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### Course: 6th grade (Illustrative Mathematics) > Unit 7

Lesson 8: Extra practice: Negative numbers# Negative numbers, variables, number line

Given a, b, and c shown on the number line, Sal determines if statements like -b < c are true.

## Want to join the conversation?

- who invented math exactly??(10 votes)
- People to answer this question can not be 100% certain that they are correct. It goes back MILLIONS of years(14 votes)

- Normally, to the left of the zero are negative numbers and to the right of the zero are positive numbers in number line, now how a negative number can be to the right of the zero. !(13 votes)
- I am a bit confused to your question but a negative number can never be to the right of the zero.(0 votes)

- I am confused on this whole lesson.(5 votes)
- Can you make a video just like this but with numbers? For me it was kind of confusing with the letters. Thank you!(4 votes)
- The letters are variables, meaning numbers in disguise, so to say. They can have ever changing values.(0 votes)

- i do not understand werent negative no.s to the left of zero?(2 votes)
- so -a is the opposite of +a, and if the +a was on the left of the number line, then -a will on the right of the nuber line?(2 votes)
- Yes, -a is on the other side of 0(0 votes)

- This could be explained better. It does not address the natural confusion that arises of why letters are numbers and why items to the left of zero are not negative.(1 vote)
- The letters are called "variables." These variables are usually used as a substitute for an unknown number. Items to the left of zero are negative. For example, b could be representing -1. But, when it asks for negative b, then my example's negative b would be --1. --1 then becomes +1 or just 1 since the two negatives cancel out. Let me know if this is still hard to understand!(3 votes)

- Normally, to the left of the zero are negative numbers and to the right of the zero are positive numbers in number line, now how a negative number can be to the right of the zero. !(2 votes)
- shouldend we already know that negatives are less than positives and so -A is less than B we should know that when we first see that at least smart people should know right?(2 votes)
- Well, no, look at my reply to your other commment.(0 votes)

- a, b, and c aren't numbers. Or is he just saying that because they stand for numbers?(0 votes)
- Yes, they stand for numbers. That's the concept of a variable :)(7 votes)

## Video transcript

- [Voiceover] So we
have a number line here with zero at the center and
then on that number line we've marked off some numbers. So, to the left of the number line we have the number a, and then we have the number b here, a little bit closer to zero, and then on the right side of zero we have the number c. And then after that, we have a bunch of statements dealing with inequalities. Now, what I want you to
do is pause the video and think about which of
these statements are true, which of these statements are false, and maybe which of these
statements you don't have enough information to figure out. So, I'm assuming you've had a go at it. You've tried to figure out
which of these are true, which of these are
false, and which of these you can't figure out. So, let's do them together. So, this first statement says negative b is less than negative c. So, we do know for a fact
that b is less than c. We know that b is less than c. How do we know that? Well, b is to the left
of c on the number line. It's that straight forward. So, we know this. This is definitely true. But what about negative b? Is negative b less than negative c? So, let's think about where negative b is on this number line. So, negative b I will do in yellow. So, negative, negative b
means the opposite of b. So if b is one hash mark
to the left of zero, negative b is going to be one hash mark to the right of zero. So, that right over there,
is going to be negative b. And now, where is negative c? Once again, negative
c, this literally means the opposite of c. C is one, two, three, four, five hash marks to the right of zero. And so negative c is going to be one, two, three, four, five hash marks to the left of zero. And actually, let me do
this in a different color. So, negative c I will do in purple. This right over here is negative c. So, let's compare, is negative
b less than negative c? No, negative b is to the right of negative c on the number line. Negative b is greater than negative c. So, this is not true. Negative b is to the right of negative c. Negative b is greater than negative c. And if this is a little
confusing, just think about it. Since b is a negative number, negative b is going to
be a positive number. And since c is a positive number, negative c is going to
be a negative number. So, it makes complete sense
that a positive number is going to be greater
than a negative number. And you see it here,
negative b is to the right of negative c on the number line. So, we can rule this one out. So the next question, is
negative b greater than zero? Well, we already plotted negative b, it's going to be one to the right, or one hash mark to the right, we don't know how much each
of these hash marks represent, but it's going to be to the right of zero. So, it is greater than zero. This is true. That is true. All right, now is a greater than b? Well, let's look at it. A is to the left of b on the number line. A is more negative than b. So, a is less than b, not greater than b. So, this is not going to be the case. In order for something to be greater than something else, it would have
to be to the right of it. For a to the greater than b, it would have to be to the right of b. But we see, a is to the left of b. A is less than b. All right, one more to think about. Negative a is greater than c. So, we know that a isn't greater than c, a is to the left of c. A is a negative number,
it's to the left of zero, c is a positive number,
it's to the right of zero. But what about negative a? Well, let's draw that. Let me do this in a color
that I haven't used yet. Negative a, where would that be? Well a is one, two, three, four, five, six hash marks to the left of zero. And so negative a is going to be six hash marks to the right of zero. So, let's count that. One, two, three, four, five, six. So, negative a is going
to be right over there. And notice, negative a
is to the right of c, so negative a is greater than c. This is true. And if you get confused, if you say, wait, this looks like a negative, how can it be larger than a positive? Remember, negative a itself
is a negative number. And a itself is six
hash marks to the left. So if you take the opposite of that, you're going to get a positive number. You're going to get six
hash marks to the right. And c, which was already
a positive number, is only five hash marks to the right. And so, negative a, this is
going to be a positive number, and it's going to be greater than c. It's to the right of c.