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when you write a fraction there are actually words for the top number and the bottom number and the words are a lot more fancy than the word top number and bottom number well what mathematicians typically use is the word numerator numerator for the top number and denominator for the bottom number the nominator denominator for the bottom number now what I want to do now now that we know that the top number is the numerator of the fraction the bottom number is the denominator I want to compare pairs of fractions that have either the same denominator or the same numerator so let's look at this first pair I want to compare 4/7 to 3/7 and I have two holes right over here they're the same hole and I've divided them in two sevens I've divided them into seven equal chunks and I want to see what's larger four sevens or three sevens so what I can do is I can fill in four sevens let me select four out of the seven so that's one two three four and the fact that trying to even get to four sevens I have to have three sevens first gives you a good clue that 4/7 is probably larger or it is larger but now let's color in 3/7 just so we can compare so one two three sevens and so it's pretty clear that on the left hand side we are shared we are shading in more of the hole then on the right hand side so four sevens represents a larger fraction more of the hole than three sevens and the way that we can state that comparison mathematically is with the greater than symbol we can write four sevens is greater than is greater than three sevens now the greater than and less than symbols can sometimes be confusing this is greater than this is less than so this is greater than greater than this is less than and the way that I remember it is that the greater than symbol either symbol the small pointy side is always on the side of the smaller and the big open side is always on the side of the larger number so here big open side is opening towards the 4/7 small pointy side opening to the three sevens four sevens is greater than three sevens now what about three sevens and 3/4 so here I have different denominators but I have the same numerator and so I encourage you to pause this video and draw maybe a little boxes like this and try to judge for yourself which of these is a larger fraction is it represents a larger number well let's color them in so let's think about 3/7 first and we actually already do it here but I could do it really fast right over here so that is three sevens I've colored in three of the seven equal groups and what would 3/4 be well that's 1/4 2/4 and 3/4 and so it's pretty clear that 3/4 represents a larger fraction of the whole that 3/4 is larger or that 3/7 is smaller so we could write that 3/7 is less than 3/4 so notice same exact numerator when I divided it because this fraction symbol could also be viewed as division when I have it as more equal groups or it's a fraction of more equal groups so three out of seven versus three out of four this is a smaller number which which makes sense now let's compare these two we have the same denominator different numerators 3/4 versus 2/4 well 3/4 we've already looked at we can just shade in three of these so three of these fourths so that's 3/4 right over there and then 2/4 where we're going to only have two of the fourths 1/2 so 2/4 is clearly the smaller number 3/4 is the greater number so once again we could write 3/4 is greater than 2/4 and then finally I encourage you to pause the video try to come up with a whether 2/4 or 3 6 is a larger number well let's color it in again we've already seen 2/4 we just have to color in two of our fourths so let's just color in two of our fourths right over there and then 3 6 we've split our whole into 3 into 6 equal sections one two three four five six we need a color in three of them we need to color in three of them and as you see we are coloring coloring in the exact same amount of the whole these two fractions are equivalent these are equivalent fractions 2/4 is equal to 3 6 and as you see here they're both filling in half of the whole if we were to just draw the whole and split it only let me do this in a different color if we have our whole so our whole and we were to split it only into two sections only into two sections we are shading in exactly one out of the two sections one out of the two sections so you could say you could say that 2/4 is equal to 3 6 and they both equal 1/2 they all equal so 1/2 is equal to 2/4 is equal to 3 sixths