Math Antics - Common Denominator ECD - By mathantics
Transcript
| 00:03 | Uh huh . Hi and welcome to Math antics . | |
| 00:08 | In the last video we learned how easy it is | |
| 00:10 | to add and subtract fractions that have the same bottom | |
| 00:13 | number . We call those like fractions but often you'll | |
| 00:17 | be asked to add or subtract fractions that have different | |
| 00:19 | bottom numbers or unlike fractions . And we learned that | |
| 00:22 | the only way we can do that is to change | |
| 00:24 | our fractions so that they do have the same bottom | |
| 00:27 | number . All right then , how do we do | |
| 00:29 | that ? How can we change to unlike fractions into | |
| 00:33 | two like fractions ? How do we get our fractions | |
| 00:35 | to have a common denominator ? The answer is we | |
| 00:39 | need to use equivalent fractions . You remember what equivalent | |
| 00:42 | fractions are ? Right ? There are fractions that have | |
| 00:45 | the same value but use different top and bottom numbers | |
| 00:48 | like 1/2 and 2/4 , they both represent one half | |
| 00:52 | but with different numbers . Well , whenever we have | |
| 00:55 | two , unlike fractions that we need to add if | |
| 00:58 | we could find equivalent fractions to use instead , and | |
| 01:01 | if those new equivalent fractions had the same bottom numbers | |
| 01:04 | as each other , then we'd be all set . | |
| 01:07 | We would have to like fractions and we could add | |
| 01:09 | them using our procedure . No . Okay . But | |
| 01:12 | how do we find equivalent fractions that have a common | |
| 01:14 | denominator or the same bottom number ? Well , there's | |
| 01:17 | two main ways of doing it in this video . | |
| 01:20 | We're only going to learn the first way of doing | |
| 01:22 | it . And I like to call this way Finding | |
| 01:24 | the easiest common denominator . In the next video , | |
| 01:27 | we'll talk about another method that some of you may | |
| 01:29 | have already heard about . It's called finding the least | |
| 01:32 | common denominator . Okay , so how does this easiest | |
| 01:35 | common denominator method work ? Well , even though this | |
| 01:38 | is an easy method , it might sound a little | |
| 01:40 | complicated at first , but don't worry , it'll make | |
| 01:43 | a lot more sense once you've seen a few examples | |
| 01:46 | in this method , the common denominator is always going | |
| 01:49 | to be the product of the bottom numbers . In | |
| 01:51 | other words , it will be the number you would | |
| 01:53 | get if you multiply the bottom numbers together , basically | |
| 01:57 | all we're going to do is take the two different | |
| 01:59 | bottom numbers and make two different whole fractions using them | |
| 02:03 | . Then we're going to move the whole fractions to | |
| 02:05 | the opposite sides and multiply them by our unlike fractions | |
| 02:08 | . Doing this will give us two new equivalent fractions | |
| 02:11 | that will have the same bottom number , then we | |
| 02:14 | can add or subtract them easily . Okay , let's | |
| 02:18 | try a couple examples . So we can see this | |
| 02:19 | method in action . Let's add two fractions to over | |
| 02:22 | five and 1/3 . These are not like fractions because | |
| 02:26 | they have different bottom numbers , so we're going to | |
| 02:29 | change them . And the common denominator we'll use is | |
| 02:32 | the product of the bottom numbers . Five times three | |
| 02:35 | equals 15 . We change them by multiplying each fraction | |
| 02:39 | by a whole fraction . The first coal fraction is | |
| 02:42 | going to be 3-3 because three is the second fractions | |
| 02:46 | denominator and the second hole fraction is going to be | |
| 02:49 | 5/5 because five is the first fractions denominator . Next | |
| 02:54 | we multiply starting with our first fraction on the top | |
| 02:58 | three times two equals six , and on the bottom | |
| 03:01 | three times five equals 15 . So our first fraction | |
| 03:04 | has become 6/15 . Now for the second fraction on | |
| 03:09 | the top one times five equals five , and on | |
| 03:11 | the bottom three times five equals 15 . So our | |
| 03:15 | second fraction has become 5/15 . Now we just add | |
| 03:19 | them . Using our procedure for adding like fractions . | |
| 03:22 | We had the top numbers six plus five equals 11 | |
| 03:25 | and then we keep the same bottom number , which | |
| 03:27 | is 15 . So that means the answer to to | |
| 03:30 | over five plus 1/3 is 11/15 . That's pretty easy | |
| 03:35 | , huh ? All right . Let's see one more | |
| 03:37 | example of this method . Let's add two fractions 7/8 | |
| 03:41 | and 3/10 . Our common denominator for this . Problem | |
| 03:44 | is going to be 80 because that's what we get | |
| 03:47 | when we multiply the denominators together eight times 10 equals | |
| 03:50 | 80 . We'll multiply our 7/8 by the whole fraction | |
| 03:54 | 10/10 and will multiply our 3/10 by the whole fraction | |
| 03:58 | 8/8 . Then when we do our multiplication that eight | |
| 04:02 | times 10 will give us 80 on the bottom of | |
| 04:04 | both fractions . For the top of the first fraction | |
| 04:07 | we have seven times 10 equals 70 . And the | |
| 04:10 | top of the second fraction we have three times eight | |
| 04:13 | equals 24 . Now that we have like fractions , | |
| 04:16 | we can just add the top number's 70 plus 24 | |
| 04:20 | equals 94 keep the bottom number the same 80 . | |
| 04:24 | So 7/8 plus 3/10 equals 94/80 . Some of you | |
| 04:30 | see that this answer could be simplified . Be sure | |
| 04:32 | to check out our videos on mixed numbers and simplifying | |
| 04:34 | fractions to see how you could do that for your | |
| 04:37 | final answer . All right . That's the first way | |
| 04:40 | you can find the common denominator and change your unlike | |
| 04:42 | fractions into like fractions so you can add or subtract | |
| 04:45 | them easily remember . Practice is really important in math | |
| 04:49 | . So be sure to do the exercises for this | |
| 04:51 | section . So you really get the hang of it | |
| 04:52 | after that . Check out the next video and I'll | |
| 04:55 | show you how to use a different method to find | |
| 04:57 | what we call the least common denominator . Thanks for | |
| 05:00 | watching . And I'll see you next time . Yeah | |
| 05:03 | , learn more at math Antics dot com |
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