# Adding/subtracting negative numbers | Pre-Algebra | Khan Academy

Welcome to the presentation

on adding and subtracting negative numbers. So let’s get started. So what is a negative

number, first of all? Well, let me draw

a number line. Well it’s not much of a

line but I think you’ll get the picture. So we’re used to the positive

numbers, so if that’s 0, you have 1, you have 2, you have 3,

you have 4, and you keep going. And if I were to say what’s 2

plus 2, you’d start at 2 and then you’d add 2 and

you’d get to 4. I mean most of us

it’s second nature. But if you actually drew

it on a number line you’d say 2 plus 2 is 4. And if I asked you what’s

2 minus 1 or let’s say what’s 3 minus 2? If you start at 3 and

you subtracted 2, you would end up at 1. That’s 2 plus 2 is equal to 4

and 3 minus 2 is equal to 1. And this is a joke for you. Now what if I were to

say what is 1 minus 3? Huh. Well, it’s the same thing. You start at 1 and we’re going

to go 1 — well, now we’re going to go below 0 —

what happens below 0? Well then you start going

to the negative numbers. Negative 1, negative 2,

negative 3, and so on. So if I start at 1 right here,

so 1 minus 3, so I go 1, 2, 3, I end up at negative 2. So 1 minus 3 is equal

to negative 2. This is something that you’re

probably already doing in your everyday life. If I were to tell you that boy,

it’s very cold today, it’s 1 degree, but tomorrow it’s going

to be 3 degrees colder, you might already know intuitively,

well then we’re going to be at a temperature of

negative 2 degrees. So that’s all a

negative number means. And just remember when a

negative number is big, so like negative 50, that’s actually

colder than negative 20, right? So a negative 50 is actually

even a smaller number than negative 20 because it’s even

further to the left of negative 20. That’s just something you’ll

get an intuitive feel for. Sometimes when you start you

feel like oh, 50’s a bigger number than 20, but it’s a

negative 50 as opposed to a positive 50. So let’s do some problems, and

I’m going to keep using the number line because I

think it’s useful. So let’s do the

problem 5 minus 12. I think you already might

have an intuition of what this equals. But let me draw a

line, 5 minus 12. So let me start with minus 10,

minus 9, minus 8 –I think I’m going to run out of space —

minus 7, minus 6, minus 5 — I should have this pre-drawn —

minus 4, minus 3, minus 2, minus 1, 0, 1, 2, 3, 4,

I’ll put 5 right here. 5 minus 12. So if we start at 5 — let me

use a different color — we start at 5 right here and we’re

going to go to the left 12 because we’re subtracting 12. So then we go 1, 2, 3, 4,

5, 6, 7, 8, 9, 10, 11, 12. Negative 7. That’s pretty interesting. Because it also happens

to be that 12 minus 5 is equal to positive 7. So, I want you to think a

little bit about why that is. Why the difference between 12

and 5 is 7, and the difference between — well, I

guess it’s either way. Because in this situation we’re

also saying that the difference between 5 and 12 is negative 7,

but the numbers are that far apart, but now we’re starting

with the lower number. I think that last sentence just

completely confused you, but we’ll keep moving forward. We just said 5 minus 12

is equal to minus 7. Let’s do another one. What’s negative 3

plus 5 equals what? Well, let’s use the

same number line. Let’s go to negative 3 plus 5. So we’re going to

go to the right 5. 1, 2, 3, 4, 5. It’s a 2. It equals 2. So negative 3 plus

5 is equal to 2. That’s interesting because 5

minus 3 is also equal to 2. Well, it turns out that 5 minus

3 is the same thing, it’s just another way of writing 5

plus negative 3 or negative 3 plus 5. A general, easy way to always

do negative numbers is it’s just like regular subtraction

and addition and subtraction, but now when we subtract we

can go to the left below 0. Let’s do another one. So what happens when you get

let’s say 2 minus minus 3? Well, if you think about how

it should work out I think this will make sense. But it turns out that the

negative number, the negative signs actually cancel out. So this is the same thing

as 2 plus plus 3, and that just equals 5. Another way you could say is —

let’s do another one — what is negative 7 minus minus 2? Well that’s the same thing

as negative 7 plus 2. And remember, so we’re doing to

start at negative 7 and we’re going to move two to the right. So if we move one to the right

we go to negative 6, and then we move two to the right

we get negative 5. That makes sense because

negative 7 plus 2, that’s the same thing as 2 minus 7. If it’s 2 degrees and it gets 7

degrees colder, it’s minus 5. Let’s do a bunch of these. I think the more you do the

more practice you have, and the modules explain it pretty well,

probably better than I do. So let’s just do a

ton of problems. So if I said

negative 7 minus 3. Well, now we’re going

to go three to the left of negative 7. We’re going to get 3 less

than negative 7 so that’s negative 10, right? That makes sense, because if we

had positive 7 plus 3 we’re at 7 to the right of 0 and we’re

going to go three more to the right of 0 and we

get positive 10. So for 7 to the left of 0 and

go three more to the left we’re going to get negative 10. Let’s do a bunch more. I know I’m probably confusing

you, but practice is what’s going to really help us. So say 3 minus minus 3, well,

these negatives cancel out so that just equals 6. What’s 3 minus 3? Well, that’s easy

that’s just 0. What’s minus 3 minus 3? Well now we’re going to get

three less than minus 3, well that’s minus is 6. What’s minus 3 minus minus 3? Interesting. Well, the minuses cancel out

so you get minus 3 plus 3. Well, if we start three to the

left of 0 and we move three to the right we end up at 0 again. So that makes sense, right? Let me do that again. Minus 3 minus minus 3. Anything minus itself

should equal 0, right? That’s why that equals 0. And that’s why it makes sense

that those two negatives cancel out and that’s

the same thing as this. Let’s do a bunch more. Let’s do 12 minus 13. That’s pretty easy. Well, 12 minus 12 is 0, so

12 minus 13 is negative 1 because we’re going to

go one the left of 0. Let’s do 8 minus 5. Well, this one is just a

normal problem, that’s 3. What’s 5 minus 8? Well, we’re going to go all the

way to 0 and then 3 more to the left of zero, so it’s minus 3. I could draw a

number line here. If this is 0 this is 5, and now

we’re going to go to left 8, then we end up and negative 3. You could do that

for all of these. That actually might

be a good exercise. I think this will give you good

introduction and I recommend that you just do the modules

because the modules actually, especially if you do the hints,

it has a pretty nice graphic that’s a lot nicer than

anything I could draw on this chalkboard. So try that out and I’m going

to try to record some more modules that hopefully won’t

confuse you as badly. You could also attend the

seminar on adding and subtracting negative numbers. I hope you have fun. Bye.

Thank you so much. THIS helped a lot on my quiz

Just realized why this is in 240p lol it was posted in 2006

11 years later and this still helps me. Thank you!

OMFGGFGGGG I LOVEE UUUUUUU legit im soobadd a mathss thas its difficult for Me who ever teaches!M i GOT THISSSSSS XXX

I'm never going to be friends with math

But it's understandable

This guy's breathing in the introduction is soooooooooooooo loud…

me 2017

This really helped me to make the click. Thanks 🤓

I would like you guys to do more double digit problems with this adding and subtracting integers. Also like my math teacher has thrown in using like sets of three or four integers in one problem, i need examples of those too!😩

This vidoe posted 10 years ago i was 11 years old. how old am i now ?

Now I get my homework "yeah" 😁😁😁

I was three when this was posted

ur voice is anoying

"The more you do the more practice you have." – Khan Guy 2006

clap clap clap clap clap! 🙂

Who's here in 2017

Ok, I am confused when you say MINUS vs negative because I am thinking that MINUS means what application we are to do. Like, neg 3 minus 3. If you say 3 minus neg 3, then say that those are both SAME SIGNS to be canceled out, then apparently the 3’s are being added to equal 6. Should it have been written -3 MINUS -3= ? Or the way you had it? 3 Minus -3=? Sorry if this is a stupid question cuz I suck at math so…

I hate it when u study this in yr 3 and u forget it in yr 7.

helpful thx

uuuuugh ill never get this!

6th grade sucks!

im not saying that every other grade doesnt

Lol I was freaking 1 when they posted this

its monday my dooooooooooooooooooooood

But subtracting and adding negative large numbers aint easy with the number line 🙁

The smartest way to add and subtract relative numbers https://youtu.be/oO-K-tKw0WI

omg this video has my age*-*

He speaks to fast

He speaks to fast

I realized this was published in 2006. Yay that was the year I was born.

who here in 2018

I have feelings for this man.

This was posted when I was.. Actually I wasnt even 1 year old yet! I have an exam tomorrow, this better help me! (Ill try to come back and tell you the results asap)

Who's here watching in 2018

This was the year i was born, 2006!! Im 11

Who’s here 2018

i still don't understand how to subtract negative numbers from positive numbers.

I didn't now how to do this?

When ur adding or subtracting numbers a easy way to do it is to cover up the signs for a second, take the bigger number minus the smaller number, and then use the sign of the bigger number. For example: -5 + 8 =__. 8-5= 3. The bigger number is positive therefore -5 + 8 = 3. This also works when subtracting (unless the sign is the same)

lol try whotching this whith the resolution at 144p

Made when i was born

2 plus 2 is 4 minus 1 thats 3 quick maths

I wasn't even born when they posted this

Now im smarft

Wow I was 1 years old when you posted this video I feel so embarrassed

danngg dis iz old

How did 3-(-3) became 6?

omg this video is older than me

Good

if you count to the negative direction of the negative direction on the number line you count to the positive direction.

if you're not(not 3) what are you? you're 3.

not going to lie, took me a bit. lol

B.E.D.M.A.S is not true this is a bracket [ this is a parentheses (

i got confused at the crossing out but we good now it makes sense thank you teacher lol

It's 2018 when I'm writing this. I notice that there are several comments about how old this video is. I guess it was made about 12 years ago. Hopefully, some day someone will write that this video was made 500 years ago.

2018

Not good at teaching negative numbers

lol This video is -1 year older than mee

hehe math jokes

Danm, thanks so much for clearly explaining this, I’m consistently forgetting these rules but I know this time time it’s really gonna stick with me.😊😊👍🏻👍🏻👍🏻🥊🔥ima ace that test tmrw

I am Japan I like it

thank you

uploaded the day i was born xD

I was 0 so old

My math teacher told me to watch this video.

I needed a video to help me KHAN ACADEMY YOU ARE THE REASON I HAVE A GOOD MATH GRADE

i am doing this in school and its fun 🙂

I searched this up for my homework because I was having a little bit of trouble and this helped so much !

good video

Im on college and still struggle with negative numbers

good

I'm asian

Anyone from 2018?

Im pretty sure this guy has so many veiws due to the fact that many mindless students who didn't pay attention in class.

Lesson learned

"When you have a learning channel spot out for kids who dont pay attention". ~Simply

this was published when i was born

Wow! Math = this vid only has 1 pixel!

This help me with my math so much thanks dude!!

very boring. his voice sounds like he is really disinterested

Thx I really needed the help u keep doing what you do best just wanted to say thx bro

240p quality lol

Anyone in 2019?

2019?

144p lol

the way he goes like "I hope you have.Bye …." this teacher is GENIUS WITH PPL!!!!!!!!!

Oh YeAh YeAh

This is exactly why, some people never reach high levels in math.

lol

You didn’t do any adding

Sub to me!

Thnx for helping me I understand it now

Whoa 2006!? Geez good old days

This guy doesn’t use Fahrenheit

y

ok but why is subtracting a negative number the same as adding a positive? i get how it works with adding because you can put the numbers either way around when adding but you can't do that when subtracting

This is the only video that made the most sense

went to subscribe when I realised i already was! slap that thumb if this has happened to you! (pls slap it anyway :')

Yooo i was looking for a video like this and i ended up on this 11 yr-old video

This video is older than me lol

How do you do it with larger numbers?

Why is there 2 subtraction sighs there is supposed to be one

it really helps me to learn

Bruh this was made 2 days after I was born

anyone 2019?

wow bro you a legend

Still doesn't explain the concept behind WHYa negative minus a negative equals a positive. Many mathematics majors I've been tutored by still cannot adequately explain the concept behind it.