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Current time:0:00Total duration:4:16

Video transcript

what I want to do in this video is get some practice comparing fractions with the different denominators so let's say I wanted to compare 2 over 4 or 2/4 and I want to compare that to 5 over 12 or 5 twelfths and I encourage you to pause the video and figure out which one is greater 2/4 or 512 or maybe they are equal so let's think about this a little bit when I just look at it it's not obvious which one is larger and there's several ways that we can look at this one way is we can try to have the same denominator we can rewrite these so that we can have the same denominator so one way to think about can I write 2 over 4 as something over 12 can I write 2 over 4 as something over 12 well think about it if instead of having four it's if you have 12 you now have three times as many sections that you've divided something into so two pieces would then turn into three times as many pieces so you multiply the numerator by 3 as well if you multiply the denominator by 3 you multiply the numerator by 3 as well so 2/4 is the same thing as 6 12 another way to think about it is 2 is half of 4 6 is half of 12 now can we compare 6 12 can we compare 6 12 to 5 twelfths well I have more twelfths here more twelfths here I have 6 of them versus 5 twelfths now I can make the comparison and I could say look if I have 6 of something in this case that's the thing I have 6 of is 12 that's going to be more than having 5 of the 12 so 6 12 is greater than 5 twelfths and I always think of the greater than sign you always you're always going to be opening to whichever one is larger so this is the greater than sign so six twelfths is greater than 512 then 2/4 is greater than 512 cause two forts and six wells are the exact same thing now let's tackle let's tackle another one this one might be a little bit more interesting let's say we want to compare 3 over 5 and we want to compare that to 2 two over three and like always pause the video and see if you could figure this out I'll give you a hint try to rewrite both of these so that they have the same denominator so let's try to do that so five and so five isn't a multiple of three threes into multiple of five so we need to find a common denominator well a common denominator would be something that is divisible by both five and three so the easiest thing I can think of is 15 which is five times three so let's write 3/5 as something over 15 and let's write 2/3 as something as something over 15 so two thirds I'm going to write as something over 15 well to go from five to 15 I multiplied by three so I multiplied by three so if I multiply the denominator by three I need to multiply the numerator by 3 so x three so 3/5 is going to be the same thing as 9/15 I multiply the numerator and the denominator both by the same number which doesn't change its value I'm just rewriting it 3/5 is the same thing as 915 and now let's look at 2/3 to go from 3 to 15 you multiply by five so we do the same thing with the numerator we need to multiply the numerator by 5 2 times 5 is 10 so 2/3 is the same thing as 10 15 and now we can make a comparison because we have a certain number of 15s compared to another number of 15s so what's larger 9 15 or 10 15 well 10 if you have 10 of something is going to be more so 10 15 is larger than 9 15 s so I put the symbol that opens to the larger one and so this one is a less than symbol 9 15 is less than 10 15 s but since 9 15 is the same thing as 3/5 and 10 15 s is just another way of rewriting 2/3 we can also put the less than symbol there 3/5 is less than is less than 2/3