Math Antics - Basic Division - Free Educational videos for Students in K-12

Math Antics - Basic Division - By Lumos Learning

Transcript


00:03	Uh huh . Hi . Welcome to math antics .
00:08	In this video lesson , we're going to learn the
00:09	basics of division . And if you really understand these
00:12	basics , then it will make it much easier learning
00:15	how to do long division , which is the subject
00:17	of our next video . Okay , so here's how
00:20	basic division works . You get a problem like this
00:23	19 divided by three , which means you have a
00:25	total of nine , and you want to divide it
00:27	into three equal groups . And if you can remember
00:31	that nine is an answer to one of the multiplication
00:33	facts , or that it's an answer on the multiplication
00:35	table , then you can see that since three times
00:38	three is nine , then nine divided by three is
00:41	three . It's that simple . Well , at least
00:44	it was that simple when you learned about the fact
00:46	families . Now it's going to get a little bit
00:49	tricky , because most division problems aren't quite this easy
00:52	. Like this 19 divided by four . The trouble
00:56	here is that nine and four aren't part of a
00:58	fact family , so you can't just find the answer
01:00	on the multiplication table . That's because nine is not
01:03	a multiple for there's no hole number that you can
01:06	multiply four by and end up with nine . That
01:09	means that nine can't be divided equally into four groups
01:13	without having something left over . Like if you had
01:16	nine cookies and four kids , each kid could have
01:19	two cookies , but there would be one left over
01:21	. And in division , that leftover amount is called
01:24	the remainder . So the answer to nine divided by
01:27	four is two with the remainder of one . Yeah
01:30	, all right . So it's not that hard to
01:32	figure out a simple division problem when you have a
01:34	picture like this . But what about when we just
01:37	have numbers to do that ? We use a special
01:39	division procedure . Up until now , you probably views
01:43	this division symbol the most . It works well for
01:45	very simple division problems , like the ones in our
01:48	fact families . But now that we're gonna be doing
01:51	some harder problems , we need a new division symbol
01:53	. This one , this division symbol is special because
01:56	it's almost like a stage that will help us solve
01:59	our division problem . And there's three special areas of
02:02	the stage where the three main parts or characters of
02:04	our division problem will go . The first area is
02:08	here under the long horizontal line on our division symbol
02:11	. This is the area where we put the number
02:13	that will be dividing up the fancy math term for
02:16	this is the dividend . Most of the time ,
02:18	the biggest number will go here because we usually start
02:21	with a big amount and want to divide it into
02:23	smaller groups . The second area is out in front
02:26	of the curved part of the divisions of this is
02:29	the area where we put the number will be dividing
02:31	by the math term . For that is the divisor
02:34	. In other words , this number will tell us
02:36	how many groups will be dividing our big amount into
02:40	. And the third area is up above the horizontal
02:42	line . This is where our answer will go once
02:44	we figure out what the answer is . The answer
02:47	to a division problem is called the quotient . The
02:49	answer tells us how many will end up with in
02:52	each group . So whenever you have a complicated division
02:55	problem to do , the first step is to rewrite
02:57	your problem in this form . If you have nine
03:00	divided by four like this , you put the nine
03:02	down here . That's the number we're dividing up ,
03:04	and you put the four out here . That's the
03:06	number we're dividing by , and you're ready to start
03:09	the next step of the procedure . The next step
03:12	is the most important step , because it's where you
03:14	figure out the answer and to figure out the answer
03:17	, which is how many you'll end up within each
03:19	group . After you divide , you have to ask
03:21	yourself a really important question involving the other two numbers
03:25	. The question is , how many fours will it
03:27	take to make nine or almost I ? And the
03:30	key to answering this question is for the number to
03:32	be just right . Do you remember the story of
03:35	Goldilocks and the Three Bears ? One chair was too
03:38	big and one chair is too small , but the
03:40	other chair was just right . Well , it's the
03:42	same way . With our division problem , I choose
03:45	an answer that's too big or too small . It'll
03:47	cause trouble for me . Here's what I mean .
03:50	Let's say that I decide that I only need one
03:52	for it to make knives , so I'll write a
03:54	one up here in the spot for the answer .
03:57	Well , now , the next step in the procedure
03:59	is to multiply that answer . I put there the
04:02	one by the number of groups out front here before
04:06	, and I write the answer to that multiplication down
04:09	below the number . I'm dividing up the nine .
04:12	I do that so I can subtract that amount from
04:14	the nine to see how much I'm going to have
04:16	left over to see how big the remainder will be
04:19	. And when I do that , I see that
04:21	nine minus four will give me 55 That's a pretty
04:24	big remainder . In fact , the remainder is bigger
04:27	than the number I'm dividing by . And that's why
04:30	this answer is trouble . If the remainder is bigger
04:33	than the number you're dividing by , it means that
04:36	you should have picked a bigger answer because each of
04:38	the groups are divided up into could have gotten more
04:41	than they did . Your answer was too small ,
04:44	and so the remainder was too big . Okay ,
04:46	then I guess I'd better come up with a better
04:49	answer to the question . How many fours will it
04:51	take to make nine or almost night ? This time
04:54	I think I'll pick three , so I put a
04:57	three in the answer space . And then I follow
04:59	the next step of the procedure like I did .
05:01	Before I multiply the answer . I chose three by
05:04	the number of groups . Four . And I write
05:07	the answer to that multiplication problem . 12 down below
05:11	the number . We're dividing up the nine . Now
05:14	I can subtract that number to see what my remainder
05:16	will be . Or can I ? This looks like
05:19	trouble again . The answer to my multiplication is bigger
05:22	than the number we're dividing up , so I can't
05:24	subtract it . The remainder would be less than zero
05:27	, and I can't have a remainder less than zero
05:30	. That can't be right . Here is the problem
05:33	. When you choose an answer that's too big .
05:35	It's like trying to give too many to each group
05:38	, and then you run out of things to give
05:39	before the groups are equal . And if the groups
05:42	aren't equal , they get all upset . Okay ,
05:52	so one was too small . They gave us too
05:54	big of a remainder and three is too big .
05:57	There wouldn't be any remainder at all , and the
05:59	groups want to be equal , which causes big problems
06:02	. So let's try to if we say that to
06:05	force will make nine or almost nine . Our problem
06:08	looks like this to goes in the answer spot ,
06:11	and then we do our multiplication procedure . We multiply
06:14	that to buy the four , and we get eight
06:17	. Then we write the eight below the nine so
06:19	we can subtract it and find our remainder nine .
06:22	Minus eight equals one , so that means a remainder
06:25	is one that sounds good . It's less than a
06:28	number of groups , and you can see with our
06:30	cookie problem that it's exactly right . Nine cookies ,
06:34	divided into four groups gives two cookies to each group
06:38	with one left over as a remainder , which will
06:40	put right up here in our answer within our for
06:43	remainder perfect . And now you can see how you
06:46	can do division without using pictures or cookies . But
06:49	just with numbers and a procedure to follow , let's
06:52	try a couple more so you really see how it
06:54	works . Let's try 23 divided by five . We
06:58	start as always , by making sure our problem is
07:01	written correctly using our new division symbol . The 23
07:04	is what will be dividing up . It's our dividend
07:07	, so we put it under the line and the
07:09	five is what we're dividing by our divisor . So
07:12	it goes out front . Okay , so now we
07:15	ask , How many fives will it take to make
07:18	23 or almost 23 ? Well , 15 would be
07:23	way too small . Two fives is 10 . That's
07:26	also too small . Three fives would be 15 .
07:29	4 fives is 20 . Oh , that sounds promising
07:32	. 55 is 25 that would be too much .
07:36	So it sounds like four is a really good number
07:38	two pick for her answer . So let's put that
07:40	on the answer line . Next . We need to
07:42	do the step where we multiply . The answer .
07:45	Four by the number of groups . Five . And
07:48	we get 20 which will right below the number .
07:50	We're dividing up 23 . Now we subtract those numbers
07:54	to see what our remainder is . 23 minus 20
07:57	is three . Well , that's good . Three is
07:59	less than our number of groups , so it's a
08:01	reasonable remainder . So our answer to 23 divided by
08:05	five is four with a remainder of three . Let's
08:09	do one more before you try working some out on
08:11	your own . Okay , let's do 57 . Divided
08:14	by six first we set up our problem and then
08:17	we ask the question , How many sixes do we
08:19	need to make 57 or almost 57 ? Well ,
08:22	this one's a little more tricky , so I think
08:24	I might use a multiplication table to help me out
08:28	. The nice thing about a multiplication table is that
08:30	it shows me all the multiples of the number .
08:32	For example , since I want to know how many
08:34	sixes I need , I can look on this row
08:37	of the chart and see all the multiples of six
08:39	. Here they are . 6 , 12 , 18
08:42	, 24 30 36 42 48 54 60 . We
08:49	need the multiple that's 57 or almost 57 . And
08:52	since 57 is not on the list , it looks
08:54	like 50 . Tour is the next closest thing without
08:57	being too big , like 60 . And to get
09:00	54 we need to add nine sixes , so we'll
09:02	choose nine as our answer . Next we multiply nine
09:06	by six , which we already know will give us
09:09	54 because that's what our multiplication table showed us .
09:13	Now we need to subtract 54 from 57 . That
09:16	gives us a remainder of three again . That's good
09:19	, because that's less than our divisor . So 57
09:22	divided by six , equals nine with a remainder of
09:25	three . All right , that's all for this lesson
09:29	. And if you're new to division , that's plenty
09:31	to get you started . It's really important to master
09:33	these basic division problems that just involve one step that
09:37	leaves you with the remainder in the next video .
09:39	We're going to learn how to take this basic procedure
09:42	we've learned and repeat it multiple times in a process
09:45	called Long Division . But before you move on ,
09:48	make sure you really practice what you've learned in this
09:50	video . First , good luck , and I'll see
09:53	you next time . Learn more at math antics dot
09:57	com .

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