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

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


Math Antics - What Percent Is It? - By Mathantics



Transcript
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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