Math Antics - What Percent Is It? - Free Educational videos for Students in K-12

Math Antics - What Percent Is It? - By Mathantics

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00:03	Uh huh Hi , welcome to Math Antics . In
00:08	this video , we're going to learn how to do
00:09	another common type of problem involving percents . We're going
00:13	to learn how to figure out what percent is it
00:16	. In our last video , we learned how to
00:18	do a really common percent problem which was finding a
00:21	percent of a number . For example , we learned
00:24	how you could solve a problem like what is 20
00:28	of 50 . And the answer to that problem is
00:30	ted So we could say that 10 is 20 of
00:34	50 . Let's look closely at that statement for a
00:37	minute notice that there's three different numbers in it ,
00:40	10 , 20 and 50 . And that's because the
00:43	percentage is really a relationship between three numbers . Well
00:47	actually it's a relationship between four numbers , but the
00:50	fourth number is always 100 . So you always know
00:53	it to see what I mean . Think back to
00:55	our video about percents and equivalent fractions . In that
00:59	video we learned that a percent is really an equivalent
01:02	fraction that has 100 as the bottom number . So
01:05	we could rewrite our statement like this . 10/50 equals
01:09	20 over 100 . This is exactly the same as
01:13	saying that 10 is 20 of 50 . So these
01:17	are the four components of a percent problem . But
01:20	since we know that 100 is always going to be
01:22	the bottom number of this equivalent fraction , the% .
01:25	We can just rewrite it using the percent symbol .
01:28	That way we can focus on the other three numbers
01:31	that can change . And we're going to give each
01:33	one of these three numbers and names so that we
01:35	don't get confused . We're going to call the top
01:38	number of the fraction the part we have or just
01:41	the part for short . And we're going to call
01:43	the bottom number the total . And we're going to
01:46	call the number in front of the percent . Sign
01:48	the percent or percentage . And since there's three different
01:52	numbers that can change in a percentage problem , that
01:54	means there's three different questions that you can ask To
01:57	see these three questions . Let's rewrite our original statement
02:01	10 is 20 of 53 different times . But in
02:06	the first statement we replace the 10 with the word
02:08	what and it becomes what is 20 of 50 .
02:12	And the second statement , we replace the 20 with
02:15	what and it becomes 10 is what ? Percent of
02:18	50 . And then the third statement , we replace
02:21	the 50 with what and it becomes 10 is 20
02:24	of what doing this is helpful because whenever you're given
02:28	a problem involving percents , the first thing you need
02:31	to figure out is what the problem is asking you
02:33	to find , you know which number is missing .
02:36	In the first statement , the part we have is
02:38	missing . In the second statement , the percent is
02:41	missing , And in the 3rd statement , the total
02:44	is missing . And these three statements represent the three
02:47	most common types of percentage problems . The first type
02:51	is what we learned in the last video finding a
02:53	percent of a number in this type of problem .
02:56	We know the percent and we know the total ,
02:58	but we don't know what part of that total we
03:01	have . The second type of problem is what we're
03:04	going to learn in this video in this type of
03:06	problem . We know both the total and we know
03:09	what part of the total we have , but we
03:11	need to figure out what percentage of the total that
03:14	part is . We need to find what percent is
03:17	it . And the third type of problem is what
03:20	we'll learn in the next video for that type of
03:22	problem . We know what part we have and we
03:25	know what percent of the total it is . We
03:27	just don't know the total itself . Have I lost
03:30	you yet ? Don't worry . It will make a
03:32	lot more sense after we look at a few examples
03:35	. So let's look at an example of a type
03:38	two problem where we know the part we have and
03:40	we know the total but we don't know what the
03:42	percent is . This example is a word problem and
03:46	it says Your uncle who really likes to travel has
03:49	visited 35 of the 50 . U.S . States .
03:53	What percent of the States has he visited ? The
03:56	keywords in this problem are what percent ? Because they
03:59	let us know that it's the percent that's missing .
04:02	So the two numbers that it gives us must be
04:04	the total and the part we have . Well in
04:07	this case it's not really the part we have .
04:10	It's the part that our uncle is visited . But
04:12	you get the idea and sometimes it can be hard
04:15	to tell which number the total is often it's the
04:18	bigger number but not always . And that's where the
04:21	word of can help us out . The word of
04:24	usually goes in front of the number . That's the
04:26	total . So when you see Of the 50 .
04:29	U.S . States It's a clue that 50 is the
04:31	total . All right then . So we put 50
04:34	on the bottom of the fraction and 35 on top
04:38	. Now we're ready to figure out the part that
04:39	we don't know the percent To find the 1% .
04:43	All we need to do is convert the fraction into
04:46	its percent form . That means we need to convert
04:48	it into an equivalent fraction that has 100 as the
04:51	bottom number . Well , one way we could do
04:54	that would be to look for a number that we
04:56	can multiply both the top and lot of numbers by
04:59	that would change the bottom number into 100 . Well
05:02	, the number two looks like it would work if
05:04	we multiply the bottom by 22 times 50 gives us
05:07	100 . And then we also need to multiply the
05:10	top by two and 2 times 35 equals 70 .
05:14	So now we can see that 70 over 100 is
05:16	equivalent to 35/50 . And since 70 over 100 is
05:21	just 70% . It means that her uncle has visited
05:24	70 of the states and all I got was this
05:27	lousy t shirt . All right . That way of
05:31	finding a percent seems pretty easy . You just write
05:34	the numbers that you know as a fraction and then
05:36	you convert that fraction into an equivalent fraction with 100
05:40	as the bottom number . And that tells you what
05:42	percent it is . The trouble is that weighs only
05:46	easy if it's easy to change the bottom number into
05:48	100 . Why ? For example , what if instead
05:51	of 50 you had 80 as the bottom number ?
05:54	What could you multiply 80 by to get 100 ?
05:57	Well that's not as easy to figure out . So
05:59	even though finding an equivalent fraction is sometimes a good
06:02	way to convert a fraction into a percent form .
06:05	I'm going to show you another way that I think
06:07	is even better . The second way is based on
06:10	the fact that a fraction is just the division problem
06:13	where the top number is divided by the bottom number
06:16	. If you do the division , you'll end up
06:18	with a decimal value of the fraction . And as
06:21	we saw in our first video about percents , it's
06:24	easy to convert from a decimal value into a percent
06:27	. You just move the decimal 0.2 places to the
06:30	right , which is the same as multiplying by 100
06:33	. The only drawback to finding a percent this way
06:36	is that it involves division and division can sometimes be
06:39	tricky if you don't have a calculator , but if
06:41	you do have a calculator or if you're really good
06:44	at long division , then this way works best to
06:47	see this way in action . Let's try this word
06:49	problem . Your aunt has baked 80 cookies and because
06:53	she's a very nice aunt , she gave you 28
06:56	to take home with you . What percent of the
06:58	cookies did she give you you ? Okay , so
07:01	we know that the total is 80 and that the
07:03	part we got was 28 . That means that our
07:05	fraction will be 28/80 . Using our calculator , we
07:09	enter 28 divided by 80 and we get 0.35 .
07:14	That's the decimal form of the fraction . And now
07:17	to go from the decimal form to 1% , we
07:20	just move the decimal two places to the right that
07:22	gives us 35 . So when her aunt gave us
07:26	28 out of the 80 cookies , she gave us
07:28	35 of the cookies that she baked . Mm mm
07:34	hmm . Whoa . Oh all right . So that's
07:41	how you find out what percent is it ? You
07:44	make a fraction from the part that you have and
07:46	from the total . Um and then you convert that
07:48	fraction into its percent form either by figuring out what
07:52	the equivalent fraction would be Or by just dividing to
07:55	get the decimal value and turning that into 1% .
08:05	there's two things that you can do that will help
08:07	make it clearer . You first you can rewatch the
08:09	video to catch anything , you might have missed the
08:11	first time through , and second you can practice using
08:15	the procedures on your own , which will really help
08:17	you understand them better , Good luck and as always
08:21	, thanks for watching Math Antics and I'll see you
08:23	next time , learn more at Math Antics dot com
00:0-1	.

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