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Current time:0:00Total duration:4:23

let's say that this circle right over here represents one one hole and we've divided this circle into 1 2 3 4 5 equal sections so each of these sections represents one-fifth each of these each of these sections represents one-fifth of the circle and we've seen this already 1/5 1/5 1/5 and 1/5 and if we were to then color in some of this so let's say we're coloring 3 of these sections so that's one of those sections right over there another one right over here so we've colored in two of the fifths and then three of the fish notice you put those 3 1/5 together how much have we now shaded in we've shaded in 3/5 of the whole so the fraction that's actually shaded in now is 3 3/5 fifths 3/5 is what's shaded in now let's do something in some ways a little bit simpler but also in some ways kind of interesting let's start with a hole again so once again this is one hole let me label it one hole so it's one hole and instead of dividing it into five equal sections I'm just going to divide it into one equal section so if I were to shade in if I were to shade this in so if I were to shade it in just like that so I'm shading in my one hole I'm shading in my one equal section how many of the equal sections are now shaded in well just to remind ourselves there is one equal section and I have shaded in exactly one of those one equal section I've shaded in the whole thing or I could say that 1/1 which you'll never hear someone actually say is shaded in or I could say that the whole thing is shaded in so this is equal to one whole so that's a whole that's interesting and I want you to keep in mind remember look we have 3 we literally have 1 2 3 fifths and we literally call that three-fifths now this is one hole now what happens if we were to do this multiple times so if we were to let me copy and paste that so now I have another one hole and then another one hole right over here so now in total how many holes do I have well I have three one two three holes so I could say and I've actually shaded in three holes so this is this one right over here is equal to let me make sure I label it right this right over here is equal to if I were to take the combination this is equal to three three holes or if I were to think of in terms of numbers just the number line this is literally this would represent the number three but what's another way I could represent it notice when I took a 1/5 another 1/5 and another 1/5 I could call that 3/5 so now if I take 1 1 1 1 another 1 1 and another 1 1 well I should be able to call this 3 3 once or 3 first or however you want to call it so I could call this 3 first so this is interesting now we're seeing where the top number on a fraction is larger than the bottom one but another way of thinking about this fraction symbol is that it's division so you could view this as 3 divided by 1 is equal to 3 or you could say well like 1 over 1 is a whole and I now have 3 of them so this is equal to 3 wholes so 3 over 1 is the same thing as the number 3 and let me make sure let me emphasize that let me draw this on a number line so once again let me let me go all the way to 3 so 0 1 2 & 3 so one whole gets us exactly 1 jump on the number line so this right over here that gets us to 1 over 1 we do another jump now we've gotten to first I guess you could say we've essentially taken two of these jumps each jump is 1 over 1 now we are 2 over 1 which is the same thing as 2 you take another jump you take another jump and we essentially get 2 or we do get 2 3 over 1 which is the exact same thing as 3