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bill has 198 marbles in his collection he then buys another 40 for a year later he decides that he has had enough of marbles and decides to split them as evenly as possible between the other 31 students in his math class roughly how many marbles will each of his classmates get and the fact that we have the word roughly here means we don't need to get the exact answer if it said roughly your estimate how many marbles each of his classmates will get that says hey we maybe we can round these numbers a little bit to make our calculations a little bit easier so let's give a go at that so yeah he starts with 198 marbles well let's round everything to the nearest 10 and maybe that'll simplify things so 198 if we were to round to the nearest 10 well we want to look at the ones place the ones place we have an 8 if you have a ones place that's 5 or greater then you're going to round up if you're going to round to the nearest 10 so if you route the nearest 10 if you round up is from 198 is actually 200 we'll just go up to 200 that's also the nearest hundred so this is approximately equal to 200 and this little squiggly equal sign that means roughly equal to or approximately equal to and so this is what he starts off with then he buys another 4444 is approximately equal to if we round to the nearest 10 we look at our ones place it's less than 5 so we're going to round to the 10 below 40 for the 10 below 44 is 40 if we go to the nearest 10 going down we get to 40 so how many total marbles did he have before he distributes them well if we take our rough two if we take our two rough estimates and if we add them 200 plus 40 he has roughly 240 marbles before he distributes them now how many students is he going to distribute them between well there's a total of 31 students there's 31 students but once again let's round this if we round this to the nearest 10 we're going to round down because our ones place has one it's less than five so we're going to round to the 10 below 31 so that is going to be 30 so if you have roughly 240 marbles and you're going to distribute them amongst roughly 30 folks then how many are each of them going to get well each of them are going to get 240 divided by divided by 30 once again this is just a rough estimate roughly 240 marbles divided by 30 folks well what's 240 divided by divided by 30 well if we say that this is equal to if we say that this is equal to the marbles per student so let's say that this is mm4 marbles per student this is another way of saying that M times 30 M times 30 is equal to 240 or that 240 is equal to M times 30 let me write it that way so that's the same thing as saying that 240 is equal to M times 30 where M is what we're trying to figure out the rough number of marbles per student so let's think about what M is and there's a bunch of ways we could do it we could just look at our multiples of 30 so 30 60 90 notice this is very similar to taking multiples of 3 but we just have a 0 now the the the multiples of 3 are now in the tens place and now we have a 0 in the ones place 90 120 which is just a 12 with a 0 150 180 180 210 240 so what is this is 30 times 1 2 3 4 5 6 7 8 so we know that 240 is equal to 30 times 8 so we could write 240 is equal to and 30 times 8 is the same thing as 8 times 30 is equal to 8 times 30 is equal to 8 times 30 or another way we could say is with the number of marbles on each of his friend is going to get is roughly 8 so this is going to be this is going to be eight so each of his classmates is going to get roughly roughly eight marbles once again this is an estimate it's not an exact answer now you might have tried to get a slightly more precise answer if you want if you didn't want to round 198 and forty-four you could have just added the two 8 plus 4 is 12 and then 1 plus 9 plus 4 is 14 1 plus 1 is 2 so the exact number of marbles he had was 242 which is pretty close to 240 so 240 was a good approximation and then when you divide that by dividing it by 30 one's a bit of a pain and luckily we can just estimate so we divided by 30 and we got 8 and this is another kind of aside here notice notice 24 24 divided by 3 is equal to 8 and if you divide 240 240 divided by 30 this is also this is also equal to 8 so if you divide something 10 times as large by something 10 times as large you're still going to get the same value but either way each of his classmates are going to get roughly 8 marbles