[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.62,0:00:05.31,Default,,0000,0000,0000,,Find the sum 15 plus\Nnegative 46 plus 29.
Dialogue: 0,0:00:05.31,0:00:07.63,Default,,0000,0000,0000,,Let's just think about\Nthis first part over here
Dialogue: 0,0:00:07.63,0:00:13.06,Default,,0000,0000,0000,,where we have 15\Nplus negative 46.
Dialogue: 0,0:00:13.06,0:00:16.42,Default,,0000,0000,0000,,And we'll worry about\Nthe plus 29 later on.
Dialogue: 0,0:00:16.42,0:00:23.68,Default,,0000,0000,0000,,So let's just do\N15-- let me do that
Dialogue: 0,0:00:23.68,0:00:26.68,Default,,0000,0000,0000,,in a different color--\Nplus negative 46.
Dialogue: 0,0:00:26.68,0:00:27.76,Default,,0000,0000,0000,,I'll do it in that orange.
Dialogue: 0,0:00:30.96,0:00:33.25,Default,,0000,0000,0000,,Let me draw a number line\Nhere, just so we can properly
Dialogue: 0,0:00:33.25,0:00:36.63,Default,,0000,0000,0000,,visualize what is going on.
Dialogue: 0,0:00:36.63,0:00:39.62,Default,,0000,0000,0000,,That's my number line.
Dialogue: 0,0:00:39.62,0:00:41.12,Default,,0000,0000,0000,,And we're starting at 15.
Dialogue: 0,0:00:41.12,0:00:44.79,Default,,0000,0000,0000,,So let's draw a 0 over here.
Dialogue: 0,0:00:44.79,0:00:47.27,Default,,0000,0000,0000,,And so we're starting at 15.
Dialogue: 0,0:00:47.27,0:00:49.08,Default,,0000,0000,0000,,15 could be right over here.
Dialogue: 0,0:00:49.08,0:00:51.93,Default,,0000,0000,0000,,So this is 15.
Dialogue: 0,0:00:51.93,0:00:56.36,Default,,0000,0000,0000,,Let me draw a big fat arrow\Nto signify this is 15.
Dialogue: 0,0:00:56.36,0:01:00.02,Default,,0000,0000,0000,,15 has an absolute value of\N15, so the length of this arrow
Dialogue: 0,0:01:00.02,0:01:01.85,Default,,0000,0000,0000,,would be 15.
Dialogue: 0,0:01:01.85,0:01:07.31,Default,,0000,0000,0000,,Now we're adding\Nnegative 46 to that 15.
Dialogue: 0,0:01:07.31,0:01:12.58,Default,,0000,0000,0000,,This is equivalent\Nto 15 minus 46,
Dialogue: 0,0:01:12.58,0:01:17.03,Default,,0000,0000,0000,,which means we are going to\Nmove 46 spots to the left of 15.
Dialogue: 0,0:01:17.03,0:01:19.13,Default,,0000,0000,0000,,A negative sign or\Na minus means we're
Dialogue: 0,0:01:19.13,0:01:21.35,Default,,0000,0000,0000,,moving to the left\Non the number line.
Dialogue: 0,0:01:21.35,0:01:23.91,Default,,0000,0000,0000,,So we're going to\Nmove 46 to the left.
Dialogue: 0,0:01:23.91,0:01:31.02,Default,,0000,0000,0000,,We're starting at 15, and we are\Ngoing to move 46 to the left.
Dialogue: 0,0:01:31.02,0:01:38.15,Default,,0000,0000,0000,,So the length of this arrow\Nright here is going to be 46,
Dialogue: 0,0:01:38.15,0:01:39.36,Default,,0000,0000,0000,,and we're moving to the left.
Dialogue: 0,0:01:39.36,0:01:43.37,Default,,0000,0000,0000,,This is the negative 46\Nthat we're adding to the 15.
Dialogue: 0,0:01:43.37,0:01:47.22,Default,,0000,0000,0000,,We're going to end up\Nat some point over here.
Dialogue: 0,0:01:47.22,0:01:48.89,Default,,0000,0000,0000,,That point is clearly 0.
Dialogue: 0,0:01:48.89,0:01:51.47,Default,,0000,0000,0000,,Because we were 15 to the right.
Dialogue: 0,0:01:51.47,0:01:53.09,Default,,0000,0000,0000,,Now we're going to\Nmove 46 to the left.
Dialogue: 0,0:01:53.09,0:01:55.36,Default,,0000,0000,0000,,So we're definitely going\Nto be to the left of 0.
Dialogue: 0,0:01:55.36,0:01:57.37,Default,,0000,0000,0000,,It's definitely going\Nto be a negative number.
Dialogue: 0,0:01:57.37,0:02:00.51,Default,,0000,0000,0000,,And we can even think\Nabout the absolute value
Dialogue: 0,0:02:00.51,0:02:01.57,Default,,0000,0000,0000,,of that negative number.
Dialogue: 0,0:02:01.57,0:02:03.22,Default,,0000,0000,0000,,We can just visualize it.
Dialogue: 0,0:02:03.22,0:02:05.79,Default,,0000,0000,0000,,This yellow arrow\Nhas a length of 15.
Dialogue: 0,0:02:05.79,0:02:09.00,Default,,0000,0000,0000,,This orange arrow\Nhas a length of 46.
Dialogue: 0,0:02:09.00,0:02:11.10,Default,,0000,0000,0000,,The blue arrow that\NI'm about to draw,
Dialogue: 0,0:02:11.10,0:02:12.89,Default,,0000,0000,0000,,which is the sum\Nof these two, is
Dialogue: 0,0:02:12.89,0:02:18.31,Default,,0000,0000,0000,,going to have this\Nlength right over here.
Dialogue: 0,0:02:18.31,0:02:21.34,Default,,0000,0000,0000,,And just visually,\Nhow can we figure out
Dialogue: 0,0:02:21.34,0:02:23.41,Default,,0000,0000,0000,,the length of this\Nblue part if we
Dialogue: 0,0:02:23.41,0:02:25.02,Default,,0000,0000,0000,,know the length of\Nthis orange part
Dialogue: 0,0:02:25.02,0:02:27.32,Default,,0000,0000,0000,,and we know the length\Nof this yellow part?
Dialogue: 0,0:02:27.32,0:02:28.60,Default,,0000,0000,0000,,Well, it's just going\Nto be the difference.
Dialogue: 0,0:02:28.60,0:02:30.68,Default,,0000,0000,0000,,It's just going to be the\Ndifference of these two.
Dialogue: 0,0:02:30.68,0:02:32.98,Default,,0000,0000,0000,,So the absolute\Nvalue of the sum is
Dialogue: 0,0:02:32.98,0:02:36.14,Default,,0000,0000,0000,,going to be the difference\Nbetween this length, 46,
Dialogue: 0,0:02:36.14,0:02:38.85,Default,,0000,0000,0000,,and 15.
Dialogue: 0,0:02:38.85,0:02:42.30,Default,,0000,0000,0000,,Let me just figure\Nthat out, 46 minus 15.
Dialogue: 0,0:02:42.30,0:02:43.74,Default,,0000,0000,0000,,6 minus 5 is 1.
Dialogue: 0,0:02:43.74,0:02:45.79,Default,,0000,0000,0000,,4 minus 1 is 3.
Dialogue: 0,0:02:45.79,0:02:48.14,Default,,0000,0000,0000,,So the length of this\Nis going to be 31,
Dialogue: 0,0:02:48.14,0:02:52.10,Default,,0000,0000,0000,,and it's going to be\N31 to the left of 0.
Dialogue: 0,0:02:52.10,0:02:56.72,Default,,0000,0000,0000,,So this is going to be\Nnegative 31 right over here.
Dialogue: 0,0:02:56.72,0:03:00.91,Default,,0000,0000,0000,,We know that this first part\Nover here is negative 31,
Dialogue: 0,0:03:00.91,0:03:05.08,Default,,0000,0000,0000,,and then to that we\Nare going to add 29.
Dialogue: 0,0:03:05.08,0:03:06.66,Default,,0000,0000,0000,,So we're going to add 29.
Dialogue: 0,0:03:06.66,0:03:07.99,Default,,0000,0000,0000,,Let me do that in another color.
Dialogue: 0,0:03:07.99,0:03:09.20,Default,,0000,0000,0000,,What does that mean?
Dialogue: 0,0:03:09.20,0:03:11.84,Default,,0000,0000,0000,,That means that we're going\Nto start at negative 31,
Dialogue: 0,0:03:11.84,0:03:13.94,Default,,0000,0000,0000,,and we're going to\Nmove 29 to the right.
Dialogue: 0,0:03:13.94,0:03:19.07,Default,,0000,0000,0000,,We're adding 29, so we're\Ngoing to move 29 to the right.
Dialogue: 0,0:03:19.07,0:03:20.81,Default,,0000,0000,0000,,So maybe that gets\Nus right about there.
Dialogue: 0,0:03:20.81,0:03:24.47,Default,,0000,0000,0000,,I'm trying to draw an\Narrow of length 29.
Dialogue: 0,0:03:24.47,0:03:27.73,Default,,0000,0000,0000,,I can draw a cleaner\Nlooking arrow than that.
Dialogue: 0,0:03:27.73,0:03:29.91,Default,,0000,0000,0000,,I'll do it right\Nover here, actually.
Dialogue: 0,0:03:29.91,0:03:35.40,Default,,0000,0000,0000,,So then we're going to\Nmove 29 over to the right.
Dialogue: 0,0:03:35.40,0:03:38.35,Default,,0000,0000,0000,,That's the 29 part.
Dialogue: 0,0:03:38.35,0:03:41.60,Default,,0000,0000,0000,,Now this is a positive\N29, and so how
Dialogue: 0,0:03:41.60,0:03:42.99,Default,,0000,0000,0000,,do we figure out what this is?
Dialogue: 0,0:03:46.32,0:03:48.57,Default,,0000,0000,0000,,This is 29 right here\Nthat we're adding.
Dialogue: 0,0:03:48.57,0:03:51.99,Default,,0000,0000,0000,,This is going to land us right\Nover here on the number line.
Dialogue: 0,0:03:51.99,0:03:54.16,Default,,0000,0000,0000,,So how do we figure out\Nwhat number that is?
Dialogue: 0,0:03:54.16,0:03:56.00,Default,,0000,0000,0000,,Well, once again, we\Ncan just visualize it.
Dialogue: 0,0:03:56.00,0:03:58.54,Default,,0000,0000,0000,,And eventually you won't have\Nto draw number lines and stuff,
Dialogue: 0,0:03:58.54,0:04:01.29,Default,,0000,0000,0000,,but I think it'll\Nbe useful here.
Dialogue: 0,0:04:01.29,0:04:02.54,Default,,0000,0000,0000,,We're starting at negative 31.
Dialogue: 0,0:04:02.54,0:04:05.72,Default,,0000,0000,0000,,We're adding 29 to it, so it's\Ngoing to make it less negative.
Dialogue: 0,0:04:05.72,0:04:08.69,Default,,0000,0000,0000,,But we're still\Nadding less than 31,
Dialogue: 0,0:04:08.69,0:04:10.75,Default,,0000,0000,0000,,so we're not going to get\Nall the way back to 0.
Dialogue: 0,0:04:10.75,0:04:12.58,Default,,0000,0000,0000,,We're still going to\Nhave a negative number.
Dialogue: 0,0:04:15.95,0:04:18.00,Default,,0000,0000,0000,,But how could we figure\Nout the absolute value
Dialogue: 0,0:04:18.00,0:04:19.87,Default,,0000,0000,0000,,of that negative\Nnumber, its distance?
Dialogue: 0,0:04:19.87,0:04:22.41,Default,,0000,0000,0000,,Well, once again, that little\Nwhite part right there,
Dialogue: 0,0:04:22.41,0:04:24.72,Default,,0000,0000,0000,,that white part plus\Nthis 29, is going
Dialogue: 0,0:04:24.72,0:04:28.33,Default,,0000,0000,0000,,to equal 31, if you just\Nthink of absolute value,
Dialogue: 0,0:04:28.33,0:04:29.75,Default,,0000,0000,0000,,if we don't think\Nabout the signs,
Dialogue: 0,0:04:29.75,0:04:31.17,Default,,0000,0000,0000,,if we just think\Nabout the length.
Dialogue: 0,0:04:31.17,0:04:34.10,Default,,0000,0000,0000,,Or another way to think\Nabout it, 31 minus 29
Dialogue: 0,0:04:34.10,0:04:36.64,Default,,0000,0000,0000,,will give us the length\Nof that white part.
Dialogue: 0,0:04:36.64,0:04:38.60,Default,,0000,0000,0000,,And of course, it's\Ngoing to be negative,
Dialogue: 0,0:04:38.60,0:04:40.33,Default,,0000,0000,0000,,because the negative\Nnumber here is
Dialogue: 0,0:04:40.33,0:04:41.74,Default,,0000,0000,0000,,larger than the positive number.
Dialogue: 0,0:04:41.74,0:04:43.48,Default,,0000,0000,0000,,And we're adding the 2.
Dialogue: 0,0:04:43.48,0:04:49.64,Default,,0000,0000,0000,,If we do 31 minus 29, you\Ncould borrow and all of that,
Dialogue: 0,0:04:49.64,0:04:51.60,Default,,0000,0000,0000,,but that's clearly just\Ngoing to be equal to 2.
Dialogue: 0,0:04:51.60,0:04:53.32,Default,,0000,0000,0000,,You could say that's 11.
Dialogue: 0,0:04:53.32,0:04:54.58,Default,,0000,0000,0000,,This is a 2.
Dialogue: 0,0:04:54.58,0:04:56.60,Default,,0000,0000,0000,,You subtract, this\Nis equal to 2.
Dialogue: 0,0:04:56.60,0:05:00.01,Default,,0000,0000,0000,,But since it's\Nnegative 31 plus 29,
Dialogue: 0,0:05:00.01,0:05:01.35,Default,,0000,0000,0000,,it's going to be a negative 2.
Dialogue: 0,0:05:01.35,0:05:02.81,Default,,0000,0000,0000,,We're still going\Nto stay negative.
Dialogue: 0,0:05:02.81,0:05:05.63,Default,,0000,0000,0000,,We haven't moved far to\Nthe right enough to pass 0.
Dialogue: 0,0:05:05.63,0:05:08.26,Default,,0000,0000,0000,,So this right here is\Ngoing to be negative 2.
Dialogue: 0,0:05:08.26,0:05:09.64,Default,,0000,0000,0000,,Or another way to\Nthink about it,
Dialogue: 0,0:05:09.64,0:05:12.17,Default,,0000,0000,0000,,the length of this white\Nbar, the absolute value,
Dialogue: 0,0:05:12.17,0:05:13.47,Default,,0000,0000,0000,,is going to be 2.
Dialogue: 0,0:05:13.47,0:05:15.71,Default,,0000,0000,0000,,2 plus 29 is 31.
Dialogue: 0,0:05:15.71,0:05:18.94,Default,,0000,0000,0000,,But we're operating to the\Nleft of 0, so it's negative 31.
Dialogue: 0,0:05:18.94,0:05:20.25,Default,,0000,0000,0000,,This is negative 2.
Dialogue: 0,0:05:20.25,0:05:22.59,Default,,0000,0000,0000,,Anyway, hopefully you\Nfound that useful.
Dialogue: 0,0:05:22.59,0:05:24.30,Default,,0000,0000,0000,,And let me make it clear.
Dialogue: 0,0:05:24.30,0:05:31.54,Default,,0000,0000,0000,,Our final answer is negative 2.