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Current time:0:00Total duration:5:23

Video transcript

so we want to figure out what one-fourth plus three-fifths minus three tenses and I encourage you to pause the video and see if you could figure this out on your own all right I'm assuming you've had an attempt let's work through this together now so the first thing that might jump out at you is look I have these fractions that I'm adding and subtracting but they all have different denominators so in order to add and subtract them in a reasonable way we'd all we'd want them we want to rewrite them so they all have the same denominator so what we really want to do is find a common multiple of 4 5 and 10 and like I always say we could use any common multiple but it simplifies things a little bit if we use the smallest common multiple or the least common multiple and one way to find the least common multiple is take the largest of these numbers and look at their multiples and keep increasing the multiples until you find one that's divisible by the other two so for example I could start at 10 10 is divisible by 5 but it's not divisible by 4 so that we can go to 20 20 is divisible by both 5 and 4 so the least common multiple of 4 5 and 10 is 20 so let's rewrite all of these fractions as something over 20 so let's start with 1/4 1/4 is what over 20 well to go from 4 to 20 you have to multiply by 5 so you have to do that you have to do the same thing to the numerator you have to multiply it by 5 1 times 5 is 5 1 over 4 is the same thing as 5 over 20 4 is 4 times 120 is 4 times 5 then we want to think about well what happens to 3/5 if I write it as something over 20 well to go in the denominator from 5 to 20 you have to multiply by 4 so you have to multiply the numerator by 4 as well so 3 times 4 is going to be equal to 12 and then we're going to subtract 3/10 but how do we write that as something over 20 well to go from 10 to 20 you multiply the denominator by 2 so if we want to have the same fraction we multiply the numerator by 2 as well so 3 times 2 is 6 so what is this going to be equal to well now my 5:20 it's +12 twentieths - 6:20 it's so what is this going to be well there's a bunch of ways you could think about it you could say well this is just going to be this is going to be 5 5 xx + 12 xx + 12 xx - 6 xx - 6 xx so another way of thinking by the way I just wrote it here 5 plus 12 minus 6 all of that over 20 this is how this this is how many xx so they are going to result so what is that equal to well that's going to be equal to all of this we are counting xx this is one way to think about it so 5 plus 12 is 17 minus 6 is 11 so we get 11 12 11 xx I have 528 I add 12 xx and I take away 6 xx its I'm going to be left with 11 20 it's let's do one more example of this just for for good practice so here I have 4/9 minus 1/6 plus 1/3 and like before I encourage you to pause the video and see if you could work this out well what I want to do is I want to rewrite all of these fractions so that they have a they have a common denominator and to find a common denominator need to find a common multiple of 9 6 & 3 and like I did before what I could do is I could start with a 9 and say ok 9 it's not divisible by 6 it is divisible by 3 but that's not good enough I want to find the common multiple of 9 6 & 3 & as small as 1 as possible so let's look at the next multiple of 9 we get to 18 and 18 is divisible by 9 of course 6 & 3 so let's go with 18 let's write everything is something over 18 so 4/9 is what over 18 well 9 times 2 is 18 that's what I do to the denominator so I've to multiply the numerator by 2 as well so this is going to be 8 over 18 well what's 1/6 over 18 well to go from 6 to 18 in the denominator I have to multiply by 3 so have to multiply the numerator by 3 as well so 1 times 3 is three and then last but not least what is one third is something over 18 well 3 times 6 is 18 so 1 times 6 is going to be 6 or you could view it another way you could say well what's 1/3 of 18 it's going to be 6 what's 1/6 of 18 it's going to be 3 4 ninths of 18 that's a little bit harder to think in your brain but that's going to be 8 18th either way I've just rewritten these fractions and I've rewritten them in the corresponding color so this this up here is the exact same thing as 8 18 minus 3 18 plus 6 18 so what is this going to be equal to well it's going to be a certain number of 18 and so I have 8 18 minus 3/18 that's going to be five eighteenth's plus 6 18th is going to be 1111 18 and we are done