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Video transcript

let's give ourselves some practice adding mixed numbers so let's say I want to add to let me write it this way let's say I want to add 2 and 4/7 plus plus 3 and 2/7 3 and 2/7 I encourage you to pause this video and try to think about what this is going to be well there's a couple of ways that you could tackle it one way you could say well let me just add the non fraction parts you could say that 2 plus 3 is equal to 5 and then you could say that 4/7 plus 2/7 is equal to well 4/7 plus 2/7 is going to be equal to 6/7 anybody wait how did I how did I do that how did I just you know just only add the fraction parts and add the whole parts but the way I did that is because 2 and 4/7 is the same thing as 2 plus 4/7 2 and 4/7 same thing is the 2 plus 4/7 and then plus 3 and 2/7 the same thing is 3 plus 2 sentence so all I did over here 2 and 4/7 plus 3 and 2/7 is 2 plus 4/7 plus 3 plus 2/7 and you could swap the order and how this happens so you could take you could just switch the order and say this is going to be 2 plus 3 2 Plus 3 plus 4/7 plus 4/7 plus 2/7 plus 2/7 and what we just figured out was that 2 plus 3 is equal to 5 right over here and at 4/7 plus 2/7 is equal to is equal to 6/7 just like that now let's do a more interesting example let's do let's say that I have 3 and three and three-fifths three and three fifths plus plus five and four five and four-fifths now what is this going to be equal to well if you do the same technique if you add the three plus the five you're going to get eight and then if you add the three fifths plus 4/5 you would get seven fifths so you get eight and seven fifths and this wouldn't be wrong this is eight and seven fifths if you add these two things together but it's a little bit strange here because seven fifths is bigger than a whole so to get a better sense of what number is really being represented here I want to rewrite this so eight and seven fifths this is the same thing as eight plus instead of seven fifths we could say this is the same thing as five fifths which is a whole plus two fifths plus two fifths now why is that interesting because five fifths notice 5/5 two fifths that's seven fifths right over there or you can consider five fifths to be one so this is 8 plus 1 which is nine and two fifths nine and two fifths so all I did here I added it the same way that I did the first problem a few seconds ago when I realized that this fraction part is greater than one I separated it into one and then a fraction that is less than one and that that whole I was that able to add to the eight to get to nine and then I would have two fifths left over eight and seven fifths because 5/5 as a whole is the same thing as nine and two fists so if I were to write this in kind of a I guess a clearer way I would say this is nine and 2/5 three and 3/5 plus five and 4/5 is nine and 2/5 and once again we wait three plus five is only eight how did I get a nine well that's because three fifths plus 4/5 is greater than one