Math Antics - Simplifying Fractions - Free Educational videos for Students in K-12

Math Antics - Simplifying Fractions - By mathantics

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00:05	in a previous video , we learned all about factoring
00:08	whole numbers and now we're going to learn how factoring
00:11	can help us when working with fractions , we're going
00:13	to learn how to simplify fractions simplifying a fraction means
00:17	rewriting the fraction using the smallest top and bottom numbers
00:20	we can without changing the value of the fraction .
00:24	To help us understand what simplifying a fraction really means
00:27	. Let's take a look at the simplest fraction ,
00:29	I can think of 1/2 . Now this is already
00:32	as simple as it can possibly be . So let's
00:35	go the other way . And complicated by dividing our
00:37	rectangle here up into more parts , the amount of
00:41	our rectangle that shaded is still the same . But
00:44	now the numbers for our fraction are 3/6 . The
00:47	numbers are bigger because our rectangle is now divided into
00:49	more parts . The fraction we have now 3/6 is
00:53	equivalent to our original fraction . 1/2 . That means
00:57	they have the same value , they represent the same
00:59	amount . So what if someone gives you the fraction
01:01	3/6 ? Like 3/6 of a candy bar ? Well
01:04	we know from our picture that that means they're really
01:06	giving you one half . But how can we show
01:09	that using math and not pictures ? Well that's where
01:12	factoring comes in . Let's take our complicated fraction 3/6
01:16	and factor both the top and bottom numbers . Now
01:19	the bottom number six can be factored into two times
01:22	three . The top number three is a prime number
01:26	. It's only factors are one and itself so we
01:29	can write that as one times three there we've rewritten
01:32	our fraction using factoring and now it kind of looks
01:35	like two fractions being multiplied together . 1/2 times 3/3
01:40	. Of course 3/3 is what I like to call
01:43	a whole fraction since its value is equal to one
01:46	. Now here's the interesting part since 3/3 equals one
01:50	and multiplying by one has no effect on a number
01:53	. We can just get rid of that . 3/3
01:55	, basically the three on the top and the three
01:58	on the bottom cancel each other out . And once
02:01	they're gone we're left with the fraction 1/2 . So
02:05	that means that the fraction 3/6 simplifies to one over
02:08	to another way of thinking about it is that we're
02:11	trying to find any whole fractions that are hiding in
02:14	the fraction . Were trying to simplify and if we
02:17	find any we can just get rid of them .
02:19	And the fraction we're left with is simpler than the
02:21	one we started with . Now that we know the
02:23	basics . Let's learn the procedure for simplifying fractions .
02:26	First replace the top and bottom numbers of the fraction
02:29	with their prime factors . Next look to see if
02:32	any of the factors are the same on the top
02:34	and bottom . If they are , then we call
02:37	them common factors because there's something that both the top
02:39	and bottom have in common . If you find a
02:42	pair of common factors , you can cancel them out
02:44	. Just draw a line through them like this .
02:47	Yeah . And last once all the common factors have
02:49	been canceled , you need to re multiply any factors
02:52	that are left over on the top or bottom .
02:54	This makes sure that you end up with only one
02:56	number on the top and bottom of your simplified fraction
03:00	. Oh , there's one important thing to remember .
03:02	If you're ever able to cancel out all of the
03:04	factors on the top or bottom of a fraction ,
03:07	don't be tempted to write in a zero , put
03:09	a one in there instead . The reason you can
03:11	write in a one is because one is always a
03:14	factor of any number . It's just we usually don't
03:16	write it in . For instance if you're going to
03:19	factor the number 15 , you just say that it's
03:21	five times three but you could also say that it's
03:24	five times three times one . In fact you could
03:27	even say it's five times three times one . See
03:32	why there's always a one left over when you're canceling
03:35	common factors . All right . So that's the basic
03:38	idea behind simplifying fractions . And once you know the
03:40	procedure it's really not that hard but you might want
03:44	to re watch this video just to make sure you've
03:45	got the idea . Now there aren't any exercises for
03:48	this video because it's really just an introduction . But
03:51	in part Two we'll see a couple more examples of
03:53	how you can use the procedure to simplify fractions and
03:56	then you'll get plenty of exercise is to do his
03:58	homework . Oh yeah . Mhm . Uh huh .
04:03	Mhm . Welcome to Part two of simplifying fractions .
04:06	In Part one , we learned the procedure for simplifying
04:09	fractions basically you just take the top and bottom numbers
04:12	and factor them down to their prime factors . And
04:15	then you see if there's any factors that are the
04:17	same on the top and bottom , we call those
04:19	common factors and if there are you just cancel them
04:22	out and once you've cancelled out all the common factors
04:26	, you re multiply whatever is left over to get
04:28	your final answer in this video , we're going to
04:31	see a couple examples of how we can use that
04:33	procedure to simplify fractions . Let's start with an easy
04:36	one . Let's simplify the fraction . 5/15 . Step
04:41	one is to factor the top and bottom numbers so
04:44	we know that 15 factors into five times three And
04:48	five is a prime number . That means it's only
04:50	factors are one and itself , but one is always
04:53	a factor . So we don't need to write that
04:55	down . Step two is to look for common factors
04:58	and cancel them and we can see that there's a
05:00	five on the top and there's a five on the
05:01	bottom . There not directly over each other , but
05:04	that doesn't matter . They still form a common factor
05:06	pair and so we can cancel them out . Like
05:08	this , Step three is to reorganize our answer .
05:12	Now we don't have any factors that need to be
05:14	recombined by multiplying we just have a three on the
05:17	bottom and we don't have any factors left over on
05:19	top . But you'll remember that there's always a factor
05:22	of one . So 5/15 simplifies to 1/3 . Yeah
05:28	. All right . I think we need to see
05:30	another example , but a harder one this time .
05:33	Let's simplify the fraction 30/36 . The procedure is the
05:37	same . Step one is we factor the top and
05:40	bottom numbers all the way down to their prime factors
05:43	. Let's do the top number . 1st , 30
05:46	factors into five times six . Five is prime ,
05:49	But six can be factored into two times three ,
05:53	so are 30 on top becomes five times two times
05:57	three . Now , the bottom number 36 can be
06:00	factored into six times six and each of those six
06:03	is can be factored into two times three . So
06:06	our bottom number becomes two times three times two times
06:10	three . Well , it looks like we do have
06:12	some common factors . There's a two on both the
06:15	top and bottom that will cancel each other out .
06:18	And even though there's more than 12 on the bottom
06:20	, we can only cancel one of them out because
06:22	there's only 12 on top . Remember you always have
06:25	to cancel common factors as pairs . Now we can
06:29	see that there's another pair , we can cancel ,
06:31	there's a three on both the top and bottom so
06:34	we can just cross those out . Okay , that's
06:36	all the common factors we can cancel . So now
06:39	all we have to do is see what's left over
06:41	. We have a five on the top and at
06:43	two times three on the bottom , we don't want
06:45	to leave our problem looking like this so we need
06:47	to recombine any factors that didn't cancel . That means
06:51	multiplying together are two and three on the bottom ,
06:53	which gives us six . There were left with the
06:56	fraction 5/6 . That's a simplified form of the fraction
07:00	30/36 . They both have the same value , but
07:03	the simplified one is written using the smallest numbers possible
07:08	. Now , some of you may have been taught
07:09	that the way to simplify fractions is to find the
07:12	greatest common factor of the top and bottom numbers and
07:14	just cancel that . Basically , that's what we are
07:17	doing when we cancel all of the common factors using
07:20	our procedure . In fact , if you multiply all
07:24	of the common factors together , you'll get the greatest
07:27	common factor or G C F is I like to
07:30	call it , you know , to to sound cool
07:32	. All right . So that's how you simplify fractions
07:36	. But I'll bet some of you are wondering why
07:37	would we even want to simplify fractions ? That's a
07:40	good question . Basically . It's to make life simpler
07:43	. Well , at least for your teacher who has
07:45	to grade all your homework for you , it just
07:48	makes life more complicated . No , just kidding ,
07:51	simplified fractions . Make your life easier to because usually
07:55	simplified fractions are much easier to work with . For
07:58	example , if your friends said to you here ,
08:01	you can have 27 54th of my sandwich , it
08:03	would have been much easier if they had just said
08:06	that you could have one half of their sandwich ,
08:08	since one half is the simplified form of 27 54th
08:12	. So now whenever you see a fraction , you
08:14	can ask yourself , could that be any simpler ?
08:17	And if so , you'll know just what to do
08:20	. So get on out there , work on those
08:22	exercises , start making the world a simpler place for
08:25	assault , learn more at math antics dot com .

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