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# Equivalent fractions and different wholes

CCSS.Math:

## Video transcript

so if I were to give you the fraction one-third I could rewrite it if I multiply both the numerator and the denominator by 2 1 times 2 is 2 and 3 times 2 is 6 so we know that 1/3 is the same thing as 2 6 this is true the 1/3 is just another way of saying 2/6 now given that we know that which of these I guess you could say picture equations actually show us that that is true show that to us visually now we could start with this first one we have 3 equal sections so each of these sections are 1/3 and we have one of those thirds shaded in now if we go on the right side we have 6 equal sections so they are it's divided into sixths and we have two of them shaded in 1/2 and the important thing to realize is is over here we divided the same rectangle to the thirds as we divide into sixths over here we are comparing fractions of the same whole and so you see that if you were to take these two magenta boxes and put them together they actually do have the same area as this one larger this one larger rectangle so this one looks like a good a good picture explanation or visual explanation for why 1/3 is equal to 2 6 you take the same rectangle divide it into thirds and take one of them and then you take that same exact rectangle divided into 6 and pick two of them you shade it in the same amount one-third over here is the same thing as 2 6 over here now the important thing to realize is is that you're taking 1/3 and 2/6 of the exact same rectangle when you look over at these figures you see that this is 1/3 this is 1/3 of this figure right over here it split into 3 equal sections and this is one of them that's shaded in and then this is this is right over here to 6 you have six equal sections and we've shaded in two of them but and we know that 1/3 is equal to 2 6 but this picture isn't true this shaded area right over here is less than this shaded area over here so you're say wait why doesn't it work why is it this 1/3 the same thing as 2 6 well because you're taking 2/6 of a larger hexagon here here you're taking 1/3 of a smaller figure here taking 2/6 of a larger vigor you can't compare fractions of different holes this at 2/6 of a larger hole is going to be larger than one-third of a smaller hole the only time that 1/3 and 2/6 are going to be equivalent is if they are of the same hole like we saw up here so this is not true and say it for the same reason this right over here is 1/3 and this over here is 2 6 but this is 1/3 of a smaller circle then this 2/6 is so this is not true and by the same logic we have these other these other pictures over here and over here we're not talking about 1/3 and 2/6 here we're talking about let's see splitting something into 1 2 3 4 5 6 7 8 so we're talking about eighths and in this case it's 1 2 3 4 5 6 6 eighths and we're comparing it let's see over here they're dividing into 4 and they've shaded in 3 now it is true that 6 eighths is equal to three-fourths 6 divided by 2 is 3 8 divided by 2 is 4 so if you divide if you multiply or divide the numerator by the exact same thing then you're going to get an equivalent fraction now 6 8 is equal to 3/4 but this picture isn't true because 6 eighths would be equal to 3/4 if you're talking about taking 6 8 and 3/4 of the same size in this case diamond these things are not the same size so you can't make this picture statement same thing for this one over here these circles are of different sizes so taking taking the same fraction of different sizes you can't say that they're going to be equal this last one you're taking the fractions of the same whole it's kind of this weird error left pointing arrow looking shape but they are the same shape and you see here we've divided that shape into eighths and we have shaded in 6 of them 1 2 let me do that in a yellow so you can see it 1 2 3 4 5 6 and over here we have divided it into fourths and we have shaded in three of them and we have shaded into three of them and so this statement is true we knew it we already knew that 6/8 and three fourths are the same thing but this this this picture right over here visually shows us that because we're taking 6/8 of the same hole as we're taking three fourths of and you see that here this area this area that I'm shading in a different color so the area that I'm shading in six of these equally area are these triangles with equal areas the same thing as 4 OS three of these parallelograms over there three of the four these have the same area you could see that one of these one of these like that one right over there could be equivalent to this over here you cool it to that over there actually let me do it for all of them this one over here could be equivalent to let's see if you were to flip it over it would be equivalent to that over there and then finally I think you see where this is going this one over here is equivalent to this one over here so we have the same fraction shaded in we just divided the one on the left and two more equal pieces than we did on the right but these are equivalent fractions and this picture shows us that 6/8 is indeed equal to 3/4 once again 6/8 of the same whole is equal to 3/4 of that same whole