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Video transcript

so once again we have three equal or I say we say three identical objects they all have the same mass but we don't know what the mass is of each of them but what we do know is that if you total up their mass it's the same exact mass as these nine objects right over here and each of these nine objects have a mass of one kilogram so in total you have nine kilograms on this side and over here you have three objects they all have the same mass and we don't know what it is we're just calling that mass X and what I want to do here is try to tackle this a little bit more symbolically in the last video we said a little bit why don't we just why don't we just multiply one third of this and multiply one third of this and then we're essentially we're going to keep things balanced because we're doing one third of the same mass that this total is the same as this total that's why the scale is balanced now let's think about how we can represent this symbolic see symbolically so the first thing I want you to think about is can we set up an equation so where can we set up an equation that expresses that we have these three these three things of mass X and that in total their mass is equal to the total mass over here can we express that as an equation like if you a few seconds to do it well let's think about it over here we have three things with mass X so their total mass we could write as we could write their total mass as X plus X plus X and over here we have nine things with mass of one kilogram I guess we could write 1 plus 1 plus 1 as 3 plus 1 plus 1 plus 1 plus 1 how many set 1 2 3 4 5 6 7 8 9 and actually this is a mathematical representation and we've set it up as an equation this is algebraic representation it's not the simplest possible way you can do it but it is a reasonable way to do it if we want we can say well if I have an X plus another X plus another X I have three X's so I could rewrite this as 3 X 3 X + 3 X will be equal to well if I sum up all of these ones right over here one plus one plus one we're doing that we have nine of them so we get three X is equal to nine and let make sure I do that one two three four five six seven eight - nine so that's how we would set up and so the next question is what would we do what can we do mathematically actually to either one of these equations but we'll focus on this one right now what can we do mathematically in order to essentially solve for the X in order to figure out what that mystery mass actually is and I'll give you another second or two to think about it well when we did it the last time we're just the the scales we said okay we've got three of these X's here we want to have just one X here so we can say whatever this X is if the scale stays balanced is going to be the same as whatever we have there there might be a temptation to subtract two of the x's maybe from this side but that won't help us and we can even see it mathematically over here if we subtract two x's from both sides on the left hand side you're going to have three X minus two X and on the right hand side you're going to have nine minus two X and you're just going to be left with three of something minus two of something is just 1 of something so you will just have an X there if you get rid of two of them but on the right hand side you're going to get nine minus two x's so the X is still didn't help you out you still have a mystery mass on the right hand side so that doesn't help so instead what we say is and we did this the last time we said well what if we took one-third of these things if we take one-third of these things and take one-third of these things we should still get the same mass on both sides because the original things had the same mass and the equivalent of doing that mathematically is to say why don't we multiply both sides by one-third or another way to say it is we could divide both sides by 3 multiplying by 1/3 is the same thing as dividing by 3 so we're going to multiply both sides by 1/3 when you multiply both sides by 1/3 visually over here if you have three X's you multiply it by 1/3 you're only going to have one X left if you have nine of these 1-kilogram boxes you multiply it by 1/3 you're only going to have you're only going to have three left and over here you can even visually if you divide by three which is the same thing as multiplying by 1/3 you're going to you divide by three so you divide by three you have an X is equal to a 1 plus one plus one and X is equal to three or you see here and X is equal to three over here you do the math one third times three is one you left with 1x so you're left with X is equal to nine times one-third or you can even view it as nine divided by three which is equal to which is equal to which is equal to three