1
00:00:00,000 --> 00:00:01,070


2
00:00:01,070 --> 00:00:05,310
a plus b times open
parentheses c plus d is

3
00:00:05,310 --> 00:00:10,120
equal to a plus bc plus
bd represents which

4
00:00:10,120 --> 00:00:12,656
of the following properties?

5
00:00:12,656 --> 00:00:15,030
So to get from the left-hand
side to the right-hand side,

6
00:00:15,030 --> 00:00:17,490
it looks like what they did
is they multiplied the b times

7
00:00:17,490 --> 00:00:18,400
the c plus d.

8
00:00:18,400 --> 00:00:20,732
In fact, they
distributed the b. b

9
00:00:20,732 --> 00:00:25,680
times c plus d is b
times c, plus b times d.

10
00:00:25,680 --> 00:00:28,910
So this is clearly the
distributive property.

11
00:00:28,910 --> 00:00:30,550
Let's do another one.

12
00:00:30,550 --> 00:00:34,000
4 plus open parentheses
10 plus 6, they're saying,

13
00:00:34,000 --> 00:00:37,144
is the same thing as 4
plus 10 first, plus 6.

14
00:00:37,144 --> 00:00:39,560
So on the left-hand side, we're
doing the 10 plus 6 first,

15
00:00:39,560 --> 00:00:40,920
and then we're adding the 4.

16
00:00:40,920 --> 00:00:43,296
On the right-hand side, we're
adding the 4 plus 10 first,

17
00:00:43,296 --> 00:00:44,461
and then we're adding the 6.

18
00:00:44,461 --> 00:00:46,380
And we're saying they're
equal to each other.

19
00:00:46,380 --> 00:00:49,084
It doesn't matter how we
associate these numbers.

20
00:00:49,084 --> 00:00:51,000
Here we're associating
the 10 and the 6 first,

21
00:00:51,000 --> 00:00:52,224
and then we're adding the 4.

22
00:00:52,224 --> 00:00:54,140
Here we're associating
the 4 and the 10 first,

23
00:00:54,140 --> 00:00:55,590
and then we're adding the 6.

24
00:00:55,590 --> 00:00:57,905
So this is the associative
property for addition.

25
00:00:57,905 --> 00:01:00,940


26
00:01:00,940 --> 00:01:02,990
Let's do several more.

27
00:01:02,990 --> 00:01:06,300
a plus b is equal to b
plus a represents which

28
00:01:06,300 --> 00:01:07,697
of the following properties?

29
00:01:07,697 --> 00:01:09,530
So it doesn't matter
which order I'm adding.

30
00:01:09,530 --> 00:01:12,150
It doesn't matter if I
do a plus b or b plus a.

31
00:01:12,150 --> 00:01:15,431
This is the
commutative property.

32
00:01:15,431 --> 00:01:17,360
Do another one.

33
00:01:17,360 --> 00:01:19,450
Which one of the
equations on the right

34
00:01:19,450 --> 00:01:21,830
represents the associative
property of addition?

35
00:01:21,830 --> 00:01:23,750
So remember,
associative property--

36
00:01:23,750 --> 00:01:25,960
we're talking about
it doesn't matter

37
00:01:25,960 --> 00:01:27,567
how we associate the numbers.

38
00:01:27,567 --> 00:01:29,900
So we might do the operation
on two of the numbers first

39
00:01:29,900 --> 00:01:33,480
and then on the third, or on
maybe two of the other numbers

40
00:01:33,480 --> 00:01:35,100
and then on the one
that's left over.

41
00:01:35,100 --> 00:01:37,910
So let's see what over
here looks like that.

42
00:01:37,910 --> 00:01:40,810
So this right over here, this
is the commutative property.

43
00:01:40,810 --> 00:01:43,280
This right over here is
the distributive property.

44
00:01:43,280 --> 00:01:45,700
This one right over here--
on the left-hand side,

45
00:01:45,700 --> 00:01:47,450
we add b plus c first.

46
00:01:47,450 --> 00:01:49,625
On the right-hand side,
we add a plus b first.

47
00:01:49,625 --> 00:01:51,500
And these two things
are equal to each other.

48
00:01:51,500 --> 00:01:53,400
It doesn't matter
how we associate it,

49
00:01:53,400 --> 00:01:56,080
if we associate b plus c
first or a plus b first.

50
00:01:56,080 --> 00:02:00,030
So this is the associative
property of addition.

51
00:02:00,030 --> 00:02:03,140
Let's do-- which one of
the equations on the right

52
00:02:03,140 --> 00:02:04,660
represents the
distributive property

53
00:02:04,660 --> 00:02:07,700
of addition over multiplication?

54
00:02:07,700 --> 00:02:08,460
So let's see.

55
00:02:08,460 --> 00:02:11,140
This first one, they're just
changing the associations.

56
00:02:11,140 --> 00:02:13,260
Here, this is commutative,
this last one.

57
00:02:13,260 --> 00:02:15,705
Here, they're actually
distributing the b

58
00:02:15,705 --> 00:02:17,090
over the c plus d.

59
00:02:17,090 --> 00:02:21,260
So b times c plus d is the
same thing as bc plus bd.

60
00:02:21,260 --> 00:02:23,424
So it's that one
right over there.

61
00:02:23,424 --> 00:02:24,590
Maybe do a few more of this.

62
00:02:24,590 --> 00:02:25,870
This is a lot of fun.

63
00:02:25,870 --> 00:02:28,910
a plus b plus c is equal
to a plus b plus c,

64
00:02:28,910 --> 00:02:31,820
so this once again, they're
re-associating the numbers.

65
00:02:31,820 --> 00:02:34,360
But it doesn't matter which
order we associate them in.

66
00:02:34,360 --> 00:02:39,596
So this is the
associative property.

67
00:02:39,596 --> 00:02:41,220
Which one of the
equations on the right

68
00:02:41,220 --> 00:02:44,020
represents the commutative
property of addition?

69
00:02:44,020 --> 00:02:46,930
So commutative-- we don't
care about the order

70
00:02:46,930 --> 00:02:48,700
in which we're
doing the operation.

71
00:02:48,700 --> 00:02:51,460
So a plus b is
equal to b plus a.

72
00:02:51,460 --> 00:02:54,385


73
00:02:54,385 --> 00:02:56,010
Which one of the
equations on the right

74
00:02:56,010 --> 00:02:58,099
represents the commutative
property of addition?

75
00:02:58,099 --> 00:02:59,640
Well, that's what
they just asked us.

76
00:02:59,640 --> 00:03:02,940
a plus b is equal to b plus a.

77
00:03:02,940 --> 00:03:04,920
And we are done.