Number opposites

what I want to do in this video is think about what it means to have an opposite of a number so let me draw a number line here so let's draw a number line now let's put some numbers on this number line so we can start at 0 and if we go to the right we have positive numbers 1 2 3 4 5 as we go to the left we get more and more negative so negative 1 negative 2 negative 3 negative 4 and I could keep going on and on and on so let's pick one of these numbers let's say that we pick the number 3 what is going to be the opposite of the number 3 well the opposite of the number is a number that's the same distance from 0 but on the other side so 3 is 3 to the right of 0 1 2 3 so its opposite is going to be 3 to the left of 0 1 2 3 so the opposite of 3 is negative 3 let me make a little table here so if we have the number the number and then we have its opposite we have its opposite so we just figured out that if you have the number 3 its opposite is going to be negative 3 now what if your number is negative what if your number let's say the number negative 4 what's the opposite of that and I encourage you to pause the video and try to think about it on your own well you say okay negative 4 is right over here that's negative 4 it is 4 to the left of 0 1 2 3 4 to the left of 0 so its opposite is going to be 4 to the right of it so 1 2 3 4 it's going to be positive it's going to be positive 4 and so you're probably starting to see a pattern here the opposite of a number is going to be the opposite sign of that number if you had if you have a positive three here its opposite is going to be negative three if you start with negative four its opposite is going to be positive four so one way to think about it it's going to it's going to have the same absolute value but have a different sign or another way to think about it is however if this is three to the right of zero its opposites going to be three to the left of zero or if the number is four to the left of zero its opposite is going to be four to the right of zero so let's do one last one what is the opposite of what's going to be the opposite of of one well one is one to the right of zero so its opposite is going to be one to the left of zero or negative one or another way to think about it one is positive so it's opposite is we're going to change the sign instead of being positive it's going to be negative it's going to be negative one either way that you could think about it