Math Antics - Common Denominator LCD - Free Educational videos for Students in K-12 | Lumos Learning

## Math Antics - Common Denominator LCD - Free Educational videos for Students in k-12

#### Math Antics - Common Denominator LCD - By mathantics

Transcript
00:03 uh huh . In the last video we learned how
00:07 to find what I like to call the easiest common
00:10 denominator . And personally I prefer to use that method
00:13 of getting a common denominator whenever I can because it's
00:16 quick and easy to remember but I can think of
00:19 at least two cases where it would be better to
00:21 use a different method to convert unlike fractions into like
00:23 fractions . The first case is when one of the
00:27 fractions bottom numbers is a multiple of the other fractions
00:30 bottom number . And the second case is when your
00:32 teacher says that you have to use this other method
00:35 . This new method is called finding the least common
00:38 denominator because it involves using the smallest common denominator .
00:42 We can find instead of just using the product of
00:44 the bottom numbers like we did in the first method
00:47 to find the smallest or at least common denominator of
00:51 two fractions , we need to figure out what the
00:53 smallest or at least common multiple of the two bottom
00:56 numbers is now in case you've forgotten a multiple of
00:59 a number is just the result of multiplying it by
01:02 another whole number like 12 or three . So here's
01:06 what we're gonna do to find the least common denominator
01:08 or L . C . D . For short .
01:10 First we'll take the two different bottom numbers and start
01:16 one times the numbers and then two times and then
01:19 three times and four times and so on . It
01:23 helps to arrange these multiples in a small table almost
01:26 like a scoreboard so that you can keep things organized
01:28 and easy to find . We'll stop making multiples as
01:31 soon as we find an answer , that's the same
01:33 for both numbers . That answer is called the least
01:36 common multiple and it will become our new common denominator
01:40 . Once we know what the least common denominator is
01:42 , we have to figure out which whole fractions will
01:45 need to multiply our unlike fractions by to get equivalent
01:48 fractions with that common denominator . The solution is to
01:52 use the same numbers that resulted in the common multiple
01:55 . For example , if you multiplied by four to
01:58 get the common multiple for the first , unlike fraction
02:01 , then you'll use 4/4 as your whole fraction .
02:04 And if you multiplied by three to get the common
02:07 multiple for the second , unlike fraction , then you'll
02:09 use 3/3 as your whole fraction for it . Have
02:13 I lost you yet ? Should make a lot more
02:15 sense . After you've seen a few examples , let's
02:22 one is to take our two bottom numbers and make
02:25 multiples of them to see if we can find a
02:27 common multiple First . Let's multiply them both by what
02:30 ? Well , that's easy . We have eight and
02:32 24 . Next we multiply them both by two and
02:35 that gives us 16 and 48 . I still don't
02:38 see anything in common . So let's multiply them both
02:40 by three . Three times eight is 24 3 times
02:44 24 is 72 . But look , we have something
02:47 in common . Now we have a 24 in each
02:49 column . We have found the least common multiple of
02:52 the numbers eight and 24 . And it happens to
02:55 be 24 . That makes sense if you remember your
02:57 multiplication tables that three times 8 equals 24 . So
03:02 now we know we're going to use 24 as a
03:04 common denominator . But what whole fractions do we need
03:07 to get it ? The answer lies in our multiples
03:09 chart to get our common multiple . We had to
03:12 multiply our eight by three . So we're going to
03:14 use the whole fraction 3/3 for our first fraction And
03:19 our common multiple for 24 was just itself . We
03:22 multiplied by one . So we could use the whole
03:24 fraction 1/1 . But we really don't need to sense
03:28 multiplying by one . Won't change anything . We already
03:31 have the denominator of 24 on that side , so
03:34 we don't need to change it . Okay , now
03:36 we multiply on top three times three gives us nine
03:40 and on the bottom eight times three gives us 24
03:43 just like we wanted . Now we have like fractions
03:46 and we can use our simple procedure to add them
03:48 . We add the top number's nine plus five equals
03:51 14 . And we keep the same bottom number .
03:53 24 . Okay . Ready for one more example ,
03:57 let's find the L C D for these fractions to
04:00 over nine and 7/12 . Again , let's start by
04:04 making a list of multiples for our two bottom numbers
04:07 . To look for a common multiple . Nine times
04:09 one is nine and 12 times one as 12 .
04:12 Of course nine times two is 18 and 12 times
04:16 two is 24 . Nine times three is 27 12
04:20 times three is 36 . 9 times four is 36
04:24 . Ha ha we found it . 36 is the
04:27 least common multiple of nine and 12 . So we'll
04:30 use that as our common denominator . Now let's figure
04:33 out which whole fractions we need to use to make
04:36 our fractions have that denominator . We use 4/4 for
04:39 our first unlike fraction since four times nine was 36
04:43 we use 3/3 for our second . Unlike fraction because
04:46 three times 12 was 36 there . Now when we
04:50 multiply we get to new but equivalent fractions that have
04:54 a common denominator . Now we can add them with
04:56 our simple procedure on the top eight plus 21 equals
05:00 29 we keep the same bottom number 36 . So
05:04 that's how you use at least common denominator method .
05:07 And it's really not that hard once you get the
05:09 hang of it . So don't forget to do the
05:11 exercises for this video , because the way to really
05:14 learn math is to do it . Good luck .
05:20 Antics dot com .
Summarizer

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