Identify and order absolute values

we're told to list an order from smallest to largest so each of these quantities it looks like we have expressions inside of absolute value signs and just as a bit of review absolute value just means your distance from zero or another way to think about it is if you're it's a negative number inside of the absolute value sign it becomes positive if it's already positive it stays positive so let's think about these numbers so the first one is the absolute value of five the absolute value of five how far is five away from zero well it's five away from zero so it's equal to five so if I were to actually draw a number line you would see that zero is here five is over here this distance right there is five so the absolute value five is five now the next quantity they want to do what they want us to figure out is the absolute value absolute value of nine minus seven well this is the same thing as the absolute value of two nine minus seven is two and once again two is just two units away from zero so it's just two if you have a positive value in the absolute value sign it just is itself the absolute value of 2 is 2 then we have the absolute value of 5 minus 15 absolute value of 5 minus 15 well that's going to be the same thing as the absolute value 5 minus 15 is negative 10 so it's the same thing as the absolute value of negative 10 now there's two ways you can think about it if it's a negative number inside of the absolute value sign it just becomes the positive version of it so it just becomes 10 another way to think about it is if you had negative 10 you would plot it it would be out here someplace negative 10 we'd have to extend the number line it is 10 to the left of 0 that's what the absolute value is telling us then we have the absolute value of 0 we have the absolute value of 0 well 0 is just 0 away from the number line absolute value of 0 is just 0 that is just 0 that's just right there it is has no distance from the origin and then finally we have the absolute value of negative 3 absolute value of negative 3 that's 3 to the left of or you can just think of it as getting rid of this negative sign so it is equal to three so now that we've expressed them all is just simple integers let's list them in order from smallest to largest so of all of these values which is the smallest this one is the smallest the absolute value of zero so let me write that down absolute value of zero what's the next smallest what's the next month since we have a two there this is the next smallest right there and that original expression was the absolute value of 9 minus seven so the absolute value of nine minus seven and then what's the next smallest so we have this three and then we have a five and a ten so the next smallest is this three right here that three and that original expression was the absolute value of negative three absolute value of negative three then we have this five over here which was just the absolute value of five and then finally we have this ten over here which was the absolute value of five minus 15 five minus 15 and we are done