Math Antics - Types of Fractions - By mathantics
Transcript
00:03 | Uh huh . Now that you know that fractions are | |
00:07 | special numbers written like division problems . We're going to | |
00:10 | learn about some different types of fractions and where they're | |
00:13 | located on the number line because fractions are division problems | |
00:17 | . Their value depends on the top and bottom numbers | |
00:20 | and the relationship between them , there are a few | |
00:22 | basic rules about that relationship that will help us estimate | |
00:26 | the value of a fraction and know about where it | |
00:28 | should be on the number line . The first rule | |
00:31 | is if the top number of a fraction is zero | |
00:34 | , then the value of the fraction is always zero | |
00:36 | . No matter what the bottom number is . For | |
00:38 | example 0/2 and zero over 20,000 are both just zero | |
00:44 | . I like to call these fractions zero fractions . | |
00:47 | You know because because the equal zero , oh and | |
00:51 | by the way , you can never have zero as | |
00:53 | the bottom number of a fraction because you can't divide | |
00:55 | something into zero parts . So don't even try it | |
00:59 | . The next rule is this if the bottom number | |
01:02 | is bigger than the top number , then the value | |
01:04 | of the fraction will be greater than zero , but | |
01:06 | less than one . That means it will be somewhere | |
01:09 | in this section of the number line . Any fractions | |
01:12 | that have values in this range are called proper fractions | |
01:15 | . Because we can use these values to represent smaller | |
01:17 | parts of things are third rule is this If the | |
01:21 | top number and bottom number are the same , then | |
01:23 | the value of the fraction is always just one . | |
01:26 | So whether you have 1/1 or 5/5 or 100 over | |
01:30 | 100 the value is always just one . I'm going | |
01:34 | to call this kind of fraction a whole fraction because | |
01:36 | its value represents one whole . Oh and in case | |
01:40 | you're wondering this rule doesn't apply to 0/0 because like | |
01:44 | I told you , having a zero on the bottom | |
01:46 | of a fraction is a big no , no . | |
01:48 | Okay . Our last rule is this . If the | |
01:51 | top number is greater than the bottom number , Then | |
01:54 | the value of the fraction will be bigger than one | |
01:57 | . That means it will be somewhere in this section | |
01:58 | of the number line which goes on forever . These | |
02:01 | are called improper fractions because even though they're written like | |
02:04 | regular fractions , since their value is greater than one | |
02:07 | , they aren't really used to represent smaller parts of | |
02:09 | things . All right . These rules show that we | |
02:12 | have four main types of fractions . We have zero | |
02:15 | fractions , proper fractions , whole fractions and improper fractions | |
02:20 | . Knowing that these main types are in order from | |
02:22 | smallest to largest on the number line allows you to | |
02:25 | do some very simple comparisons between the four types of | |
02:28 | fractions . That's because we know that a zero fraction | |
02:32 | is always less than a proper fraction , and a | |
02:34 | proper fraction is always less than a whole fraction and | |
02:37 | a whole fraction is always less than an improper fraction | |
02:40 | . Let's do a few comparisons to get the hang | |
02:42 | of it . Here we have 1/5 and 0/8 . | |
02:46 | Since 1/5 is a proper fraction and 0/8 . zero | |
02:50 | fraction . 1/5 is greater than 0/8 . Now , | |
02:54 | let's do 3/8 and 2/2 . 3/8 is a proper | |
02:59 | fraction , and 2/2 is a whole fraction . So | |
03:02 | that means that 3/8 is less than 2/2 . Now | |
03:06 | , what about 9/9 and 32/32 ? Now , that's | |
03:10 | easy . Since they're both whole fractions and whole fractions | |
03:13 | are always equal to one . These fractions are equal | |
03:17 | . And finally , what about one half and 5/4 | |
03:21 | ? Now , we know that one half is a | |
03:22 | proper fraction , but 5/4 is an improper fraction because | |
03:26 | it's top number is bigger than its bottom number . | |
03:28 | So that means that one half is less than 5/4 | |
03:32 | . Now that we know that there are four basic | |
03:35 | types of fractions and we've learned where they fit on | |
03:37 | the number line . Let's learn more about how the | |
03:39 | relationship between the top and bottom numbers affects the value | |
03:43 | of a fraction . Let's go on a journey down | |
03:45 | our number line . Now we're gonna start with this | |
03:47 | zero fraction 0/20 and its value puts us here at | |
03:51 | zero on the number line . To get moving all | |
03:54 | we have to do is start changing the value of | |
03:56 | our fraction by increasing the top number . We're going | |
03:58 | to leave the bottom number the same the whole time | |
04:00 | . No . All right , let's go . We | |
04:04 | haven't gotten very far from zero yet . And you | |
04:06 | might have noticed that the top number is still very | |
04:08 | small compared to the bottom number . But as the | |
04:10 | top number gets bigger , the value of our fraction | |
04:13 | is increasing . That tells us that if a fractions | |
04:16 | top number is a lot smaller than its bottom number | |
04:19 | than its value is going to be close to zero | |
04:21 | in this part of the number line . Look at | |
04:27 | this , we're almost to 10 on top . And | |
04:29 | since 10 is half of 20 , we're almost to | |
04:32 | one half on the number line . It's pretty easy | |
04:35 | to figure out what half of something or double something | |
04:37 | is . And we can use that to help us | |
04:39 | compare fractions . Like we know that 9/20 is going | |
04:42 | to be really close to one half on a number | |
04:44 | line . All I know . All right . So | |
04:49 | we've passed one half now and we're making our way | |
04:51 | to the number one . Notice that our top number | |
04:54 | keeps increasing and it's getting closer and closer to 20 | |
04:57 | . In fact , when it reaches 20 , we'll | |
04:59 | have arrived at one because 20/20 is a whole fraction | |
05:03 | . Knowing this can also help you estimate of fractions | |
05:05 | value whenever you see a fraction with the top and | |
05:08 | bottom number that are almost the same like 19/20 . | |
05:12 | You know that the value is close to one . | |
05:14 | Yeah . There we've passed one now but we're still | |
05:18 | going and our top number is now bigger than our | |
05:20 | bottom number . Which means we have an improper fraction | |
05:23 | . You can see that the bigger the top number | |
05:26 | gets , the bigger the value of the fraction . | |
05:28 | And we could keep on going forever , but that | |
05:30 | might take all day . Okay . So our journey | |
05:34 | showed us some pretty useful regions of the number line | |
05:36 | . The region near zero where the top number is | |
05:38 | much smaller than the bottom number . The region near | |
05:41 | one half where the top number is about one half | |
05:43 | of the bottom number . The region near one where | |
05:46 | the top number and bottom number are about the same | |
05:49 | . And the region past one where the top number | |
05:51 | is bigger than the bottom number and it keeps on | |
05:53 | going forever . Knowing about these regions can sometimes help | |
05:57 | you quickly estimate the value of some fractions . For | |
06:00 | example , you can estimate that 1/16 is going to | |
06:04 | be pretty small , close to zero on the number | |
06:06 | line . And you can estimate that 29/31 is going | |
06:10 | to be almost one because there's not much difference between | |
06:13 | the top and bottom numbers . And if you have | |
06:16 | the fraction 14/30 , you can estimate that it will | |
06:19 | be about one half since 14 is close to 15 | |
06:23 | and 15 is half of 30 . Alright . That | |
06:26 | wraps up this section and I hope it's helped you | |
06:28 | understand the different types of fractions and where they are | |
06:30 | on the number line . You'll understand even better if | |
06:33 | you do the exercises for this section . Good luck | |
06:36 | . And I'll see you next . Yeah , learn | |
06:39 | more at math antics dot com . |
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