
Dialogue: 0,0:23:31.01,0:23:37.54,Default,,0000,0000,0000,,But we haven't finished just\Nyet. What if you multiply and
Dialogue: 0,0:23:37.54,0:23:39.92,Default,,0000,0000,0000,,divide by negative numbers?
Dialogue: 0,0:23:40.48,0:23:41.88,Default,,0000,0000,0000,,What happens there?
Dialogue: 0,0:23:42.68,0:23:46.20,Default,,0000,0000,0000,,Well, again, I'm going to use\Npatterns. I like using patterns
Dialogue: 0,0:23:46.20,0:23:50.04,Default,,0000,0000,0000,,because it gives me a bit of\Nconfidence that I'm doing things
Dialogue: 0,0:23:50.04,0:23:54.52,Default,,0000,0000,0000,,correctly and I always start off\Nwith things that I know. So if I
Dialogue: 0,0:23:54.52,0:23:57.40,Default,,0000,0000,0000,,start off with negative five\Ntimes by positive 4.
Dialogue: 0,0:23:58.14,0:24:02.41,Default,,0000,0000,0000,,I know the answer is negative 20\Nbecause the signs are different
Dialogue: 0,0:24:02.41,0:24:04.55,Default,,0000,0000,0000,,and 5 * 4 is 20.
Dialogue: 0,0:24:05.08,0:24:10.82,Default,,0000,0000,0000,,Next one in the sequence\Nnegative five times by three.
Dialogue: 0,0:24:10.82,0:24:17.71,Default,,0000,0000,0000,,That will give us negative 15\Nnegative 5 * 2 negative, ten
Dialogue: 0,0:24:17.71,0:24:24.60,Default,,0000,0000,0000,,negative 5 * 1 is negative,\Nfive negative 5 * 0 is
Dialogue: 0,0:24:24.60,0:24:26.32,Default,,0000,0000,0000,,equal to 0.
Dialogue: 0,0:24:27.94,0:24:29.10,Default,,0000,0000,0000,,Now look at the pattern.
Dialogue: 0,0:24:30.62,0:24:35.57,Default,,0000,0000,0000,,Is a bit like a dejavu. We've\Ndone this before. Look at the
Dialogue: 0,0:24:35.57,0:24:40.14,Default,,0000,0000,0000,,answers. You can see that we\Nare increasing by 5 each time
Dialogue: 0,0:24:40.14,0:24:44.72,Default,,0000,0000,0000,,as we multiply by one less\Neach time. That seems a bit
Dialogue: 0,0:24:44.72,0:24:46.62,Default,,0000,0000,0000,,odd, but stay with Maine.
Dialogue: 0,0:24:47.97,0:24:52.91,Default,,0000,0000,0000,,The next multiplication, if we\Nkeep the pattern in the
Dialogue: 0,0:24:52.91,0:24:57.85,Default,,0000,0000,0000,,calculations, the same would be\Nnegative five times by negative
Dialogue: 0,0:24:57.85,0:25:03.14,Default,,0000,0000,0000,,one. And according to our\Npattern, that will equal 5 more
Dialogue: 0,0:25:03.14,0:25:05.83,Default,,0000,0000,0000,,than zero, which is positive 5.
Dialogue: 0,0:25:06.59,0:25:11.43,Default,,0000,0000,0000,,Negative five times negative 2,\Nwhich is the next calculation in
Dialogue: 0,0:25:11.43,0:25:16.27,Default,,0000,0000,0000,,sequence. That would be five\Nmore than five, which is 10.
Dialogue: 0,0:25:16.80,0:25:19.60,Default,,0000,0000,0000,,Negative five times by negative
Dialogue: 0,0:25:19.60,0:25:22.35,Default,,0000,0000,0000,,3. Is 15th.
Dialogue: 0,0:25:23.04,0:25:27.67,Default,,0000,0000,0000,,Negative five times negative\Nfour is 20.
Dialogue: 0,0:25:29.88,0:25:35.80,Default,,0000,0000,0000,,So. It's really great. See that\Nwhen we multiply negative
Dialogue: 0,0:25:35.80,0:25:37.92,Default,,0000,0000,0000,,numbers together in pairs.
Dialogue: 0,0:25:38.42,0:25:40.62,Default,,0000,0000,0000,,We get a positive answer.
Dialogue: 0,0:25:41.74,0:25:46.05,Default,,0000,0000,0000,,Negative by negative gives it a\Npositive negative negative
Dialogue: 0,0:25:46.05,0:25:48.92,Default,,0000,0000,0000,,positive, negative negative\Npositive negative negative
Dialogue: 0,0:25:48.92,0:25:54.19,Default,,0000,0000,0000,,positive is not great. Dead\Neasy. So if I had this
Dialogue: 0,0:25:54.19,0:25:58.50,Default,,0000,0000,0000,,calculation negative 6 times by\Nnegative three, you multipliers
Dialogue: 0,0:25:58.50,0:26:04.73,Default,,0000,0000,0000,,normal. 6 * 3 is it teen? And\Nthe answer is positive positive
Dialogue: 0,0:26:04.73,0:26:09.04,Default,,0000,0000,0000,,via team because it's two\Nnegatives makes the positive.
Dialogue: 0,0:26:09.57,0:26:16.37,Default,,0000,0000,0000,,And the same goes with\Nthis one. If we had
Dialogue: 0,0:26:16.37,0:26:19.77,Default,,0000,0000,0000,,negative 9 times by negative
Dialogue: 0,0:26:19.77,0:26:22.04,Default,,0000,0000,0000,,229382. Two negatives.
Dialogue: 0,0:26:22.59,0:26:26.36,Default,,0000,0000,0000,,The answer is a positive, so\Nagain we get the same answer
Dialogue: 0,0:26:26.36,0:26:28.87,Default,,0000,0000,0000,,it team but different numbers\Nin the calculation.
Dialogue: 0,0:26:29.91,0:26:33.62,Default,,0000,0000,0000,,But remember where else did we\Nget a positive answer?
Dialogue: 0,0:26:34.60,0:26:37.06,Default,,0000,0000,0000,,When you multiplied 2 positive
Dialogue: 0,0:26:37.06,0:26:41.44,Default,,0000,0000,0000,,numbers together. So if you\Nmultiplied 6 by three, you'll
Dialogue: 0,0:26:41.44,0:26:46.06,Default,,0000,0000,0000,,get it team and when you\Nmultiplied 9 by two you get it
Dialogue: 0,0:26:46.06,0:26:49.72,Default,,0000,0000,0000,,too. So when the signs of
Dialogue: 0,0:26:49.72,0:26:54.94,Default,,0000,0000,0000,,the same. Then the answer will\Nbe positive whether they are
Dialogue: 0,0:26:54.94,0:26:58.10,Default,,0000,0000,0000,,two negatives be multiplied\Ntogether or two positive
Dialogue: 0,0:26:58.10,0:26:59.68,Default,,0000,0000,0000,,numbers being multiplied\Ntogether.
Dialogue: 0,0:27:00.79,0:27:07.45,Default,,0000,0000,0000,,And that's a lot to take\Nin for multiplication and
Dialogue: 0,0:27:07.45,0:27:10.11,Default,,0000,0000,0000,,division of negative numbers.
Dialogue: 0,0:27:10.12,0:27:16.06,Default,,0000,0000,0000,,I'd like to summarize that bit\Nby again using a diagram when
Dialogue: 0,0:27:16.06,0:27:18.54,Default,,0000,0000,0000,,the signs of the sea.
Dialogue: 0,0:27:19.48,0:27:27.33,Default,,0000,0000,0000,,A positive times by a positive\Nor a negative times by a
Dialogue: 0,0:27:27.33,0:27:30.17,Default,,0000,0000,0000,,negative. The
Dialogue: 0,0:27:30.17,0:27:33.81,Default,,0000,0000,0000,,answer. Is
Dialogue: 0,0:27:33.81,0:27:40.86,Default,,0000,0000,0000,,positive. Is a\Npositive number when the signs
Dialogue: 0,0:27:40.86,0:27:48.02,Default,,0000,0000,0000,,are different. I positive\Ntimes by a negative or
Dialogue: 0,0:27:48.02,0:27:51.54,Default,,0000,0000,0000,,a negative times by a
Dialogue: 0,0:27:51.54,0:27:54.27,Default,,0000,0000,0000,,positive. The answer.
Dialogue: 0,0:27:55.76,0:27:57.46,Default,,0000,0000,0000,,Is negative.
Dialogue: 0,0:28:00.40,0:28:07.15,Default,,0000,0000,0000,,And the same goes the same\Nrules go if you divide.
Dialogue: 0,0:28:07.95,0:28:15.14,Default,,0000,0000,0000,,So if\NI had
Dialogue: 0,0:28:15.14,0:28:22.68,Default,,0000,0000,0000,,these examples.\NNegative 6 divided
Dialogue: 0,0:28:22.68,0:28:26.87,Default,,0000,0000,0000,,by. Negative\N2.
Dialogue: 0,0:28:28.73,0:28:34.67,Default,,0000,0000,0000,,My answer will be do the\Ndivision first 6 / 2, which is 3
Dialogue: 0,0:28:34.67,0:28:38.91,Default,,0000,0000,0000,,and then think about the signs\Nnegative negative signs saying
Dialogue: 0,0:28:38.91,0:28:41.03,Default,,0000,0000,0000,,so. The answer is positive.
Dialogue: 0,0:28:41.96,0:28:49.21,Default,,0000,0000,0000,,And if we had this\Ndivision negative 12 divided by
Dialogue: 0,0:28:49.21,0:28:55.13,Default,,0000,0000,0000,,positive 3. Do the division is\Nnormal 12 / 3 is for.
Dialogue: 0,0:28:55.65,0:28:58.31,Default,,0000,0000,0000,,Think of the signs\Nsigns, different
Dialogue: 0,0:28:58.31,0:29:00.98,Default,,0000,0000,0000,,negative and a\Npositive. So the
Dialogue: 0,0:29:00.98,0:29:02.31,Default,,0000,0000,0000,,answer is negative.