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Studying for a test? Prepare with these 3 lessons on Module 3: Rational numbers.

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# Negative numbers, variables, number line

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.