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

Math Antics - Comparing Fractions - By mathantics

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00:03	Uh huh . Hi there . Welcome to Math .
00:07	Antics . In this video we're going to learn how
00:09	to compare fractions . Mm This fraction has 25 more
00:14	fiber than this fraction . But this fraction has try
00:18	sodium phosphate . Well , it's not quite like that
00:22	, comparing fractions just means telling which one is bigger
00:25	. You know , just like we do with regular
00:27	numbers when we use the greater than less than and
00:30	equal to signs . That sounds easy . Right ?
00:33	But unfortunately , unlike regular numbers , it's not always
00:36	easy to tell which fraction is bigger just by looking
00:39	at them . That's because the value of a fraction
00:41	depends on both the top and bottom numbers and how
00:44	they relate to each other . For example , if
00:47	you have to compare these two fractions 1/3 and 1/10
00:51	. Some of you might be tempted to say that
00:53	1/10 is bigger because you know that 10 is bigger
00:56	than three . Right ? But we need to remember
00:59	that the fraction is really a number written like a
01:02	division problem and its value depends on that division .
01:05	So in this case the 1/3 is really the bigger
01:09	fraction because its decimal value what you get when you
01:12	divide is 0.33333 But the value of 1/10 is only
01:17	0.1 . Okay , so comparing fractions isn't quite as
01:22	easy as comparing regular numbers but that doesn't mean it's
01:25	going to be that hard . We're going to learn
01:27	to methods for comparing fractions that make it very easy
01:31	. The first method is called cross multiplying and it
01:34	takes advantage of the fact that it's easy to compare
01:36	fractions with the same bottom numbers . If two fractions
01:39	have the same bottom numbers then we can just compare
01:42	the top numbers . That's because we're comparing the same
01:45	size parts were comparing 4th 2/4 8th , 2/8 10th
01:49	2/10 and so on . And the top number just
01:52	tells us how many of those parts we have .
01:54	So it's easy to see that 5/8 is more than
01:57	3/8 . But many times you'll have to compare fractions
02:00	that have different bottom numbers or different sized parts .
02:03	Fortunately there's a trick we can do to make the
02:06	comparison easy in the math antics videos about common denominators
02:11	. We learn a simple method for changing unlike fractions
02:13	with different bottom numbers into like fractions with the same
02:17	bottom number . Basically it shows how you can multiply
02:20	two unlike fractions by whole fractions made from the different
02:23	bottom numbers . So you end up with the same
02:26	bottom number . This will give you two new equivalent
02:29	fractions that you can easily add subtract or compare .
02:33	But there's a shortcut for comparing fractions as long as
02:37	we know that the bottom numbers of our fractions are
02:39	the same . We don't really need to know what
02:41	that number is . We just need to know what
02:44	the top numbers will be since those are the ones
02:46	that will actually compare . So instead of multiplying each
02:49	fraction by a whole fraction , we can just multiply
02:52	the top number of each fraction by the bottom number
02:55	of the other fraction . This is called cross multiplying
02:58	because if you draw a diagram of what you're multiplying
03:01	it forms a criss cross pattern after you cross multiply
03:04	you'll have two numbers . That would be the new
03:06	top numbers . If you have made like fractions and
03:09	those numbers will show you which fraction is greater .
03:12	Let's try this cross multiplying method on an example or
03:15	two . Let's compare the fractions 7/8 and 4/5 .
03:20	We start by multiplying the second fractions . Bottom number
03:23	five by the first fractions . Top number seven .
03:26	And that gives us 35 for the new top number
03:29	on this side . You'll always keep the answer on
03:31	the side of the top number that you multiplied Now
03:35	for the other side . The bottom number eight times
03:37	the top number four gives us 32 for its new
03:40	top number . Ha ha ! Now it's easy to
03:43	see that the fraction 7/8 is greater than the fraction
03:47	4/5 because it's new . Top number , 35 is
03:50	greater than the other new top number 32 . Let's
03:54	do one more comparison by cross . Multiplying let's compare
03:57	6/11 to 9/15 . 1st will multiply 15 by six
04:02	to get the new top number of the first side
04:04	which is 90 . And you can always use a
04:06	calculator to do the multiplication is if you need to
04:09	Next we multiply 11 x 9 to get the second
04:12	new top number which is 99 . So that tells
04:15	us that the second fraction 9/15 is greater than the
04:19	first fraction because it's new . Top number 99 is
04:22	bigger . Pretty simple . Huh ? Okay . Cross
04:26	multiply is pretty cool . But there's another way to
04:28	compare fractions that you need to know about . But
04:30	this one is only really good . If you can
04:32	use a calculator , remember the reason that fractions are
04:36	tricky to compare is because they're really division problems .
04:39	But if we want to we can just do the
04:41	division and get the answer which is the decimal value
04:44	of the fraction . So if you have two fractions
04:46	to compare you can just do the division , preferably
04:49	using a calculator and then compare the decimal values .
04:53	For example let's say I offered to give you either
04:55	5/12 of a pizza or 7/15 of a pizza .
04:59	Now you happen to be really hungry so you want
05:01	to choose the biggest amount but it's not very easy
05:04	to tell just by looking which is bigger . 5/12
05:06	or 7/15 . This is where decimal values can really
05:10	help you out . If you convert the fractions to
05:12	decimals by doing division it will make it much easier
05:15	to see which one's bigger . Five divided by 12
05:18	is about 0.42 and seven divided by 15 is about
05:22	0.47 yep . That makes comparing them much easier since
05:27	0.47 is greater than 0.42 It means that 7/15 is
05:32	greater than 5/12 and that means that you'd rather have
05:35	7/15 of the pizza . Sometimes when you compare fractions
05:39	this way you'll find two fractions that look different but
05:42	have the same decimal value like 3/8 and 15/40 .
05:47	If you convert each fraction to a decimal you'll see
05:50	that they both have the value 0.375 two fractions that
05:54	have different top and bottom numbers but the same value
05:57	are called equivalent fractions . If two fractions are equivalent
06:01	then you can just use the equal sign to show
06:03	the comparison between them like this . All right .
06:07	So those are two great methods you can use to
06:09	compare fractions . Cross . Multiplying is simple and works
06:12	great even if you don't have a calculator and comparing
06:15	the decimal values by dividing is easy . If you
06:18	do have a calculator as always practice . Makes perfect
06:22	. So spend some time doing the exercises for this
06:24	section and I'll see you next time learn more at
06:28	math . Antics dot com .

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