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

Math Antics - Common Denominator LCD - By mathantics

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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
01:14	making multiples of each of them . We start with
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
02:17	start with this problem . 3/8 plus 5/24 . Step
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 .
05:16	And I'll see you next time learn more at math
05:20	Antics dot com .

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