[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:01.07,Default,,0000,0000,0000,,
Dialogue: 0,0:00:01.07,0:00:05.31,Default,,0000,0000,0000,,a plus b times open\Nparentheses c plus d is
Dialogue: 0,0:00:05.31,0:00:10.12,Default,,0000,0000,0000,,equal to a plus bc plus\Nbd represents which
Dialogue: 0,0:00:10.12,0:00:12.66,Default,,0000,0000,0000,,of the following properties?
Dialogue: 0,0:00:12.66,0:00:15.03,Default,,0000,0000,0000,,So to get from the left-hand\Nside to the right-hand side,
Dialogue: 0,0:00:15.03,0:00:17.49,Default,,0000,0000,0000,,it looks like what they did\Nis they multiplied the b times
Dialogue: 0,0:00:17.49,0:00:18.40,Default,,0000,0000,0000,,the c plus d.
Dialogue: 0,0:00:18.40,0:00:20.73,Default,,0000,0000,0000,,In fact, they\Ndistributed the b. b
Dialogue: 0,0:00:20.73,0:00:25.68,Default,,0000,0000,0000,,times c plus d is b\Ntimes c, plus b times d.
Dialogue: 0,0:00:25.68,0:00:28.91,Default,,0000,0000,0000,,So this is clearly the\Ndistributive property.
Dialogue: 0,0:00:28.91,0:00:30.55,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:00:30.55,0:00:34.00,Default,,0000,0000,0000,,4 plus open parentheses\N10 plus 6, they're saying,
Dialogue: 0,0:00:34.00,0:00:37.14,Default,,0000,0000,0000,,is the same thing as 4\Nplus 10 first, plus 6.
Dialogue: 0,0:00:37.14,0:00:39.56,Default,,0000,0000,0000,,So on the left-hand side, we're\Ndoing the 10 plus 6 first,
Dialogue: 0,0:00:39.56,0:00:40.92,Default,,0000,0000,0000,,and then we're adding the 4.
Dialogue: 0,0:00:40.92,0:00:43.30,Default,,0000,0000,0000,,On the right-hand side, we're\Nadding the 4 plus 10 first,
Dialogue: 0,0:00:43.30,0:00:44.46,Default,,0000,0000,0000,,and then we're adding the 6.
Dialogue: 0,0:00:44.46,0:00:46.38,Default,,0000,0000,0000,,And we're saying they're\Nequal to each other.
Dialogue: 0,0:00:46.38,0:00:49.08,Default,,0000,0000,0000,,It doesn't matter how we\Nassociate these numbers.
Dialogue: 0,0:00:49.08,0:00:51.00,Default,,0000,0000,0000,,Here we're associating\Nthe 10 and the 6 first,
Dialogue: 0,0:00:51.00,0:00:52.22,Default,,0000,0000,0000,,and then we're adding the 4.
Dialogue: 0,0:00:52.22,0:00:54.14,Default,,0000,0000,0000,,Here we're associating\Nthe 4 and the 10 first,
Dialogue: 0,0:00:54.14,0:00:55.59,Default,,0000,0000,0000,,and then we're adding the 6.
Dialogue: 0,0:00:55.59,0:00:57.90,Default,,0000,0000,0000,,So this is the associative\Nproperty for addition.
Dialogue: 0,0:00:57.90,0:01:00.94,Default,,0000,0000,0000,,
Dialogue: 0,0:01:00.94,0:01:02.99,Default,,0000,0000,0000,,Let's do several more.
Dialogue: 0,0:01:02.99,0:01:06.30,Default,,0000,0000,0000,,a plus b is equal to b\Nplus a represents which
Dialogue: 0,0:01:06.30,0:01:07.70,Default,,0000,0000,0000,,of the following properties?
Dialogue: 0,0:01:07.70,0:01:09.53,Default,,0000,0000,0000,,So it doesn't matter\Nwhich order I'm adding.
Dialogue: 0,0:01:09.53,0:01:12.15,Default,,0000,0000,0000,,It doesn't matter if I\Ndo a plus b or b plus a.
Dialogue: 0,0:01:12.15,0:01:15.43,Default,,0000,0000,0000,,This is the\Ncommutative property.
Dialogue: 0,0:01:15.43,0:01:17.36,Default,,0000,0000,0000,,Do another one.
Dialogue: 0,0:01:17.36,0:01:19.45,Default,,0000,0000,0000,,Which one of the\Nequations on the right
Dialogue: 0,0:01:19.45,0:01:21.83,Default,,0000,0000,0000,,represents the associative\Nproperty of addition?
Dialogue: 0,0:01:21.83,0:01:23.75,Default,,0000,0000,0000,,So remember,\Nassociative property--
Dialogue: 0,0:01:23.75,0:01:25.96,Default,,0000,0000,0000,,we're talking about\Nit doesn't matter
Dialogue: 0,0:01:25.96,0:01:27.57,Default,,0000,0000,0000,,how we associate the numbers.
Dialogue: 0,0:01:27.57,0:01:29.90,Default,,0000,0000,0000,,So we might do the operation\Non two of the numbers first
Dialogue: 0,0:01:29.90,0:01:33.48,Default,,0000,0000,0000,,and then on the third, or on\Nmaybe two of the other numbers
Dialogue: 0,0:01:33.48,0:01:35.10,Default,,0000,0000,0000,,and then on the one\Nthat's left over.
Dialogue: 0,0:01:35.10,0:01:37.91,Default,,0000,0000,0000,,So let's see what over\Nhere looks like that.
Dialogue: 0,0:01:37.91,0:01:40.81,Default,,0000,0000,0000,,So this right over here, this\Nis the commutative property.
Dialogue: 0,0:01:40.81,0:01:43.28,Default,,0000,0000,0000,,This right over here is\Nthe distributive property.
Dialogue: 0,0:01:43.28,0:01:45.70,Default,,0000,0000,0000,,This one right over here--\Non the left-hand side,
Dialogue: 0,0:01:45.70,0:01:47.45,Default,,0000,0000,0000,,we add b plus c first.
Dialogue: 0,0:01:47.45,0:01:49.62,Default,,0000,0000,0000,,On the right-hand side,\Nwe add a plus b first.
Dialogue: 0,0:01:49.62,0:01:51.50,Default,,0000,0000,0000,,And these two things\Nare equal to each other.
Dialogue: 0,0:01:51.50,0:01:53.40,Default,,0000,0000,0000,,It doesn't matter\Nhow we associate it,
Dialogue: 0,0:01:53.40,0:01:56.08,Default,,0000,0000,0000,,if we associate b plus c\Nfirst or a plus b first.
Dialogue: 0,0:01:56.08,0:02:00.03,Default,,0000,0000,0000,,So this is the associative\Nproperty of addition.
Dialogue: 0,0:02:00.03,0:02:03.14,Default,,0000,0000,0000,,Let's do-- which one of\Nthe equations on the right
Dialogue: 0,0:02:03.14,0:02:04.66,Default,,0000,0000,0000,,represents the\Ndistributive property
Dialogue: 0,0:02:04.66,0:02:07.70,Default,,0000,0000,0000,,of addition over multiplication?
Dialogue: 0,0:02:07.70,0:02:08.46,Default,,0000,0000,0000,,So let's see.
Dialogue: 0,0:02:08.46,0:02:11.14,Default,,0000,0000,0000,,This first one, they're just\Nchanging the associations.
Dialogue: 0,0:02:11.14,0:02:13.26,Default,,0000,0000,0000,,Here, this is commutative,\Nthis last one.
Dialogue: 0,0:02:13.26,0:02:15.70,Default,,0000,0000,0000,,Here, they're actually\Ndistributing the b
Dialogue: 0,0:02:15.70,0:02:17.09,Default,,0000,0000,0000,,over the c plus d.
Dialogue: 0,0:02:17.09,0:02:21.26,Default,,0000,0000,0000,,So b times c plus d is the\Nsame thing as bc plus bd.
Dialogue: 0,0:02:21.26,0:02:23.42,Default,,0000,0000,0000,,So it's that one\Nright over there.
Dialogue: 0,0:02:23.42,0:02:24.59,Default,,0000,0000,0000,,Maybe do a few more of this.
Dialogue: 0,0:02:24.59,0:02:25.87,Default,,0000,0000,0000,,This is a lot of fun.
Dialogue: 0,0:02:25.87,0:02:28.91,Default,,0000,0000,0000,,a plus b plus c is equal\Nto a plus b plus c,
Dialogue: 0,0:02:28.91,0:02:31.82,Default,,0000,0000,0000,,so this once again, they're\Nre-associating the numbers.
Dialogue: 0,0:02:31.82,0:02:34.36,Default,,0000,0000,0000,,But it doesn't matter which\Norder we associate them in.
Dialogue: 0,0:02:34.36,0:02:39.60,Default,,0000,0000,0000,,So this is the\Nassociative property.
Dialogue: 0,0:02:39.60,0:02:41.22,Default,,0000,0000,0000,,Which one of the\Nequations on the right
Dialogue: 0,0:02:41.22,0:02:44.02,Default,,0000,0000,0000,,represents the commutative\Nproperty of addition?
Dialogue: 0,0:02:44.02,0:02:46.93,Default,,0000,0000,0000,,So commutative-- we don't\Ncare about the order
Dialogue: 0,0:02:46.93,0:02:48.70,Default,,0000,0000,0000,,in which we're\Ndoing the operation.
Dialogue: 0,0:02:48.70,0:02:51.46,Default,,0000,0000,0000,,So a plus b is\Nequal to b plus a.
Dialogue: 0,0:02:51.46,0:02:54.38,Default,,0000,0000,0000,,
Dialogue: 0,0:02:54.38,0:02:56.01,Default,,0000,0000,0000,,Which one of the\Nequations on the right
Dialogue: 0,0:02:56.01,0:02:58.10,Default,,0000,0000,0000,,represents the commutative\Nproperty of addition?
Dialogue: 0,0:02:58.10,0:02:59.64,Default,,0000,0000,0000,,Well, that's what\Nthey just asked us.
Dialogue: 0,0:02:59.64,0:03:02.94,Default,,0000,0000,0000,,a plus b is equal to b plus a.
Dialogue: 0,0:03:02.94,0:03:04.92,Default,,0000,0000,0000,,And we are done.