How To Add Integers Of The same and opposite signs
8 views
Feb 19, 2025
In section 2.1, we were introduced to integers. Now, as we move into section 2.2, we will explore how to add two integers with both the same and opposite signs, followed by a discussion on adding more than two integers with varying signs. Chapters: 00:00 Introduction 00:43 How to use the number line to add negative numbers 02:43 Rule for adding integers of the same sign 03:13 Examples of adding integers of the same sign 04:41 How to use the number line to add integers of opposite signs 07:52 Rule for adding integers of opposite signs 08:43 Examples of adding integers of opposite signs 14:09 How to add multiple integers of opposite and the same signs
View Video Transcript
0:00
so we talked about integers and you know
0:03
what they are we talked about whole
0:04
numbers we talked about integers
0:08
yes so now we're going to learn how to
0:11
add integers again we getting down to
0:14
like serious business now and I can
0:16
guarantee you a lot of people do not
0:18
like negative
0:21
numbers they get they SC they free
0:23
sometimes cuz it's always it's a
0:25
negative number I don't know what I'm
0:26
doing but I guarantee you if you stick
0:28
to what I'm teaching you morning you
0:30
going to be all right okay so keep in
0:33
open mind and and then we're going to
0:35
learn how to do this so now the first
0:36
thing we're going to learn how to do is
0:38
we're going to learn how to use the
0:40
number line to add negative number right
0:44
now right after before I even go into
0:46
this what is1 +5 does anybody know
0:49
what's 1 + 5 yeah6 -6 so who's
0:52
comfortable with negative numbers here
0:55
you are most of you guys are comfortable
0:56
still shaky all right so now we're going
0:59
to learn how to do that using the number
1:00
line right and now I'm going to teach
1:02
you a rule here right so if I want to
1:05
add -1
1:07
+5 right so here's what I'm going to do
1:10
here first if I want to use the number
1:13
line to understand what is going on -1
1:15
is behind zero correct and we all agree
1:18
on it right so if I'm here this is1 this
1:22
Gap here represent -1 okay now if I want
1:26
to
1:26
add5 from1 I'm going to go how many
1:29
steps to the left five five so if I
1:33
start here I'm going to go one 2 3 4
1:36
five where did that L at -6 right so -1
1:41
+5 is -6 now one of the things that I
1:44
tell students is this let's say you
1:49
owe a dollar in your bank account right
1:52
you owe your bank account you owe $1
1:54
what does that mean in terms of are you
1:57
yet you can pay it off really easily
1:59
well you ow $1 goad you can pay it off
2:01
EAS but you owe $1 that mean you $1 what
2:04
negative right and then you go out and
2:07
you are being irresponsible you spend
2:09
another $5 right you owe one and you
2:12
spend another
2:13
five now how much money do you
2:16
ow six are you positive or negative
2:20
negative right so you're negative cuz
2:23
now you owe $6 so this is how you
2:26
understand how to add negative numbers
2:28
when you owe something it's
2:30
right so1 + is equal to
2:36
what what -6 right 1 + 5 is -6 okay so
2:42
the rule is this when adding numbers of
2:46
the same sign the rule is add them up
2:51
and then keep the sign does that make
2:53
sense when adding numbers of the same
2:56
sign add them up and keep the sign
3:01
does that make sense yes sign like
3:02
negative or positive mhm right sign like
3:06
negative or positive for
3:08
example if you have to apply this rule
3:11
here again if the the bank account step
3:13
helps you that use that I should wait to
3:15
learn so what is -6 + -7
3:18
kiny H what is -6
3:24
+7
3:26
13-3 right -3 because these two numbers
3:30
are negatives I'm adding them so
3:32
according to the rule when you add
3:34
numbers of the same sign because they
3:37
are both negative you add them up and
3:38
you keep the sign does that make sense
3:40
right so basically this is saying I owe
3:43
$6 and I spend another $7 because I'm
3:46
being irresponsible now I owe how much
3:48
money $13 and your mom is going to be
3:50
mad because you went around spend the
3:52
money that you don't have right so the
3:55
same thing here what is -10 + -2 uh V
4:02
-12 right -12 all right and then what
4:06
is4 +
4:10
-6 -1 right so we are getting careful
4:13
with these numbers this is a pretty easy
4:14
step okay so again the rule is this when
4:19
you add numbers at the same sign you
4:21
always want to add them up and just skip
4:22
the sign like 4 + 5 is
4:25
9 5 + 2 is 7 9 + 9 is-8 because you just
4:31
add them up and then keep the sign all
4:33
right so and if this V concept helps you
4:36
please use that right now second we're
4:40
going to learn how to add numbers of
4:43
opposite signs okay opposite means you
4:46
have a positive and a negative right now
4:50
how do you add those so what if I have 6
4:52
+ -4 what does that give
4:55
me yeah two two right 6+ 4 is two why
5:01
how do we get that so if you use the
5:02
number line again right let's use the
5:04
number line and we're going to use the
5:05
bank account uh thing here so six is
5:08
what six unit from what zero right and
5:12
if I add4 am I going right or
5:15
left left left right if I'm here six is
5:18
here if I add4 to 6 I'm going 1 2 3 4
5:23
and I land where at two so 6 +4 is two
5:29
correct
5:30
same way let's say you have $6 in your
5:32
bank account right and then you went in
5:36
Spain $4 yes I like to think of it like
5:40
I have six holes and they're all they're
5:43
all or like four hole I have six holes
5:47
or actually no four holes sorry four
5:49
holes and they're all negative holes and
5:51
I fill them up with the Positive dirt
5:53
that's right you can do that anywh you
5:56
can come up with something that can kind
5:57
of help you right I like to use the bank
5:59
account because I know everybody likes
6:01
money anybody here doesn't like money
6:03
you don't what anybody here doesn't like
6:06
money you
6:08
don't you don't like money you give me
6:11
all your money then I'll take all your
6:12
money yeah all right we all like money
6:15
right we don't love it but we like it
6:17
because you need money you like money
6:19
don't you Bill right
6:22
so so 6 plus4 is basically saying give
6:26
me my money oh my God stop yay
6:30
y right so you have
6:32
$6 in your bank account and you went and
6:36
add -4 so basically if you spend four
6:39
now you're left with two right now this
6:41
can go either way all right everybody
6:44
say hi to me S
6:47
Glo
6:50
sorry all right so now we're going to go
6:52
the other way right and we're going to
6:54
come up with a rule so now let's say I
6:57
want to add I want to do
7:00
four right
7:02
plus
7:04
-7 if you think in terms of holes like
7:07
you say she says right you have seven
7:09
holes and you fill them up with four a
7:12
lot of dirt right you put dirt in that
7:13
so now how many holes do you have three
7:16
three so negative3 right or if you want
7:19
to think in terms of bank account you
7:21
have
7:23
$4 right and then you went and spend how
7:26
much money seven right four plus7 and
7:30
you went and spend $7 now how much do
7:33
you owe are you positive or negative
7:35
negative negative now you ow $3 so this
7:38
is how you have you need to think in
7:39
terms of like positive and negative
7:42
right so 3 +5 will give you what then
7:46
obviously negative do right -2 so and
7:51
the rule is this the rule is when adding
7:55
numbers of opposite signs subtract them
7:59
and keep the sign of the higher number
8:02
does that make sense right when adding
8:05
numbers of opposite signs always
8:07
subtract them and then keep the sign of
8:10
the higher number example 4
8:14
+3
8:19
G 4
8:24
+3 how
8:27
is7 what's the rule when adding numbers
8:31
of opposite signs always do
8:33
what it's one you subtract them you keep
8:36
the sign of the higher number right
8:39
think can to the back
8:41
account Caleb what's 10 +
8:49
-77 right and then Danielle was 6
8:57
+9 six
9:00
9
9:02
think when adding numbers of opposite
9:05
signs always subtract them and then keep
9:08
the sign of the higher
9:11
number no always subtract
9:16
them what is it
9:20
three3
9:22
there3 right you see it it's not very
9:26
obvious this can be confusing cuz a lot
9:28
of time we look we go wo we're just so
9:30
used to like adding positive numbers
9:32
that when we come to negative and
9:33
positive we can kind of get hung up on
9:35
that so we need to spend a lot of extra
9:37
time practicing these okay so what I'm
9:40
do what I'm going to do is I'm going to
9:41
give you a bunch of stuff to work
9:43
on oh my gosh that sounds so fun it is
9:47
fun isn't
9:48
[Music]
9:51
it all right so let's start I don't
9:53
understand why you like math no hate I'm
9:55
just in there I don't know how I like
9:57
math like it's easy but it's not fun
10:00
have so many
10:07
my is that any
10:09
[Music]
10:15
subject I'm so good at solving my
10:18
problems uh last year with Ethan Wilson
10:22
I just kidding it was a
10:25
[Music]
10:26
joke for real though in the past all
10:30
right I'm going call on I'm going call
10:32
on everyone here so who has to say
10:34
something here I think uh yes uh I -10
10:41
+99 19 I want it to become second nature
10:44
right um Emily -3
10:50
+1 8 you're not helping that doesn't
10:55
help by giving answers to your classmate
10:58
you're not helping all right uh uh Nora
11:02
5 +
11:06
-2 three all
11:09
right Kinsley -7 +
11:14
6
11:16
11 11 11 are we positive on that no but
11:22
yeah it was wrong what is
11:25
it 111 right I meant to say negative all
11:29
right um Dexter -2 + 20 + -2 -22 -22 all
11:39
[Music]
11:52
right1 mhm
12:00
8
12:07
+1 what is
12:10
it
12:13
think negative what all right -2 um what
12:18
the oh
12:19
alen -7 +
12:26
-74 thank you Danielle
12:30
uh 10 +
12:38
-10 zero not negatives right
12:42
Z it could
12:45
[Music]
12:46
be negative Z could mean you don't owe
12:49
money and positive Z could mean you
12:51
don't money either ki9
12:58
+7 of course I've always been
13:03
broke 16 thank you years
13:10
AG 3
13:12
+
13:24
1577 uh
13:27
Vicki yeah
13:29
20 +
13:35
1 19 all
13:37
right
13:39
a
13:41
20 +
13:46
-21 1
13:48
Kaleb yes
13:51
-6
13:53
plus um
13:56
30 36 36 all right so we are comfortable
14:00
now right so I'm assuming we are
14:02
comfortable so now we're going to move
14:03
up and we're going to talk about adding
14:05
more than just two integers now I have
14:08
three integers okay so we got to keep
14:10
moving cuz we can't we have some
14:12
deadline here so we got to we got to
14:14
keep moving how much time do we have so
14:17
now we're going to talk about adding
14:18
more than just two integers right so we
14:20
going to come up with some techniques to
14:22
do that so let's say I have -6 + -15 + 9
14:30
and I have um
14:33
7 + -1
14:37
+
14:39
26 + -3 right so now how do we do this
14:43
here now we have not just two integers
14:47
now we have three integers so I want you
14:49
all to work on that independently and
14:51
then you tell me what you got so now we
14:53
have
14:55
-6 +15 + 9
14:59
[Music]
15:06
and then we have 7 +1 + 26 +
15:13
-13 I can't see the board sorry
15:39
got
15:42
it probably
15:50
not you got first one
16:03
than
16:09
yeah tell me how you get
16:19
this back to
16:24
the got 30 21
16:30
look what is
16:33
that
16:34
plus so what
17:07
[Music]
17:11
add
17:22
that's all right let's try and work on
17:24
this one here right I -6 + -15
17:29
+ 9 right we going to do them we going
17:33
to go step by step everybody got -6 +5
17:37
is equal to
17:39
what - 21 right and now we have - 21 we
17:44
going to bring this down + 9 right again
17:48
going back to the rule one of them is
17:50
positive one of them is negative so
17:53
automatically I have to do what subtract
17:55
them right and then I keep the sign of
17:58
with the higher number or assume this
18:01
you have 21 holes and you fill up nine
18:04
holes how many more holes you have to
18:05
fill up 12 right so you have to be -12
18:10
because you still have 12 holes or this
18:12
is -12 all right so we need to spend
18:15
more time on this section yeah are you
18:17
the calculators no now I need you to get
18:22
this without a calculator this is going
18:23
to be no calculators because I need you
18:25
to understand the concept all right did
18:27
you get the -12 good all right I got
18:30
that next one we have 7 + -1 + 26 + -3
18:37
we going to do them two by two right
18:39
what 7
18:41
+1 six right you have seven you have a
18:45
lot of dirt and you add only one hole to
18:47
one hole you still have what six more
18:50
bag of dirt left or whatever if you want
18:52
to use that analogy I like to the whole
18:54
Stu I really like that right six now we
18:57
have 26 we have 13
19:01
holes how many more holes do I have to
19:03
fill up oh do have yeah I thought that
19:05
was3 yeah that's yeah3 yeah 26 and you
19:10
13 hold right 26 +3 what is
19:14
[Applause]
19:15
it 26
19:21
+3 13 right 13 and then 6 + 13 is what
19:28
19
19:29
right good so we need to spend time on
19:33
these section because this is not that
19:35
evident right we got to spend more time
19:38
understanding these things yes but what
19:39
about the other time we did negatives
19:41
and positives the charts say it again
19:43
the
19:46
charts the chart yeah which chart one I
19:52
don't oh no that's different that's
19:54
that's for
19:55
multiplication yeah so let me give you
19:57
more a couple more things to work one
19:58
because I think we need to spend a lot
20:00
of time in this
20:03
section because this is this is really
20:06
like essential to understanding the rest
20:09
of the stuff we going to do equations
20:12
and they require
20:14
more and that all right and then I also
20:18
want you to
20:19
do 11 + -2 +
20:24
-10 and then
20:27
-5 + 4 +
20:31
-5 plus go ahead and do
20:34
this right we have 4 + -2 +7 yeah do we
20:41
um add the ones in the parentheses
20:44
together you can go from left to right
20:46
there's many ways to do this you can go
20:49
this two first and then whatever you get
20:51
here add it to this or you can do this
20:53
two first and then add it to that one so
20:55
it's really because remember addition is
20:58
what
20:59
what's the r the property commun right
21:01
so we can do either way
21:04
yep
21:06
yeah yeah in the meantime work on the
21:09
Stu right 4 + -2 + -7
21:34
all right I stop the video here we don't
21:36
really need this anymore