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# Equivalent fractions with models

CCSS.Math:

## Video transcript

so we're going to do in this video is think about equivalent fractions so let's say we have the fraction 3/4 and I want to think about what is an equivalent number of eighths so 3/4 is equal to how many eighths and to represent that how many I could put a question mark there but instead of a question mark I'll just put a letter so what should Y be 3/4 is equal to Y eighths what does y need to be to make this true and before I tell you to go pause this video and try to work on it on your own which I will do in a little bit I'll give you a little bit of a hint so let's try to represent 3/4 or I'll represent it for you so I will do it with this rectangle so I'm going to divide it into four equal sections so let's see that would be dividing it roughly in half I'm hand drawing it so it's not perfect but these should be equal sections the areas of each of these sections should be equal so there you go this is my hand-drawn version of that and so three of those four and I will do that in purple three of those four it could be one two and then just for kicks I will do this one out here so that is 3/4 right over there so if I were to think about this in terms of eighths so I'm going to draw another whole but this time instead of just splitting them into fourths I'm going to split it into eighths so let's do the fourths first just cuz it's easy to look at the one above that so that's my fourths and then I'll divide each of the forts into two so that gives me eight all right almost there the drawing is really the hardest part here and so each of these is an eighth it's hand drawn but imagine if they were eight equal sections so how many eighths is equal to 3/4 pause the video and try to work it out on your own all right well we can just look at this visually so this first fourth we could say that's equivalent to filling out this eighth and this eighth so that first fourth is equal to two eighths this second fourth is equal to another two of these eighths and then this third fourth is equal to another two of the eighths so how many eighths have I shaded in well I have one two three four five six eighths so I have 6 over 8 so 3/4 is equivalent to 6 eighths so in this scenario y is equal to 6 eighths or we could say six eighths is equal to Y now let's do another example so we could see here in this top circle is we've divided it into six equal sections so each of these are one of the six equal sections or 1/6 and we can see that one two three four of them are shaded in so we have represented in that top circle that is four four out of six so what I want to think about is how many thirds are equivalent to four sixths pause this video and think about it so once again how many thirds are equivalent to four sixths instead of just putting a question mark there I'll put the letter X so what should X be for these two things to be equivalent or another way to think about it is four over six is equal to x over over three four sixths is equal to how many thirds all right now let's do this together and so one way you could think about it let's see four one-third for us to be make this equal to one-third it looks like that is equivalent to what I am circling in the orange up here and that also makes sense if I were to divide 1/3 into two so now I would have this would be 1/6 and that would be 1/6 so you need two sixths to make up a third or each third is equivalent to two sixths so this is one third right over here and that is equivalent to two of these sixths but we are not completely done yet we have another 2/6 so we could say those two sixths are equivalent to another third and it's a little tricky because they didn't put this six the next to that sixth but you could imagine if we were to move let's say we were to move this sixth so I'm gonna color this one in white so if I were to move that sixth two right over here so we're shading this one in instead so then you can see that these two sixths right over here these two sixths are equivalent to this third right over there so what you can see is is that our four sixths and remember I moved this one over so I'm not shading this one in any more but you can see the four sixths that I've shaded in is equivalent to two thirds or another way to say it is X would be equal to two X would be equal to two four six is equal to X thirds or four six is equal to two thirds