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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