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Adding integers on the number line
Practice adding positive and negative integers using a number line. Created by Sal Khan.
Video transcript
- [Instructor] So we've
already spent some time introducing ourselves to the idea of adding or subtracting
positive and negative numbers, and what I now want to do in this video is do a bunch of examples using
the adding negative numbers on the number line
exercise on Khan Academy so that we can think about
different ways to model or think about or visualize
adding and subtracting positive and negative numbers. So this question asks us,
which number line model represents the expression
negative two plus negative seven? And a number line model seems
like this really fancy thing, but they're just saying,
well, which of these diagrams, which of these drawings,
are a way to think about what negative two plus negative seven is? So let's think about it. I wanna start at negative two, and then to that, I
wanna add negative seven. So let's see what's going on here. So this number line model,
I guess we could call it, it's starting, this is
positive two right over here, it is to the right of zero,
and then it subtracts seven. So this is the model that
would be for positive two plus negative seven, or
positive two minus seven, but that's not what we have over here. We have negative two minus seven. This one right over here,
let's see, this first, I guess you could say
this line, this arrow, it's going one, two, three,
four five, to the left of zero. so starting at negative
five, and then it goes another one, two, three,
four to the left of that. So you could view this as
negative five minus four, or you could view this as
negative five plus negative four, but that's not what we have up here. And then this last one,
hopefully, this is the answer, otherwise, there'd be a
mistake in the exercise. Let's see, we have this first
arrow that takes us two steps to the left of zero, so one,
two, so this is negative two, and then we take another seven
steps to the left of that, so one, two, three,
four, five, six, seven. So you can think of this arrow
as representing negative two, and then we're going to add to that, so we're starting from
this tip of this arrow, we're gonna add a negative seven, which makes us move
seven to the left again to get to negative nine, so
that's definitely the model that represents that expression. Let's keep going. All right. Which number line model
represents the expression six plus negative two? So here, they've taken our number lines, but they've made them go up and down. They've made them vertical. So one way to think about it. I wanna start at six and then
I wanna add negative two, so on a vertical number line like this, and it seems like we're
increasing as we go up, I wanna start at six above zero. So I wanna start at six above zero, but then I want to add negative two, which should take me two steps back down. This one takes me two steps even higher. So this one right over here
is positive six plus two or positive six plus positive two. This one over here, we're
starting at positive four, and then we're adding two, so that's not what we're talking about. This one over here, this
big arrow, this tall arrow, this is going, it's pointing up. It gets us to positive six. The tip of the arrow is
right at positive six, but then we go back down two, so this would be positive
six plus negative two. You could think of this arrow
as representing positive six, and then this arrow is
representing negative two. It takes us two down. So if you take positive
six plus negative two, you do the positive six, and then for the tip of your arrow, from there, you could
start the negative two, and you go two back down
and you end up at four, so it's definitely that
one right over there.