11 - Subtracting with Regrouping (Borrowing) - Part 1 (3rd Grade Math & 4th Grade Math) - Free Educational videos for Students in K-12

11 - Subtracting with Regrouping (Borrowing) - Part 1 (3rd Grade Math & 4th Grade Math) - By Math and Science

Transcript


00:01	Hello . Welcome back . The title of this lesson
00:03	is called subtracting two digit numbers with renaming . Another
00:07	way to say this you might see in some books
00:09	is subtracting two digit numbers with borrowing . Now the
00:13	first time you see borrowing it looks a little bit
00:15	weird and a little bit cumbersome and complicated but it's
00:19	actually very easy to understand . Once we get some
00:21	practice , what I want to do is just work
00:23	a couple of problems and show you what we're doing
00:26	, get the answers . And then I'm going to
00:28	explain to you why you're actually allowed to do this
00:30	, why it actually works . And then we're going
00:32	to finish all of the rest of the problems to
00:34	give you a lot of practice . It's easier just
00:36	to tell you what we're doing by just solving the
00:38	first problem . So let's go and do that right
00:41	now . The first problem Is going to be 23
00:45	uh minus 15 . Right ? So we write it
00:50	stacked up on top and bottom like this and we
00:53	always go to the right hand column first , we
00:55	start with the top number and subtract the bottom number
00:57	. So we have three minus five . Now you
01:01	see there's a problem right away because if I have
01:03	three marbles and try to subtract five marbles from it
01:07	, how can I do that ? How can I
01:09	take three minus five ? If I only have three
01:12	, how can I take more away ? How can
01:14	I take five away ? It's something that you don't
01:16	think you're allowed to do . So because of this
01:18	, we never ran into this with any of the
01:20	other problems because all of the other problems had a
01:23	top number that was bigger than the bottom , but
01:25	in this case you can see that three is not
01:27	bigger than five . So what do you do ?
01:29	Let me go through how to solve it , and
01:32	then we're gonna talk about why it works . So
01:34	what I want to do is uh go through and
01:37	tell you exactly what we're going to do This three
01:40	is not bigger . So we're not allowed to really
01:42	subtract it . What we're gonna do is borrow ,
01:44	we're gonna borrow from the column next door , we're
01:47	gonna borrow from the two . Here's what you actually
01:49	do . We make this three , we do a
01:52	single strike through of this three and right on top
01:54	we turn the three into 13 . Right ? You're
01:57	gonna say how can you do that ? Well because
01:59	we borrow from the other column and we change this
02:02	to into A one . So what you have to
02:05	do when your paper is strike through the three and
02:07	make it 13 and then you in order to do
02:10	that , it has to come from somewhere we're borrowing
02:12	from the column next door . So the two turns
02:14	into a one . Now what you do is you
02:17	look in this column and say it's 13 minus five
02:20	, we know how to do that . Start with
02:21	13 in your mind and go down 12 11 ,
02:25	10 98 Okay , So we landed on eight .
02:29	So we write the number eight down below in this
02:32	column . Now we're done with this column . The
02:34	next column over , we have 1 -1 . You
02:37	all know that 1 -1 is zero . We could
02:39	put a zero here but zeros in front as a
02:42	as a as a number in the front doesn't really
02:44	do much . So the zero in the front doesn't
02:46	mean anything . And so we can just leave it
02:47	off and say that the answer is eight . Now
02:50	a couple things I want to do is let's just
02:52	check that this is correct . The original problem was
02:54	23 -15 . We can start with 23 and go
02:57	down 15 , 22 , 20 1918 , 17 ,
03:02	16 , 15 , 14 , 13 , 12 ,
03:05	11 , 10 , 98 You see we subtracted 15
03:09	. We still got to eight . So this is
03:10	the right answer . And we had to do the
03:12	borrowing because three was smaller than five . So we
03:15	made it 13 . And in order to do that
03:17	we had to take it from the next door neighbor
03:19	to the left . I want to do one more
03:22	and then I want to explain more about why we're
03:24	allowed to do this . Let's say we have 26
03:29	And we're subtracting from it 19 . Okay , how
03:32	do we do that ? We have the same problem
03:35	in the right hand column . It's 6 -9 .
03:38	If I have nine I'm sorry , six apples and
03:41	I want to take nine away . You can't really
03:43	do it because you only have six to begin with
03:45	. So when you have that situation you have to
03:47	change it or you might say rename , which is
03:50	why it's called renaming . You might also think of
03:52	it as borrowing . We take the six and we
03:55	strike through it and we make it actually 16 .
03:58	But in order to do that we have to borrow
04:00	it from the next door neighbor . So the two
04:02	now becomes a one . You do not want to
04:05	scribble through the numbers . You want a single line
04:07	through the numbers so you can still read what you're
04:09	doing and you want to write clearly on top what
04:12	the new numbers become . Now in the right hand
04:16	column you have 16 minus nine . Starting with 16
04:19	. Go down 15 , 14 , 13 , 12
04:22	, 11 , 10 , 987 You landed on 77
04:28	goes in the right hand call on the left hand
04:31	column . You have one minus one . You could
04:33	write a zero here , but you don't need zeros
04:35	in front of your number . So really the answer
04:37	is seven . If you go 26 go 19 down
04:41	from that , you're going to land on the number
04:42	seven . That's the final answer . Now , I
04:44	don't want to spend all day talking about why this
04:47	works , but I do want to talk a little
04:49	bit about it . Let's look at the first problem
04:51	here . It was 23 and we we're subtracting 15
04:56	. Okay , so you might say , how am
04:59	I able to make this 13 by striking through the
05:02	two . If I turned the two into a one
05:05	, how am I how does that make it better
05:07	? Well , the thing that you need to realize
05:09	or understand Is that this number 23 ? These columns
05:14	mean different things . This column here is called the
05:17	ones call These because it's 21 , 22 , Every
05:24	number in that column is just it's value is one
05:27	. Okay , But every number in this column ,
05:30	this is called the actually the tens column . When
05:35	you think about it for 23 . This number doesn't
05:38	mean to . This number means 20 . So this
05:41	means 20 plus three . This 23 . When we
05:46	write it together like this , you know that this
05:48	number means three . But this number doesn't really mean
05:50	to It really actually means 20 . That's what we
05:53	mean by the tens column . Because it's too uh
05:57	and you have this is worth 10 and you have
05:59	two of them . So there's 20 . This guy
06:02	means the one here does not really mean a one
06:04	. It means 10 . And this number right here
06:07	, it means five . So 20 plus three is
06:10	23 10 plus five is 15 . That's what numbers
06:14	mean when we the columns mean something . So when
06:18	we actually strike through the two and make it a
06:21	one , we're not really making it changing it from
06:24	2 to 1 . We're actually changing it from 20
06:28	because that's the value of this 20 to 10 .
06:31	And so we're borrowing 10 and that 10 that we
06:33	borrow goes next door . And that's why it makes
06:36	it 13 . So we're not really borrowing one here
06:39	, we're actually borrowing 10 . And that's why when
06:42	you add the 10 to hear it becomes 13 .
06:45	So when you cannot subtract numbers in the right column
06:48	you borrow from the next column over but you're really
06:50	borrowing 10 . And that's why these numbers in this
06:54	case became a 16 because we didn't borrow one .
06:57	Even though we put a one here we actually borrow
07:00	10 . The value of this too was 20 .
07:03	Now the value is 10 . The 10 that we
07:06	borrowed goes into here . And that's how we do
07:08	the subtraction . Now that's what it means . But
07:10	the most important thing is to get a lot of
07:13	practice with it . So we're going to continue to
07:15	do that right now let's say we have 33 -18
07:23	. Right ? Again we cannot take 3 -8 .
07:26	So what we have to do is borrow . Right
07:28	? So we say well this three is not going
07:31	to really be a three anymore . It's going to
07:32	be a 13 . And to do that I'm going
07:35	to change this three into a two . But in
07:37	the back of your mind remember that this value of
07:40	this three is not really three . It really means
07:42	30 . Why ? Because this is 30 plus three
07:46	. That's what this really means . All right so
07:49	this three going into a to really means that I
07:51	borrowed 10 and that 10 goes into here to make
07:54	the 13 . So that's what you're doing Now .
07:58	-8 . Start with 13 in your mind go down
08:00	12 11 10 98765 You land on the number 55
08:09	goes under this column . Now in these other problems
08:12	we had 1 -1 gave us zero . So we
08:14	didn't really write it here . We had 1 -1
08:17	gives us zero . We didn't really write it here
08:19	. We have 2 -1 which gives us one .
08:22	So we have to actually write it . And the
08:23	answer here is 15 . So 33 -18 is 15
08:28	. Now we're going to have to get used to
08:30	doing this renaming or borrowing whatever you wanna call it
08:33	because it's something that's not gonna go away . So
08:36	let's just get some more practice . What if we
08:38	have 45 -16 ? If you try to take five
08:44	minus the six you can't do it because it's not
08:47	big enough . So we say this five is not
08:49	five anymore , it's really worth 15 , it has
08:52	to come from someplace . So we change the four
08:54	into a three in this column . Now we say
08:57	15 minus six . Start with 15 in your mind
09:00	go down 14 13 , 12 , 11 10 nine
09:04	. And the answer that you get is nine in
09:07	this column . This column we have now a 3
09:10	-1 gives us 3 -1 is two . So you
09:13	get an answer of 29 , that's the final answer
09:16	. Yeah , we're going to do enough of these
09:18	. So you're absolutely confident in what you're doing .
09:23	What if you have 41 -27 ? If you try
09:29	to take 1 -7 , you can't do it .
09:31	So what you instead do is you say this is
09:33	not worth one anymore , it's really an 11 .
09:36	Where does it come from ? The four then ?
09:38	Has to become a three . Do not get confused
09:42	with the numbers above the 11 goes in this column
09:44	, the three is in this column . So 11
09:46	minus seven . Start with 11 . In your mind
09:48	, go down uh 10 987654 The number you land
09:55	on is actually a four . So a four goes
09:57	in this column , This column is 3 -2 ,
10:00	which you all know is one . And so the
10:02	answer to this is actually 14 , so 41 -27
10:05	is 14 . Yeah . Okay , what if you
10:10	have 51 -16 , subtract these guys again . 1
10:17	-6 . The one is not large enough , so
10:20	we're going to change this one and actually make it
10:22	11 and it has to come from somewhere , so
10:25	we strike out the five and actually make it a
10:28	four . But again , we're not really making it
10:30	for , we're borrowing 10 here because this is worth
10:33	50 and now it's worth 40 . So the 10
10:36	is really going in this column . So one is
10:38	11 minus six . Start with 11 in your mind
10:40	go down 10 98765 So we go down and we
10:46	land on the number five . So five goes in
10:49	this column Now we have four going down by one
10:52	for -1 gives us three , and the answer is
10:55	now 35 . So 51 -16 is 35 . All
11:03	right . What if we have we have just a
11:05	few more problems here . What if we have uh
11:07	53 -28 Again ? You try to do 3 -8
11:14	but it's not big enough so you can't do it
11:16	. So you strike through this and make this three
11:18	a 13 instead and it has to come from somewhere
11:21	. So it comes from next door , change the
11:23	five into a four . Start now with 13 and
11:26	subtract eight go down 12 11 10 98765 The answer
11:33	is five . So we put a five down below
11:36	and then we have four minus two . You go
11:39	down 32 so four minus two is two . Put
11:42	a two down here in . The answer for this
11:44	is 25 . Yes . Right . Yeah . Giving
11:48	a little more practice . What if we have 60-14
11:55	Again ? You try to subtract 2 -4 but you
11:58	can't do it . So we changed the two and
12:00	make it a 12 has to come from somewhere .
12:03	So the six now becomes a five . Now in
12:06	your mind start with 12 and go down four .
12:08	Start with 12 . Go down 11 , 10 ,
12:11	98 And so the answer you get here in the
12:15	right hand column is an eight and then five minus
12:17	one is a four . And so the answer you
12:20	get there is 48 . Okay , Okay . Two
12:24	more problems . What if we have 54 and we're
12:27	subtracting from it 36 . So again we try to
12:33	say 4 -6 but you can't do it . So
12:36	the four now becomes a 14 and has to come
12:39	from somewhere . So the five now becomes a four
12:42	. We've borrowed 10 and stuck it in the other
12:43	column . Now start with 14 and go down six
12:47	. So we go 13 12 , 11 , 10
12:50	, 98 You land on eight . So that's the
12:53	final answer in the right hand column . Now we
12:56	have four minus three . So you can think going
12:58	four , going down 3 to 1 , we've gone
13:01	down three , we've landed on one . The answer
13:03	is 18 54 -36 is 18 and we have only
13:07	one more problem . Okay . And it is 65
13:12	minus 26 In the right hand column . We try
13:16	to do 5 -6 but we can't do it .
13:19	So we strike through the five and actually make it
13:21	15 . It has to come from somewhere . So
13:23	, the six now becomes a five now we do
13:27	15 minus 6 , 15 . Going down 6 ,
13:30	14 , 13 , 12 , 11 , 10 9
13:34	. We land on the number nine and nine goes
13:37	in the right hand column now five minus to start
13:39	with five in the mine and go down 43 And
13:43	we land on three . So the answer is 39
13:47	. All right ? So in this lesson we have
13:49	mastered and start what we started . The concept of
13:51	subtracting two digit numbers with renaming . Also you might
13:55	see it called subtracting numbers with borrowing . And the
13:59	borrowing comes from the idea that in the right hand
14:02	column , if the number on the top is smaller
14:05	than the number on the bottom , you're not going
14:07	to really be able to subtract . So you have
14:08	to borrow . But remember , the right hand column
14:11	is really what we call the ones column . And
14:13	the left hand column is really what we call the
14:16	tens column . So this too is not really a
14:18	two . It's really a 20 plus is an invisible
14:22	plus here . A three here . So when we
14:24	strike out the two and make it a one .
14:26	We're really not subtracting one . We're subtracting 10 from
14:29	that column and that 10 goes over here to make
14:32	it 13 . That's how the borrowing process works .
14:35	Again . You might also see as I see it
14:37	as renaming because we kind of rename the problem to
14:40	make it possible . So I want you to solve
14:41	every one of these yourself . When you get the
14:44	right answers , follow me on to the next lesson
14:46	of part two where we're going to continue getting practice
14:48	, subtracting two digit numbers with renaming , also called
14:51	with borrowing .

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