Multiplying Fractions - Free Educational videos for Students in K-12

Multiplying Fractions - By Anywhere Math

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00:0-1	you and your friends show up a little late to
00:02	a birthday party and by the time you get there
00:05	there's only a half a pizza left , the three
00:08	of you split it evenly and each eat a third
00:10	of the half of pizza . How much pizza did
00:14	each of you eat ? Welcome to anywhere . Math
00:34	. I'm Jeff , Jacobson . And today we're gonna
00:36	talk about multiplying fractions . Okay , so let's talk
00:40	about that pizza , you show up a little late
00:44	and unfortunately there's only a half a pizza left ,
00:46	which is a pretty big bummer . Uh let's show
00:49	what that looks like visually . Well , let's draw
00:52	a picture of a pizza . So here's the whole
00:56	pizza , by the time you get there , there's
00:59	only half left . Okay , So here's the half
01:06	of a pizza that's left that you and two other
01:10	friends have to split . So each of you have
01:14	a third of that half . So what I'm gonna
01:17	do is I'm gonna make that I'm gonna try to
01:20	make it as even as possible . So each of
01:24	you have a third of that . So the question
01:27	is well how much pizza did you actually eat ?
01:30	And it's relative to the whole pizza ? So this
01:34	is maybe I'll do it and I'll do it in
01:37	blue . Each of you had a third 1/3 of
01:44	a one half of the pizza . So how much
01:47	total is that ? Well you see these are split
01:50	into thirds here of the half . We need to
01:54	make the same size pieces here . So I'm gonna
01:57	do the same thing and split that like that .
02:03	Now that they're all the same size pieces , we
02:05	can actually figure out what one third of one half
02:13	pizza is . Okay that's the question . Well what
02:17	is one third of one half ? Well this is
02:21	equal to one Out of six . There's 123456 total
02:27	pieces of that size in the whole pizza . You
02:31	only ate you and your friends each only ate one
02:33	of them . So the answer is yeah one .
02:38	Okay . Six . Now let's look at how can
02:42	we actually get there uh With just the math without
02:46	actually drawing a picture . If you remember of inward
02:50	problems . That means multiplication , so I can rewrite
02:53	this as one third times one half . Yeah .
02:59	And we know it's gotta be 16 And if I
03:03	look well , how would I get 16 ? Uh
03:05	from this problem ? Well one times one is one
03:10	and three times 2 is six . So if you
03:14	notice all we had to do was multiply straight across
03:17	numerous times numerator and denominator times denominator . Let's look
03:21	at another example . Okay so example one , we're
03:24	gonna start off pretty simple . 1/5 times one third
03:28	. If you remember from that pizza problem , we
03:32	said to multiply fractions , you don't need common denominators
03:36	that's adding and subtracting . We don't care what the
03:38	denominators are . Uh we just multiply straight across .
03:42	So one times one is one And five times 3
03:47	is 15 . Now when you're working with fractions we
03:51	always want are answers in simplest form . Uh in
03:54	this case 1 15 is the simplest form . Yeah
03:59	. So I'm done . Let's look at another example
04:03	. All right , here's example number 289 times 34
04:06	So like we said before , you can just multiply
04:10	straight across . So if I do that eight times
04:12	three is 24 . nine times 4 is 36 ,
04:17	24/36 . But hold on a second , I mentioned
04:23	that when you deal with fractions , you always want
04:26	your answer . In simplest form . This is not
04:30	in simplest form and simplest form means that there aren't
04:34	any other common factors besides one with a new range
04:38	of denominator , 24 and 36 do have other common
04:42	factors Between them between besides one . Ah If you
04:48	look obviously they're both even numbers . So too is
04:51	a common factor . Uh huh . six is also
04:54	a common factor . Um 12 is also a common
04:59	factor , so there's quite a bit of common factors
05:01	. So what we need to do is simplify this
05:04	and to do it quickly . All you need to
05:07	do is basically if you can figure out what the
05:10	greatest common factor is then you can simplify it in
05:14	one step . If you can't figure out what that
05:17	is then you can all you can do any common
05:19	factor you want . You just , it just might
05:22	take you a few more steps . So 12 is
05:25	the greatest common factor of 24 and 36 . So
05:29	if I divide The numerator and denominator by 12 ,
05:34	I get 2/3.24 divided by 12 is to 36 ,
05:40	divided by 12 is three . And if you look
05:43	the reason I can do that is because all I
05:47	did was essentially Divide This fraction by one . I
05:53	didn't change the value of it , I just change
05:55	what it looked like . 24/36 Is equivalent to 2/3
06:02	. The only difference is this has a lot more
06:05	pieces but they're skinnier . Like think of a pizza
06:08	again There's 36 pieces in this in this pizza .
06:13	Uh but they're really small . So this is 24
06:16	hours at 36 here , there's only three pieces in
06:19	the pizza but they're much bigger . Uh their equivalent
06:22	the amount of it is still the same . So
06:25	dividing by one doesn't change anything divided by one is
06:28	still the same . Just like anything multiplied by one
06:31	is still the same . So these are equivalent .
06:33	Now this is not the best way to solve this
06:37	problem . I want to show you how to do
06:41	this problem much better uh and much easier . So
06:46	let's solve this problem again . Uh Using a different
06:49	method instead of simplifying at the end , I'm gonna
06:52	show you how you can simplify at the beginning .
06:56	Now first I'm gonna show you something and you don't
06:59	really need to write it down . Just follow along
07:02	and see if you can understand what I'm doing .
07:04	So eight times 3 , I can write this as
07:08	eight times 3/9 times four . Right ? We're multiplying
07:14	, that's essentially what we do , right ? Numerous
07:16	has numerator , denominator times denominator . So that's okay
07:18	. That's that's fine . I can also , since
07:20	we're multiplying I can change the order . Community of
07:23	property says I can change the order when I'm multiplying
07:26	. So that can become uh three times 8/9 times
07:32	four . That's okay . Now , I can also
07:36	break some of these uh introduce apart into a product
07:41	of their factors . So instead of three times eight
07:46	, I can write it as three times . Let's
07:50	do two three times 2 times four . Well ,
07:57	three times eight is 24 3 times two is six
07:59	times four is 24 . It's the same . I
08:01	just broke that eight into two times four . So
08:04	I'm all right there , same thing here with the
08:07	nine . I'm going to break it up three times
08:10	three uh times four . Okay , then I'm running
08:17	a little bit out of room , so I'm gonna
08:19	go over here ah I can now break them apart
08:24	into fractions again , kind of basically what it was
08:28	here , go in the opposite direction . So now
08:30	I'm gonna make it 3/3 . Right ? That by
08:34	itself times to over three times 4/4 . I can
08:41	do that because essentially it's the same thing , right
08:44	? Three times two times four Here , three times
08:47	3 times four here . Okay . Um Now hopefully
08:52	you notice something . Well , what is three times
08:55	three ? I'm signed up three times 3 . 3/3
08:58	or three thirds . Well , that's just one times
09:02	two thirds times 4/4 is the same as 14 forces
09:08	one ? Well , one times two thirds is two
09:10	thirds , two thirds times one is two . All
09:14	right . Yeah . Which is what we got before
09:19	. All we did was we tried to break uh
09:24	these numbers apart into factors so that we could find
09:29	common factors . So we know that eight and four
09:34	Had a common factor of four here . Right ?
09:38	Which , let us kind of cancel it out .
09:40	It became one . Uh we also found that three
09:44	and 9 had a common factor of three . So
09:49	the same thing , we can basically kind of cancel
09:52	that out and that becomes one And then what we're
09:55	left with is just 2/3 . You will definitely not
09:59	need to show all of this . Okay , let's
10:02	show you one word . One more way of how
10:04	to do essentially this much quicker and simpler , but
10:08	it's important to know where that comes from . Okay
10:11	, so let's try it one more time . Alright
10:13	, Let's try this problem one more time . Um
10:16	and now we're going to use the rule that is
10:19	so so so important . And that is to always
10:22	try to simplify before you multiply . Always try to
10:28	do that first . It's going to make your life
10:30	a whole lot easier . So I'm looking for common
10:34	factors between any numerator and any denominators . We don't
10:39	go common factors in the numerator by themselves or uh
10:44	sorry , enumerators by themselves or denominators . It's got
10:47	to be a numerator with a denominator so that you
10:50	set up that situation where it becomes one . So
10:53	like we said before eight and four have a common
10:55	factor of four . So four sign eight divided by
11:00	four becomes too . So I crossed out the eight
11:04	and right to four divided by four becomes 1 .
11:10	nine and 3 also have common factors . It's three
11:14	, So nine divided by three is three and three
11:18	divided by three is 1 . Now that I've simplified
11:22	it before , I multiply , it's very easy to
11:25	times one is two and three times one is three
11:30	and there's my answer . It's already in simplest form
11:34	because I simplified here first . If you do all
11:37	your simplifications , hear your answer will automatically already be
11:41	in simplest form . Okay ? Uh Here's some problems
11:43	to try on your own . All right . Here's
11:51	our last example example 31 half times two and 3/4
11:56	two and three forces a mixed number . Uh So
11:59	what you want to do first is any time you're
12:02	multiplying fractions with mixed numbers or mixed numbers with mixed
12:05	numbers , Change it to an improper fraction . Uh
12:09	And the reason is you could leave it like this
12:12	but it's going to be much more complicated . You
12:14	have to use the distributive property and it's kind of
12:17	a pain . So just trust me , change it
12:20	to an improper fraction first . So one half times
12:25	two and 3/4 . If you remember how to convert
12:27	it to an improper fraction , I just do numerator
12:30	times the whole number . So four times two is
12:32	eight plus , the numerator is 11 . The denominator
12:38	stays the same , that becomes 11 force . Okay
12:42	, now I'm ready to go . Uh and like
12:44	we said earlier , always try to simplify first .
12:47	So you're looking , are there any common factors between
12:50	the numerator and denominator that I can simplify ? And
12:53	here there isn't Don't do two and four . Remember
12:57	? Those are both denominators , you can't simplify uh
13:01	anything that's both . Denominators are both numerous has to
13:04	be numerator and denominator . So there isn't anything to
13:07	simplify . So I just multiply straight across one times
13:11	11 is 11 and two times four is eight .
13:15	Now I can leave it as a as an improper
13:18	fraction . That's in simplest form . Or I can
13:21	change it back To a mixed No . eight goes
13:25	into 11 . Once there would be three left over
13:30	. 3 , 8 left over . Okay , so
13:34	those are both uh acceptable answers unless your teacher says
13:39	they want something specific . Okay , here's some to
13:42	try on your own . As always . Thanks for
13:51	watching . And if you like this video please subscribe

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