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## Arithmetic

### Course: Arithmetic > Unit 18

Lesson 5: Intro to adding negative numbers# Adding negative numbers example

Use a number line to add -15 + (-46) + (-29). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- This is probably a really dumb question.. Sigh. Why do some of the numbers, say (-42) have brackets? And how does that effect how the number works in a equation?

@Kitt Hirasaki

So why does, in this video at the start, -15 not have brackets while the others do?(363 votes)- The first negative number does not have brackets because it is easily recognized as a negative number. The following negative numbers DO have brackets to separate the negative sign on the number from the addition/subtraction operand sign in the question.

Although brackets do mean: "do this first" it doesn't apply here because there are no operations within the brackets.

Aboslute value brackets look like this |x-y| not like this (x-y). Please don't confuse them commenters.(150 votes)

- i dont like subtracting an adding negative number s and im not very good at them what is an easy ways to remember how to add and subtract negative numbers?(118 votes)
- Adding:

same sign add, keep the same sign EX: -3 + -2 = -5

opposite sign subtract, bigger number gets the sign EX: -2 + 6 = 4(7 votes)

- How do you add -32 + 4(52 votes)
- When you add a positive number to a negative number example -32 + 4, then you ignore the negative symbol and change the plus into a minus. 32 - 4=28. Then you add the negative sign at the front to get -28. I hope this helps!(100 votes)

- I think that adding these negative numbers is kinda easy but I still dont understand how to do it.

Will someone please help me?!(38 votes)**Remember these rules***Whenever you find two numbers with same sign add and put corresponding symbol(Common symbol)*

*whenever you find nos withot common sign, subract and put greater no.sign.(8 votes)

- if you are adding all negative numbers, can you just add all the numbers together as positives and turn the sum into a negative number?(21 votes)
- Yes, that would work.(15 votes)

- Me seeing the comments from 9 years ago 😀😀😀(13 votes)
- Comments are posted by default with the top ranked ones shown first. If you want to see the more recent comments, change the sort order to "recent".(6 votes)

- “⡍⢎⠵⣉⠶⣉⢆⠣⢆⡱⡘⢦⠱⣘⠦⡑⢎⠴⡁⢎⠴⡡⢆⡳⣜...”

⡍⢎⠵⣉⠶⣉⢆⠣⢆⡱⡘⢦⠱⣘⠦⡑⢎⠴⡁⢎⠴⡡⢆⡳⣜⡸⣴⣯⠶⠿⡼⠧⣿⣼⣧⣽⡮⢧⣷⣜⣦⠵⣨⢒⡔⢦⡘⠴⣈⠆⣍⢢⠱⣌⠲⣌⢢⠱⡌⢆⡱⠌⢦⡑⢎

⡜⢣⢎⡱⢊⠴⡊⡕⢪⠔⡩⢆⠳⣌⠲⣉⢎⢲⡉⣞⣲⣙⣾⡵⠟⠋⢁⠀⢀⠀⠀⢀⢠⡤⠀⠀⠀⠀⠀⠈⠉⠙⠳⠯⣶⣦⡙⣆⠣⢞⡠⣃⠳⣄⠳⡌⢆⠳⡘⠦⡑⡍⢦⡙⢢

⡜⢣⡜⠴⡩⢖⡱⢌⡱⢊⠵⡉⠖⣌⠳⣌⢎⣧⡿⠞⠉⠁⠀⠀⣀⡴⠋⠄⢂⣌⣠⣧⣏⠀⡀⢄⣀⣁⠀⠸⡖⠀⢂⠀⠀⠋⡽⣾⣩⢖⡱⢌⡓⡌⡱⡘⢎⡡⡙⢦⠱⡘⢦⡙⢢

⠜⢣⠘⡥⡑⢎⡰⢃⠼⡡⢎⡹⡘⡔⢫⣼⣟⡏⢀⠀⠄⠈⠀⣴⢏⣤⠶⠚⠉⠁⠀⠀⠈⠗⠋⠉⠀⠈⠙⢿⠟⠓⠲⣬⡁⠀⢰⠉⠻⢾⣵⡮⣔⢣⠱⣉⠦⡑⡍⢆⢣⡙⠆⡍⢆

⢌⠣⡍⢆⡙⢦⡘⡌⢦⡑⢎⠴⡱⣩⢗⣾⡟⠀⠤⠈⠀⣴⠞⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⢧⣀⠂⠀⠹⢯⣿⣧⣇⢎⡱⢜⡘⢢⡑⡎⡜⢢

⢌⠳⡘⠦⣉⠦⢱⡘⠦⡜⣌⠲⢥⣛⡾⡿⠃⠈⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠳⣆⠁⡈⢯⣥⡿⣎⠱⣊⠜⣡⠚⠴⡉⢆

⢌⢣⡑⠣⠜⠬⡡⢎⡱⣘⠤⣛⠼⣭⣿⠃⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⡄⢿⡻⣷⣎⠳⣌⠚⡤⢋⠥⡙⢢

⠌⢦⡉⠧⡙⢆⡱⢊⡕⢢⡙⣬⢻⣽⡇⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡇⢨⣿⡾⡷⠱⣌⠓⣌⠣⢎⡱⢡

⢛⠤⡸⢠⡛⢤⢃⢇⡸⢃⠼⣠⣟⣿⡇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⢻⣿⢣⢇⡘⢧⡘⢧⠘⡄⣃

⠣⡜⢡⠣⡜⢢⠍⢦⠱⣉⠖⣣⣟⣿⢷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣇⢻⣯⣓⠎⡜⢢⡑⢎⡱⡘⠤

⠣⢜⡡⢓⣌⢣⠚⣆⠳⢌⡚⡵⣯⣿⠾⠄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⣿⣣⠏⡜⣡⢚⢢⠱⡘⢥

⢃⠎⡔⢣⠜⣂⠳⡌⢓⡌⢼⡹⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣟⢦⡋⢴⠡⠎⢆⡓⡩⢆

⠌⣎⠱⢌⢎⡔⢣⠜⡢⢍⠲⣝⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣀⡠⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡝⢦⠍⢦⣉⠳⡌⡱⢡⢊

⠜⣠⢋⠜⣢⢌⠣⢎⡱⢎⣽⡾⠿⢿⣇⠀⠀⠀⠀⠀⠀⠀⣡⠔⠊⠁⠀⠀⠀⠀⠙⢦⡀⢀⡤⠒⠊⠉⠉⠑⠢⣄⠀⠛⠎⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⠺⡅⢮⡑⣌⢓⡰⢃⢇⡊

⡘⡔⣩⢊⡔⢪⡑⢎⠶⣩⢾⡇⢠⠤⡌⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣎⠳⡘⢆⡱⢌⠦⢱⡉⢦⡘

⠰⡑⠦⡱⢌⠣⡜⡌⣞⡱⣿⣿⠈⠀⢻⣣⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣠⣧⣄⠀⡾⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣸⠿⣿⡼⣌⢣⡙⢌⡲⡉⢖⡡⠞⠤⣃

⠥⡙⢦⠱⣉⠖⡱⡘⡴⢫⣷⣿⣧⠀⠀⡟⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣇⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣼⡗⠁⣿⡱⢎⡅⡚⢤⢣⢙⢢⡱⢩⠒⡥

⠒⡍⠦⡙⢤⢋⠴⣡⢣⡓⡾⡽⣿⣇⡀⠗⠈⣧⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢠⢾⡎⠀⣸⣿⠱⢣⡘⡱⢊⠦⣉⠦⡑⢣⡙⡰

⠱⡘⢆⡙⢆⡩⢒⠥⢢⠝⣸⢳⣻⢿⣿⣿⣶⣿⣧⠀⠀⠙⠦⣀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡰⠃⣼⠀⣠⣿⢯⡙⢦⠱⣡⢋⠴⢡⠲⣉⠦⡱⢡

⢣⡙⢆⡙⢦⠱⣉⢎⡱⢊⡕⢎⡵⢯⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣤⡤⠤⠖⠋⠀⢀⣞⠀⠀⢇⣠⣿⣟⢮⡑⢎⡱⢂⠭⣊⠥⢣⡑⢎⡱⢡

⠆⡍⢎⡜⢢⠓⡌⢦⡙⢆⡚⢬⣘⢻⣞⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢰⢚⠒⠒⢲⠒⡦⢤⢤⣤⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡽⢦⡙⢢⡑⣍⠲⡡⢎⡱⢌⠎⡔⢣

⢊⡜⢢⠜⣡⢋⡜⢢⡕⢪⠜⡲⢌⣳⢾⣿⣿⣿⣿⣿⣿⣽⣿⣦⣀⠀⠀⠈⠘⢷⣯⣭⣥⣷⣴⠞⠁⠀⠀⠀⢀⣤⣾⣿⣷⣻⣿⣿⣿⣿⣿⡽⢦⠑⣣⠘⡤⢣⡑⢎⡔⣉⠚⡜⠤

⠆⡜⣡⠚⡅⢎⡔⢣⠜⣡⢎⡱⢊⡞⣯⣿⣿⣟⣿⣿⣯⣷⣿⣿⣻⣷⣤⡀⠀⠀⠙⠿⠟⠋⠀⠀⠀⢀⣠⣴⣿⣟⡿⣟⣿⣽⣿⣿⣿⣿⣿⡽⢦⡙⢤⢋⡔⢣⠜⢢⢆⡱⢣⠜⡡

⠱⡘⢤⠓⡜⢢⠜⡡⢞⡰⢢⠜⣣⢽⣳⣿⡿⢾⣿⣿⣿⣿⣟⡾⣷⢯⣟⣿⣷⣶⣤⣤⣤⣤⣤⣶⣾⡿⣟⣯⡷⣿⣽⣻⣟⣿⣿⣿⣿⣿⣿⣝⡣⢜⢢⠣⢜⢢⡙⢆⠎⡔⢣⢎⠱

⢣⠙⢢⡍⡜⢡⡎⢱⠊⡔⢣⡞⣵⣿⣿⣿⣿⣶⣿⣿⣿⢳⣯⣿⡟⠛⠛⠋⠁⠈⠙⣿⣯⣿⣽⣯⣷⣿⢻⣽⢻⣷⣯⣷⡟⣿⣿⣿⣿⣿⢻⣿⣷⠊⣥⠓⡌⡆⢱⠊⡜⡌⢣⡜⢢

⣌⠱⠎⡴⢩⢅⠪⡑⢎⡱⢎⠶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣾⣧⣀⣤⡇⠀⢲⣷⣸⣿⢷⣯⣟⣾⣽⣻⡯⢿⣾⣽⣳⣿⣿⡆⠀⠀⠀⠀⢰⣿⡹⣌⠲⡑⣌⠣⢎⢥⡙⠦⣑⠌

⣄⡋⢖⠡⣃⢎⡱⣉⠦⣑⢎⡿⣹⣿⠛⠛⠛⠛⠛⢛⣿⣿⣿⣾⣟⡿⣿⢷⣿⡿⣟⡿⣯⡿⣾⣽⡟⡉⠀⠠⣤⣽⣿⣻⣿⣿⡇⠀⠐⠀⠀⢈⣿⡳⣌⢣⡑⢦⡙⡌⠦⣌⠣⡜⢨

⢢⡉⢦⡙⡰⢊⠴⡡⠞⡤⢋⡾⡽⣿⣷⣶⣶⣶⣶⣾⣿⣻⣾⣿⣞⣿⡽⣯⣷⢿⣻⣽⡷⣿⣽⣾⡀⣷⣌⣲⣾⣿⢷⣻⣿⣿⣷⣶⣶⣶⣶⣾⣟⡳⣌⠣⡜⡄⢳⢈⠳⣄⠳⣘⠢

⢢⢉⠖⠬⡱⣉⠖⣡⠓⣌⠳⡸⣝⣯⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢾⣽⣻⡷⣿⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⢭⡓⢬⠱⡘⡜⡌⠣⢎⠴⠱⣌⠱

⠢⣍⠚⡴⠱⡌⢎⠥⣋⠔⣣⠱⣎⢷⣻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣷⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣟⢮⣑⢣⢣⠑⢦⣉⠳⣌⠪⡕⣌⠲

⠱⣌⠣⡜⢣⠜⡌⠶⡡⠞⡴⣫⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣎⣧⢊⡝⣂⠖⡱⢌⡓⡸⢄⢣

⡑⢆⠳⢌⢣⠚⣌⠣⣕⢫⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⡜⡤⢋⠴⠣⢜⠡⢎⠆

⠸⣌⠳⣌⠣⡝⣠⠓⣬⢷⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⡰⣉⠎⡱⢊⡱⢊(8 votes) - what's the effect of parenthesis and is it different than brackets?(7 votes)
- Both parentheses and brackets have the same effect at this stage of math. They both say "Do the stuff inside me first". In my experience, most people use a parenthesis for an initial level of priority and brackets for a secondary level, as in:

3 * [4 + (7 - 3) * (5 / 2)]

= 3 * [4 + (4) * (5/2)]

= 3 * [4 + 10]

= 42

Keep in mind that this is by no means a hard and fast rule, and you're free to use them in whichever order you want, or to only use one or the other since the clarity of the problem isn't too affected.(3 votes)

- if you add negatives do you go down all the time? this honestly seems too good to be true:)(2 votes)
- -1 + -1 + -1 + -1 is the same as -1 -1 -1 -1. Both equal -4.

One way to think about it....

You borrowed a dollar from a friend to buy a soda. You now have -1 dollars since you owe him a dollar.

You do the same thing tomorrow, the next day, and the day after that. Each day you borrow another dollar. After four days, you are four dollars in debt: -4(11 votes)

- How do I add -8+3=?(4 votes)
- Think of it like this: Let's say you have lost 8 points in a game (-8) and you win a round and gain 3 points (+3). Now what is your overall score? If you have -8 points and you gain 3, you will have -5 points as your score.

Hope this helps :)(7 votes)

## Video transcript

Find the sum of negative 15 plus
negative 46 plus negative 29. To do this, let's
just first visualize what each of these
numbers look like. So I'm going to draw a
number line for each of them. Negative 15 might look
something like this. So if this is 0 and let's
say that this is negative 15, I could represent
negative 15 as-- if I'd like to-- an arrow that
points from 0 to negative 15. The length of the arrow is
the absolute value of this. It's the distance from 0. So the length here is 15. And the negative says that
we are pointing to the left. So the absolute value is 15. That's the length of that arrow. Let's do the same
thing for negative 46. So once again, let me
draw my number line. 0 is going to be
right over there. And negative 46 is going
to be someplace over here. Negative 46. Notice, same exact idea. The distance between negative
46 and 0-- or another way to think about that is the
absolute value of negative 46-- this distance right over
here is going to be 46. And its direction
is to the left. That is why we get to
the number negative 46. The negative really tells you
whether you're to the left or to the right of 0,
but the absolute value says how far are you to
the left or the right of 0. And then, finally, let's do
the same thing for negative 29. So once again, let me
draw my number line. I want to use the yellow again. So draw my number line. Let's say this is 0. Then negative 29 is going
to be roughly over here. I'm estimating it. And once again, negative 29
is exactly 29 away from 0. So this length right over here
is 29, and it is to the left. That is why it is negative 29. If it was positive 29, it
would be 29 to the right of 0. So we've represented
all of these numbers. And you can see what their
absolute values are like. And now let's think about
what happens if you add them. So one way to think about
adding these numbers is if you added
these arrows, if you put this arrow on
top of this arrow or to the left of this
arrow, if you started where this arrow leaves off-- and
then you put this green arrow, and then you put
the orange arrow. So let's do that. Let's draw that. It's going to be a
longer arrow now. So we're going to start at 0. First, we have the negative 15. So we're going to move
15 spaces to the left to get us to negative 15. Then we're going to go
46 spaces to the left to get us to negative
15 plus negative 46. So let me draw that. So then we're going
to go-- and we're going to figure out what
that number is in a second. So then we're going
to go 46 to the left. That's about that far. Really just this arrow,
I'm now placing it. I'm starting off where
the negative 15 left off, and then I'm putting
that arrow after that. And we don't know yet what
number this gets us to. We're going to have to
do a little math here. And that's actually the
point of this problem. But we know what the
length of this arrow is. The length of this arrow is 46. It is 46 to the
left, and we know the length of this
magenta arrow is 15. And then, finally, we
have this orange arrow. The orange arrow, which we
know has a length of 29. Although, it's 29 to the left. It looks like that. It has a length of 29. So when all is said
and done, where are we? Where do we end up
on our number line? Well, the total length
that we are to the left is going to be 15
plus 46 plus 29. But it's going to
be to the left, so it's going to be negative. So what we can really view
this as, since all of these have the same sign,
is we could say, look, this is the same
thing as the absolute value of negative 15, which is
15, plus the absolute value of negative 46, which is
46, plus the absolute value of negative 29,
which is 29, but then take the negative value of it. So let's just add that. 15 plus 46 plus 29 is equal
to, let's see-- 5 plus 6 is 11. 11 plus 9 is 20. Carry the 2. 2 plus 1 is 3. 3 plus 4 is 7. 7 plus 2 is 9. So you get 90. So this entire
length here is 90. The entire length, if you add
up the arrows, you get a 90. But it is not 90 to the right. So if it was 90 to the right,
these would all be positives. And then we would just
get a positive 90. But this is 90 to the left. So when you add these guys up,
you don't get to positive 90. You get to negative 90. So one way to think about it
is these are all the same sign. So this is going to be
equal to the negative of the absolute
value of negative 15 plus the absolute
value of negative 46 plus the absolute
value of negative 29. And the reason why we're
writing this here-- this might look fancy,
but this is really just the length of
this purple arrow. This absolute value
of negative 46, that's really just the
length of the green arrow. 46. And this is just the
length of the orange arrow. So this is 15 plus 46
plus 29, gave us 90, but it is to the left. So that is why it
is negative 90.