Math Antics - Working With Parts - By mathantics
Transcript
| 00:03 | Uh huh . Now that we know how to use | |
| 00:07 | fractions to represent parts of a whole , there's a | |
| 00:09 | few different things we can do with them . First | |
| 00:12 | of all , we can compare fractions comparing fractions means | |
| 00:15 | checking to see if one fraction is greater than less | |
| 00:18 | than or equal to another fraction . That's pretty easy | |
| 00:21 | if we think of fractions as parts of objects and | |
| 00:24 | draw pictures to help us see what we have . | |
| 00:26 | Here's an example which of these fractions is greater 3/8 | |
| 00:30 | or 5/8 to answer that question , let's start by | |
| 00:34 | drawing two rectangles and divide them into eight equal parts | |
| 00:37 | . Since the rectangles are divided into eight parts , | |
| 00:40 | each of those parts is called an eighth . Now | |
| 00:43 | let's shade three parts of the first rectangle or 3/8 | |
| 00:46 | and five parts of the second rectangle or 5/8 . | |
| 00:50 | Our picture makes comparing these fractions easy . You can | |
| 00:53 | see that 5/8 is greater than 3/8 because more of | |
| 00:56 | that rectangle is shaded . Okay , now let's try | |
| 00:59 | one . That's a little harder . Which of these | |
| 01:01 | fractions is greater 3/4 or 4/5 ? Well , let's | |
| 01:06 | start again with two rectangles . But this time we | |
| 01:08 | need to divide them up differently because the fractions were | |
| 01:11 | comparing have different bottom numbers . The first rectangle will | |
| 01:15 | be divided into four equal parts , and we'll shade | |
| 01:17 | three of them to show 3/4 . The second rectangle | |
| 01:21 | will be divided into five equal parts and we'll shade | |
| 01:23 | four of them to represent 4/5 . Now to compare | |
| 01:27 | all we have to do is see which rectangle is | |
| 01:29 | shaded in the most and that tells us that 4/5 | |
| 01:32 | is greater than 3/4 there . That wasn't so hard | |
| 01:35 | after all . All right , let's try one more | |
| 01:38 | example , let's compare the fractions one half and 2/4 | |
| 01:42 | again . We start by drawing rectangles and dividing them | |
| 01:45 | up into parts two on this one and four on | |
| 01:48 | this one next we shade the parts of the rectangle | |
| 01:51 | according to our top numbers . One on this one | |
| 01:54 | and two on this one . Now all we have | |
| 01:56 | to do is compare it well , what do you | |
| 01:58 | know the same amount of each rectangle is shaded . | |
| 02:01 | That means these two fractions are equal . It might | |
| 02:05 | seem strange that two fractions can have totally different numbers | |
| 02:08 | and still represent the same amount , but they can | |
| 02:12 | fractions like that are called equivalent fractions . Equivalent fractions | |
| 02:15 | have different top and bottom numbers but are equal in | |
| 02:18 | value . We'll learn more about equivalent fractions later in | |
| 02:21 | this video , but for now let's find out what | |
| 02:23 | else we can do with fractions . Another thing we | |
| 02:26 | can do with fractions is add them together . Any | |
| 02:29 | two fractions can be added , but for now we're | |
| 02:31 | only going to add fractions if they have the same | |
| 02:33 | bottom numbers because those fractions are much easier to add | |
| 02:37 | . Like these two fractions , 1/4 and 2/4 let's | |
| 02:40 | add them together . Again , we can use drawings | |
| 02:42 | to help us solve this problem . Looking at the | |
| 02:45 | rectangles for these two fractions , we can add them | |
| 02:47 | visually just by rearranging the parts because all of the | |
| 02:51 | parts are fourths . Our answer will also be fourths | |
| 02:54 | . We can just take this 1/4 and over here | |
| 02:56 | and combine it with these 2/4 and tara , 3/4 | |
| 03:00 | So 1/4 plus 2/4 equals 3/4 . Let's try another | |
| 03:05 | one . Let's add 3/8-5/8 and we can use any | |
| 03:09 | shape we want . So I'm gonna use a circle | |
| 03:11 | this time . So we have three out of eight | |
| 03:13 | here , and five out of eight here . Just | |
| 03:16 | like our last problem , we can add these by | |
| 03:18 | combining the parts . So let's put these three over | |
| 03:21 | here with these five . Well , what do you | |
| 03:23 | know ? That fills up all eight sections ? So | |
| 03:26 | 3/8 plus 5/8 equals 8/8 or one whole circle . | |
| 03:31 | In those examples you might have noticed a pattern . | |
| 03:34 | The bottom number of our answer was always the same | |
| 03:37 | as the bottom numbers of the fractions we were adding | |
| 03:40 | , and the top number of our answer was just | |
| 03:42 | the some of the top numbers of those fractions . | |
| 03:45 | Well , that's how it works . That's the procedure | |
| 03:48 | or set of steps for adding fractions that have the | |
| 03:51 | same bottom numbers . That's important because if you can | |
| 03:54 | remember that procedure then you won't need to use drawings | |
| 03:57 | to help you add fractions . And that's a really | |
| 03:59 | good thing because what if you had to add these | |
| 04:01 | two fractions together , 15 hundreds and 10 hundreds , | |
| 04:05 | It would be way too much work to draw rectangles | |
| 04:07 | and divide them up into 100 parts . Fortunately since | |
| 04:10 | we know the procedure for adding fractions , we can | |
| 04:13 | do it without the drawings first . Let's write out | |
| 04:16 | the problem now , because we're adding fractions , we | |
| 04:18 | know that the answer will also be a fraction . | |
| 04:21 | The bottom number of our answer will be the same | |
| 04:23 | as the bottom number of the fractions were adding 100 | |
| 04:26 | And the top number of our answer will just be | |
| 04:28 | the some of our top numbers 15 plus 10 , | |
| 04:32 | which equals 25 . So as you can see , | |
| 04:35 | adding fractions with the same bottom numbers is easy when | |
| 04:37 | you know the procedure . All of this brings up | |
| 04:40 | a really important point when you're first learning about fractions | |
| 04:44 | , drawing pictures and imagining that fractions represent parts of | |
| 04:47 | cookies and candy bars can be really useful and it | |
| 04:50 | can taste good to thinking of them that way . | |
| 04:52 | It can help you understand how simple fractions work . | |
| 04:55 | And it can even help you solve some basic math | |
| 04:57 | problems . But soon you'll have to do harder math | |
| 05:00 | problems and to solve those you'll need to stop thinking | |
| 05:02 | about fractions is just parts of things and start thinking | |
| 05:05 | about them in a different way . And that's what | |
| 05:07 | we're going to be talking about in the next section | |
| 05:09 | . Before we move on , let's review what we've | |
| 05:12 | covered so far . We can draw pictures to show | |
| 05:15 | how fractions represent parts of a whole . Using drawings | |
| 05:19 | we can compare for actions to see which one represents | |
| 05:21 | the greatest amount . If we compare two different fractions | |
| 05:25 | and find that they represent the same amount , then | |
| 05:28 | we call them equivalent fractions . We can also use | |
| 05:32 | drawings to help us do simple addition . By combining | |
| 05:34 | the parts by doing this , we learned that the | |
| 05:37 | procedure for adding fractions that have the same bottom number | |
| 05:40 | is to just add the top numbers and keep the | |
| 05:43 | same bottom number . And our answer now to make | |
| 05:46 | sure you understand how to compare and add fractions visually | |
| 05:49 | . Be sure to do the exercises for this section | |
| 05:51 | . Learn more at math antics dot com . |
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