The Distributive Property - Free Educational videos for Students in K-12

The Distributive Property - By Anywhere Math

Transcript


00:0-1	Welcome anywhere . Math . I'm Jeff Jacobson . And
00:02	today we're gonna talk about the distributive property . Let's
00:05	get started . All right . Let's talk a little
00:24	bit about the distributive property . If you look at
00:27	the word distributive , it may make you think of
00:30	distribute . And if you know , distribute just means
00:33	to give something to everyone in a group . If
00:38	you think of the S . A . T .
00:39	S . When they're getting ready to start the cts
00:42	, they might say something like now we're going to
00:44	distribute the test . All that means is they're going
00:48	to give the test to everyone in the group ,
00:51	everyone in the room . The distributive property works the
00:55	same way . Instead of distributing a test , we're
00:58	distributing a number . Okay ? So here we have
01:02	seven Times the sum of three and 2 . Okay
01:06	, I'm going to distribute the seven to every term
01:10	inside these parentheses . Okay , so that's seven .
01:14	I'm going to multiply by the three . I'm also
01:16	gonna multiply the seven times the two . Okay ,
01:20	so seven times three , I'm just gonna write it
01:22	like this . I'm just gonna show you seven times
01:24	three your operations still stay the same , you just
01:28	bring them down plus seven times the two . Okay
01:32	. Well seven times three is 21 plus seven times
01:36	two is 14 which gives me 35 . Okay .
01:41	Now you might be saying well Jeff I thought if
01:45	we're doing order of operations doesn't parentheses comes first and
01:49	yeah they do . You can do the same thing
01:52	. If I did parenthesis first I would get three
01:56	plus two is five and seven times 5 is 35
02:02	. It's the same thing . Now the reason we're
02:05	talking about this distributive property right now is because we're
02:10	not going to be dealing with numerical expressions very much
02:13	anymore . Instead we're going to have something like Maybe
02:21	three Plus X . Okay , you're gonna have variables
02:24	in there and in this case you think Okay ,
02:29	I do parentheses first . Right . Well you can't
02:32	add three plus X because we don't know the value
02:34	of X . So instead we use the distributive property
02:39	to simplify Same thing . Seven times three would give
02:42	me 21 seven times X . Sorry , bring down
02:46	the operation seven times X . Is seven X .
02:49	I don't know what X is . So I just
02:51	write seven X . Let's look at the first example
02:54	. Alright , example one use the distributive property and
02:57	mental math to do eight times 53 . Now ,
03:01	some of you , if you can do this in
03:03	your head , I'm willing to bet that you're actually
03:05	using the distributive property without even knowing it . Um
03:09	the way you would do this . If you're trying
03:12	to get to a point where kind of step your
03:14	game up and be able to do this in your
03:15	head instead of 53 times eight . And doing it
03:18	like that is we think of 53 as 50 plus
03:23	three . Okay , So if you think of it
03:26	as 50 plus three , well then that allows me
03:31	to do a little bit easier multiplication . So we
03:35	use the distributive property , which means I'm distributing the
03:38	eight To the 50 and the three , which means
03:41	I'm multiplying eight times 50 Plus eight times 3 .
03:47	Well , eight times 50 is 400 plus , eight
03:52	times 3 is 24 . Which and then you do
03:55	400 plus 24 is 424 . Okay , So that's
04:01	how you would use distributive property to do something like
04:05	this in your head . Um six times 35 .
04:11	Well , you would do the same thing , but
04:13	see if you can do it in your head ,
04:14	35 is 30 and five , Six times 30 is
04:18	186 times five is 30 . 180 plus 30 gives
04:24	me 210 . Okay , So next time you have
04:31	problems like this , see if you can do in
04:34	your head , try to use the distributive property .
04:36	Let's look at another example . Okay , example number
04:39	to use the distributive property to do 1/2 times two
04:44	and 3/4 . Now you might be saying , well
04:47	why would I need to use the distributive property ?
04:49	I thought makes numbers just change it to an improper
04:52	fraction and then multiply and yes , you can do
04:55	that . But you can also use the distributive property
04:58	and we're going to show you how to do that
05:00	. Um The trick is same thing . In the
05:03	last example , you got to think of what two
05:06	and 3/4 actually means and two and 3/4 means to
05:13	plus three forth . But when we write based numbers
05:17	, we don't actually write the plus . But that's
05:19	what it means . So hopefully you can see We
05:23	can use the distributive property . I'm gonna do one
05:26	half times two plus one half times +34 Well one
05:32	half times two is one half of two is one
05:35	Plus 1/2 times 3 4 . Let's see . Well
05:41	I still got the one plus . Uh Nothing to
05:44	simplify . So one times three is 32 times four
05:48	is 81 plus 3/8 is one and 3/8 . Okay
05:56	, here's some to try on your own . Alright
06:07	, here are last examples simplify each expression . Uh
06:12	So right here my 1st 19 times the sum of
06:14	six and two X . And three . Now there's
06:18	a couple ways to do this . I know we're
06:21	talking about distributive property . So you're thinking okay I'm
06:23	gonna distribute the nine to the 692 the two X
06:26	. And nine of the three . And you can
06:28	do that and that's fine . But I don't want
06:31	you to forget about order of operations which say do
06:36	Parenthesis 1st , right ? Pandas , parentheses , exponents
06:40	multiply divide add to track . So parenthesis always look
06:45	is there anything you can simplify in the parentheses first
06:49	before you start to do your multiplication ? Before you
06:53	start to distribute And yes I can't do six plus
06:57	two X . Because I don't know what X .
06:58	Is there not like terms ? I can do six
07:01	plus three though . So I'm gonna simplify inside the
07:05	parentheses first that's gonna become nine plus two X .
07:11	Okay Now I'm ready to distribute so I'm going to
07:15	distribute the nine To this nine and the 9 to
07:19	the two x . Always remember to make sure you
07:22	distribute to every term . The most common mistake I
07:26	see students make is they'll do the nine times and
07:29	nine but they'll forget to do nine times two X
07:33	. If you draw those little arrows , I think
07:35	it's going to help you a lot and you won't
07:37	make as many mistakes . So nine times 9 gives
07:40	me 81 , bring down my Operation nine Times 2
07:45	X . is 18 X . Okay , I can't
07:50	simplify any farther . I don't know what X is
07:53	, so I can't add these together . I said
07:56	before , they're not like terms and what that means
07:59	is um like terms are things that are terms that
08:03	are alike that you can actually combine . Uh any
08:07	number . All numbers are like terms , any numbers
08:11	by themselves are like terms . But when you've got
08:13	variables in there , you have to look for the
08:16	same variables . So if this was 81 X plus
08:21	18 X . You can think of it as I
08:24	have 81 excess Plus 18 more excess . Well how
08:29	many exits do I have now ? I would have
08:31	99 XS . So you could do that . We
08:35	call those like terms But because this is just 81
08:40	, I can't combine them . They're not like terms
08:43	. So I'm finished . That's as far as I
08:46	can simplify seven W plus two times in parentheses ,
08:50	W minus five Y . Um Like I said earlier
08:54	check to see if there's anything you can do in
08:56	the parentheses . I can't do W -5 . Why
09:00	they're not like terms , I don't know their values
09:03	so I have to leave it . So my first
09:05	step then is to distribute two times w . And
09:10	then two times the five Y . Okay so seven
09:14	W . I'm not changing . That just comes down
09:17	Plus two times W . is to W I still
09:21	have my subtraction two times five Y . Would give
09:25	me 10 Y . Now I gotta look is there
09:30	anything I can simplify ? Well like we're talking about
09:33	here these are both W . I have seven W
09:37	. Here seven Ws . And to W . S
09:40	. If I add those together that would give me
09:42	nine Ws . They are like terms so I can
09:46	add them minus 10 Y . W . And Y
09:50	are different variables so they're not like terms . So
09:53	I am finished there . Okay here's some to try
09:58	on your own as always . Thank you so much
10:06	for watching and if you like this video please subscribe
00:0-1	.

Summarizer

DESCRIPTION:

OVERVIEW:

The Distributive Property is a free educational video by Anywhere Math.

This page not only allows students and teachers view The Distributive Property videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.