If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:4:54

Negative numbers, variables, number line

CCSS.Math: ,

Video transcript

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 and 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 are these are false and which of these you can't figure out so let's 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 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 straightforward 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 an yellow so negative that's 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 well 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 see 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 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 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 many 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 be greater than B would have to be to the right of B but we see a so the left of the 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 to the left of zero C is a positive number is to the right of zero but what about negative a well let's 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 take away this looks like a this looks like a negative how can it be large 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 is to the right of C