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let's compare the fraction 4/7 to the fraction 5/7 now what I want you to do right now is to pause this video and think about which of these fractions represents a larger quantity I'm assuming you've had a go at it and the one thing that might jump out at you is that they both have the same bottom number which we call the denominator they both have a denominator of 7 so one way to think about it this is literally 4/7 this is literally 5/7 so we could rewrite 4/7 as literally 4 times 1/7 and we can rewrite 5/7 as literally 5 times 1/7 it's 5/7 5/7 so now if I have 4 of something versus 5 of something which is going to be a larger quantity well clearly five of this 1/7 is going to be more so 4/7 is smaller 5/7 is larger and so what we can do is we can write a less than symbol the way that I remember less than and greater than is at the point the small side of the symbol always is on the same side as a smaller number so this could be read as 4/7 is less than 5/7 or that 4 times 1/7 is less than 5 times 1/7 now let's do another scenario but instead of having the same denominator let's have the same numerator so let's say we want to compare let's say we want to compare 3/4 versus versus 3 versus 3 over let's say versus 3 over 9 which of these two fractions is a larger number and once again pause the video and try to think about it on your own well as we as as we mentioned we don't have the same denominator here we have the same top number instead here is the same bottom number same denominator here we're going to have the same numerator we have the 3 right over there and we could view 3/4 is literally 3 times 1/4 and we could view 3/9 as literally three times 1/9 three times three times 1/9 so we have 3/4 and we have three nights so we really just have to think about what's larger a fourth or a ninth well think about if you start with a whole think about starting with a whole like this but starting with a whole let's draw often let me make a hole right over here a hole right over here so the same sized hole 1/4 is literally taking the hole in dividing it into four pieces while a ninth is taking the hole in dividing 2 9 9 equal sections I could say so let's divide this into 4 equal sections so my best attempt to hand to draw equal sections so that's two equal sections and then that looks pretty close to four equal sections so that right over there is 1/4 and let me draw nice here so let me first put this into three equal sections so those would be third and then split each of those into three equal sections so this is my best attempt at that at hand drawing 9 equal sections splitting the hole into 9 equal sections so when you see here and you might have already realized this if you divide something into four equal sections each section is going to be bigger than if you divided into nine equal sections a ninth is smaller than a fourth a ninth is smaller than 1/4 so three ninth is going to be smaller than 3/4 so once again when you want to do less than or greater than you want to put the point the small side of the symbol on the same side as a smaller number so it would look like this and this is the greater than symbol because you're literally on what you have on the left is the larger number 3/4 is greater than 3/9 and if you actually wanted to represent not just 1/4 and 1/9 we could actually color it in 3 times 1/4 well that's 1 2 3 well 3 times 1/9 or 3/9 is 1 2 3 and when you look at it that way it's pretty clear but the the important thing to realize is is that when the denominator is larger when the denominator is larger you're dividing the whole into more pieces so each piece will be smaller so making the denominator larger makes the fraction smaller making the numerator larger makes the fraction larger