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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