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Current time:0:00Total duration:5:08

Video transcript

so we have here two and two thirds plus 8 and 3/4 and I encourage you to pause the video and see if you can compute what this is so now let's work through this together and there's a bunch of ways that you can tackle this I'll do it in a couple of different ways so one way that you might see is to just rewrite this expression to just rewrite 2 and 2/3 plus plus 8 and 3/4 plus 8 and 3/4 and you might be saying why would I rewrite it this way well when you rewrite it this way it's very clear that these are the fraction parts of the mixed numbers and these are the whole number parts of the mixed numbers and maybe we can add them separately but before we even start adding the fraction parts of the mixed numbers we notice that we have different denominators here we have a 3 and we have a 4 so it would be nice to find a common denominator and we've seen multiple times in the past when you're adding fractions with unlike denominators a good common denominator would be their least common multiple the least common multiple of 3 & 4 well what's that going to be well let's look at the multiples of 4 4 is not perfectly divisible by 3 8 is not perfectly divisible by 3 12 is in fact 12 is 4 times 3 so I can rewrite both of these fractions parts with 12 as their denominator so this is going to be equal to this let me just write it this way so I can rewrite it as 2 and something over 12 now what would be that something over 12 to go from 3 to 12 in the denominator we multiply by 4 so we have to multiply the numerator by 4 as well so 2 times 4 is 8 2/3 is the same thing as 1/12 so 2 and 2/3 is the same thing as 2 & 8 12 and then we could do the same thing down here 8 and 3/4 is going to be the same thing as 8 and something over 12 well to go from 4 to 12 in the denominator you multiply by 3 so we have to multiply the numerator by 3 as well 3 times 3 is 9 and now we can add we can add and what do we get well we have 8 12 plus 9 12 that's going to be 17 17:12 well you might recognize 1712 this is greater than or equal to one so we could actually this is an improper fraction right over here so we can actually rewrite this we can rewrite this as a mixed number let me let me make it clear 17 12 so do it right over here 17 over 12 is the same thing as 1 + 5 12 how did I figure that out 12 goes into 17 one time and then I still have 5 left over 17 12 the same thing as 1 + 5 12 so what I could do is I could write the 5 12 part in the fraction part of our or I guess see the fractions place on our numbers and then I can regroup the 1 put it in the whole number column and now I can just add the 1 + 2 is 3 plus 8 is 11 so we get 11 and 5 12 11 and 5 12 now there's other ways that we could have tackled this what we could have done what we could have done is gone from this place right over here the 2 + 8 12 and the 8 + 9 12 and we could have converted these into improper fraction then added those improper fractions so we could have said this is the same thing let me rewrite it as let's see 2 is the same thing as 24 twelfths + 8 is going to be 32 12 so I could rewrite this top mixed number as 32 over 12 clearly an improper fraction and I could rewrite this bottom mixed number as let's see 8 is how many twelves that's going to be 96 twelfths plus another 9 12 is 105 12 105 12 so if what I just did looks a little bit confusing I should review the the Khan Academy videos on converting mixed numbers to improper fractions or vice versa but now I could think about adding these two and what what would I get out get 32 12s plus 105 12 which would be what a hundred and thirty 737 12 and then if we wanted to rewrite this as a mixed number we could say okay let's see twelve will go into 137 11 times so it goes 11 times 11 times 12 is 132 so you would have 5 left over so it's 11 and 512 so you could have done it either way I think this one would this the way we did it the first time would have been a little bit easier because you didn't have to deal with these really big numbers like 137 and 105 and 32 and you just dealt with more straightforward numbers say hey look 8 12 plus 9 12 to 17 12 so it's the same thing as 1 & 5 12 and then you had 1 in 5 12 plus 2 plus 8 is going to give you 11 and 5 12