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CCSS.Math:

let's see if we can figure out what 4/3 minus minus 1/5 is and if you think you know how to do it I encourage you to pause the video and give it a go so when you first look at this the thing that might jump out at you is we have different denominators here and so it's not obvious how to subtract 1/5 from 4/3 when you have these different denominators and the key is is to rewrite each of these fractions so that they have the same denominator and how do we figure out what that same denominator is well it's going to be a common multiple of 3 & 5 and ideally it's going to be the least common multiple of 3 & 5 so how can we calculate that well we could start with the larger of the two numbers say 5 and let's go through it's multiples and see when we get to one that's divisible perfectly by 3 so 5 is not divisible by 3 10 is not divisible by 3 15 is divisible by 3 in fact 15 is 3 times 5 so I can rewrite both of these fractions as something over 15 so what's 4 thirds if I were to write it as something over 15 well to get from 3 to 15 in the denominator we have to multiply we have to multiply by 5 so if you multiply the denominator by 5 if you don't want to change the value of the fraction you have to multiply the numerator by 5 as well so you have to multiply the numerator by 5 as well 4 times 5 is going to be 20 so 4/3 is the same thing as 20 15 all right now how would we rewrite 1/5 as 1/5 as something over 15 so we're going to 15 in the denominator well to go from 5 to 15 we get to multiply by 3 so if we multiply the denominator by 3 we have to multiply the numerator by 3 as well so times 3 1 times 3 is just 3 so 4/3 minus 1/5 we can rewrite that as 2015 minus 3 15 and now this becomes a lot more straightforward what is this going to be well this is going to be a certain number of 15 so we have 2015's and we're taking away 3 of those 15 so we are going to have if you have 20 or something can you take away three of them you're going to have 17 of those things in this case we talked about 15 so this is going to be 1715 and if we wanted to write it as a mixed number we could say 15 goes into 17 one time with a remainder 2 so it's 1 & 2 15 let's do another example let's see if we can figure out let's see if we can figure out what 7/10 7/10 minus minus 5 eighths is 5 over 8 and I encourage you to pause this video and see if you can calculate it yourself well just like we saw before we have different denominators but we need to rewrite them so that they have a common denominator that way we can subtract and so what's a common what's the common multiple of 10 and 8 and ideally the least common multiple doesn't have to be but it keeps things a little bit simpler well let's start with the larger of the two numbers and then keep keep finding in their multiples and find one that that is perfectly divisible by the other one by 8 so 10 is it perfectly just by 8 20 isn't 30 isn't 40 is 40 is a multiple of 10 and it's a multiple of 8 in fact it's the least common multiple of 10 and 8 so we can write rewrite both of these fractions as something over 40 so that's going to be something over 40 minus something over 40 minus something over 40 is equal to something so 7/10 is what over 40 well to get to go from 10 to 40 in the denominator we multiply it by 4 so to do the same thing in the numerator multiply the numerator by 4 7 times 4 is 28 so 7/10 is the same thing as 28 fortieths and i let's do something do the same thing with the other fraction to go from 8 to 40 in the denominator we have to multiply the denominator by 5 8 times 5 is 40 so if we multiply the denominator by 5 we have to multiply the numerator by 5 as well 5 times 5 is 25 so 7/10 minus five eighths is the exact same thing as 28:48 - 25 40s and now this makes a lot of sense it's going to be a certain number of 40 it's if I have 28 fortieths and I take away 25 of those 40 it's how many fortieths am I going to have left well I'm going to have three 40s left 28:40 it's minus 25 40 it's so I'm going to have three 40s 28 minus 25 is 3 and we are done 7 tenths minus 5/8 is 340 it's