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

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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