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# Comparing fractions visually

CCSS.Math:

## Video transcript

we have four fractions written over here and what I want you to do is think about which of these fractions are or which of these are the smallest value which of these is the largest value in which of these might be equal and there's two ways that you could do it you could try to plot them on a number line or you could try to depict them visually so pause the video now and try it on your own so let's plot these on a number line so let me give ourselves another little number line right over here you see I can draw one see so let's say this is my number line draw it as straight as I can so that's my number line that is zero let's say that this is one and then that is two so let's first try to plot where one half is on the number line so we can split the section between 0 & 1 into two equal sections so two equal sections and 1/2 would means that I would have gone I would have gone one of those two equal sections so if I just go that far I should be at 1/2 so this right over here is 1/2 now let's think about two fourths well to do two fourths we would want to split the section between 0 & 1 into four equal sections so let's do that so 0 so that's so it's one equal section two equal sections three equal sections and four equal sections so what happens where do we end up if we go two out of those four equal sections well we would end up one so we go one two equal sections so we end up right over here two fourths we end up at the exact same place so at least based on how we've drawn on the number line it looks like 1/2 is equal to 2/4 so let me write that down 1/2 is equal to 2/4 now what about four eighths well let's split the the the part of our number line between 0 & 1 into 8 equal sections so if we take each of those 4 equal sections and split them into two so now we have 1 2 3 4 5 6 7 8 I can't draw it perfectly but I'm trying to make them equal section so now it's eight equal sections and now we're going to go four of them starting at zero we're going to go one two three four so we end up at the same place again this is also equal to four eight so 1/2 is equal to 2/4 which is equal to which is equal to four eighths now what about three eighths well we've already split our number line into 8 equal sections let's go three of them one two three so three eighths is right over here three eighths is less than one-half it's less than two fourths it's less than four eight it is a smaller number let's see if that also makes sense when we try to visually depict or try to visually draw these fractions so I've done that right over here and this is one half so I have the same all these rectangles are the exact same size and this purple one over here I split it into two equal sections and we shaded in one of them so we see that this is one half now here I've created in two out of the four equal sections and you see that this looks the exact same size as the 1/2 right over here that we started with rectangles of the same size if you shade in one half or two forts it looks exactly the same and that makes sense because if you took this one right over here if you took this first one and you divided each of your two equal sections into two equal sections so you split it again then you see that this is equal to 2/4 now what about 4 eighths here I've split it up where I have this one this one this one and this one shaded in but if you rearrange them you could see that you could get exactly the same amount of the rectangle shaded in and if you want to see that divide each of these four into two so divide those into two and those in a to notice I now have one two three four out of the eight equal equal squares shaded in these two things are equal so let me make it clear this is an equal fraction which is an equal fraction of that which is an equal fraction of that and here this is three out of eight you see that it's less than it's less than this region right over here this one we've literally filled in half the entire rectangle four out of the eight if we did four out of eight here we would have also had to fill in this one right over here which we did in it we only filled in three out of the eight so it makes sense that three eighths is a smaller part of our hole than four eighths or 2/4 or 1/2 and it's likewise it's a smaller number