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so which of the following numbers is a greater one-third or one-fifth pause this video and try to answer that all right now let's think about this together and the way that I can best think about it is by visualizing them so let's imagine a whole so this is a hole right over there and then let's say that this is another hole right over there I'm gonna try to make these rectangles about looking about the same and now how would I represent 1/3 well I would divide this hole into three equal sections and so I'm gonna try to draw it divided into three equal sections so those three equal sections right over there or they're supposed to be three equal sections these are hand-drawn so give me a little slack but one of these three equal sections well that's 1/3 so that is 1/3 right over there now what about 1/5 well then I would try to divide this into five equal sections so one two three four and five equal sections and so one-fifth would be just one of these fifths so it would be that right over there so when you compare it like this what's larger 1/3 or 1/5 and if it isn't obvious just yet I could drag this one over so that we can compare them so that we can compare them directly and you can see very clearly that 1/3 it covers more of the hole it's a larger fraction of the hole than 1/5 is so 1/3 is greater than 1/5 and so you might have noticed an interesting pattern or might start thinking about a pattern you might have been tempted when you saw the 5 year 5 is larger than 3 but 1/5 is less than 1/3 or 1/3 is greater than 1/5 and that is generally true that the larger the denominator the smaller the fraction is going to be why is that because you're dividing your whole into more equal chunks so if you're gonna get dividing to three if it's one of three of the one-third of the whole or if it's one of three equal chunks of the whole it's going to be bigger than one of five equal chunks of the whole and so based on this how would you compare these two numbers how would you compare two thirds to two fifths well same idea here a third is bigger than a fifth so two thirds is definitely going to be bigger than two fifths and you could see it here two-thirds is that while two fifths is that right over there and I can do another example where I haven't even drawn it out how would you compare four over six to four over eight so for six versus four eighths well same idea a sixth is larger than an eighth one sixth is greater than one eighth because the denominator here is smaller we have the same numerator but the denominator is smaller so four of the bigger things is going to be larger than four of the smaller things so four sixths is greater than four eighths