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# Ordering rational numbers

CCSS.Math:

## Video transcript

what I'd like to do in this video is order these six numbers from least to greatest so the least of them being on the left hand side and the greatest on the right and I encourage you to pause this video and see if you can do it on your own before we work through it together so assuming you had a go at it so let's let's do it together and to help us there let's plot these numbers on a number line and I have a number line up here so there you go there is a handy number line and let's just take them one by one so the first number here we have 7/3 so let's see if we can express that in a different way if we can write that as a as a mixed number so 7/3 how many how many holes are here and a hole is going to be three thirds so this is going to be let's see this is going to be three thirds plus another three thirds is going to get us to six thirds and so you're going to have one more third left so this is 7/3 three plus three plus one is seven so this is 3/3 is one whole three thirds is one whole so this is two and one-third so 7/3 same things as one two and you see between consecutive integers we have we have these we have three spaces so we are essentially marking off thirds so two and one-third is going to be one third of the way between two and three so it's going to be right over there so that is 7/3 then we have negative five halves so same logic negative using that green color so I can do it over here negative five over two well that's the same thing as the negative of five halves and five halves is going to be two halves plus another two halves plus one half so this is two and a half this is 1 this is 1 and that's a half so this is going to be so this one plus one plus one half two and a half we have our negative out there so it's negative two and one half let's see negative one negative two and the negative 2 and a half is going to be halfway between negative two and negative three so it's going to be right over there so that is negative five over two then we have zero not too difficult it's actually labeled on our number line for us then we have negative two negative two once again on our number line for us two two steps two whole numbers to the left of zero so negative two is going to put us right over there then we have negative twelve fourths so it might jump out at you immediately 12 divided by 4 is 3 so this is going to be the same thing as negative 3 so this is negative 12 forts or if you want to use the type of logic that we used in these first two numbers you could say negative 12 over 4 is the same thing as the negative of 12 forts which is 4 fourths plus another 4/4 so that gets us to 8 4 it's plus another 4/4 that's 12 forts this is 1 2 & 3 or negative 3 so negative 3 is the same thing as negative 12 fourths and then finally one more number negative 3 point 2 5 so you could view this this is the same thing negative 3 point 2 5 is the same thing as negative 3 and 25 hundredths and 25 hundredths is the same thing as 1/4 25 is 1/4 of 100 so this is the same thing as negative 3 and 1/4 so let's see let's go negative 1 negative 2 negative 3 then we have to go forth and we're not going to be able to do it super precisely but it's going to be less than 1/3 so it's going to be right over there so that right over there is negative 3 point 2 5 so we wanted the numbers ordered from least to greatest well we've done that the least is negative three point two five then negative twelve fourths then negative five-halves then negative 2 then 0 then 7/3 and we are done