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Video transcript

Jameer is training for race and is running laps around the field if the distance around the field is 300 yards how many complete laps would he need to do to run at least at least two miles so with they tell us how far one lap is this 300 yards but we need to figure out how many laps to go two miles so a good starting point where to get everything into the same units we have distance here in terms of miles we have it here in terms of yards so let's just get everything into yards so he needs to run two miles so two miles how do we convert that to yards well I don't have it memorized how many yards there are per mile but I do have it memorized how many feet there are per mile and it's a good thing to have in the back of your brain someplace that in general you have 5,280 feet per mile it's a good number to know 5,280 feet per mile so if we want to convert we could first convert the miles to feet and then we know that there are three feet per yard and then we'll have two miles in terms of yards so two miles if we want it converted to feet we want miles in the denominator so you want miles in the denominator and we want feet in the numerator and the reason why I say that is so that this miles will cancel out with that miles and we'll just have feet there and we I just wrote down there's 5280 5,280 feet per mile or you say 5,280 feet for every one mile you could write it either way but let's just write it like that and then we could multiply so this is going to give us what if we just multiply the numbers two times 5,280 so what is that going to be maybe I should get a calculator out but we could do that in our head two times 5,000 let's think of it this way two times eighty is 162 times 200 is 400 so it's going to be 400 plus 100x T is going to be 560 and then two times 5,000 is 10,000 so it's 10,000 10,000 560 and then the miles cancel out and then the miles cancel out and we are just we are just left with and maybe let me actually multiply it out I did it in my head that time but that's not always used so let me verify for you that 5,280 times two is indeed 10,000 560 so 2 times 0 is 0 2 times 8 is 16 carry the 1 2 times 2 is 4 plus 1 is 5 2 times 5 is 10 10,000 560 so he needs to run 10,000 560 feet now we want this in terms we want this in terms of yards so 10,000 560 feet let's convert this to yards well we wanted in yards so we want yards in the numerator we want yards in the numerator and we want feet in the denominator so that the feet cancel out with that feet right there and we know that there are 3 feet for every one yard 3 feet for every 1 yard or another way to read this is that you have 1/3 of a yard for every foot and now we can multiply and it makes sense if you're going from feet to yards the number should get smaller because yards is a bigger unit you need fewer yards to go the same distance as a certain number of feet so it makes sense that we're dividing same thing 2 miles is a ton of feed so it made sense that we were multiplying by a large number here it makes sense that we're dividing so let's do this so this becomes 10,500 60 times 1/3 so it's 10,000 560 over 3 that's that in that part and then the feet cancel out and we're just left with we are just left with yards so this is 210 2 miles is five thousand ten thousand five hundred and sixty divided by three and let's figure out what that is so 3 goes into 10,000 560 it goes into doesn't go into one it goes into 10 three times three times three is nine and we subtract we get one bring down this five comes to 15 3 goes into 15 five times five times three is fifteen we have no remainder or Giro you bring down the 6 3 goes into 6 two times let me scroll down a little bit 2 times 3 is 6 subtract no remainder bring down this last 0 3 goes into 0 0 times 0 times 3 is 0 and we have no remainder so this is going to be so two miles is equivalent to three thousand five hundred and twenty yards three thousand five hundred and twenty yards that's the total distance he has to travel that's the equivalent of 2 miles now we want to figure out how many laps there are we want this in terms of laps not in terms of yards so we want the yards to cancel out we want the yards to cancel out and we want elapsed in the numerator right because when you multiply the yards will cancel out it will just be left with laps now how many laps are there per yard or yards per lap well they say the distance around the field is 300 yards so we have 300 yards for every one lap so now if we multiply this right here the yards will cancel out and we will get three thousand five hundred and twenty let me do that in a different color we will get three thousand five hundred and twenty that right there times one over three hundred when you multiply times one it just becomes three thousand five hundred twenty divided by three hundred and in terms of the units the yards cancelled out we're just left with the laps so this is how many laps he needs to run so three thousand five hundred twenty divided by three hundred well we can eyeball this right here what is 11 times three hundred let's just approximate this right here so if we did 11 times three hundred eleven times three hundred what is that going to be equal to well 11 times 3 is 33 and then we have two zeroes here so this will be 3,300 so it's a little bit smaller than that if we have 12 times 300 what is that going to be 12 times 3 is 36 and then we have these two zero so it's equal to 3600 so this is going to be 11 point something it's larger than 11 right 35 20 is larger than 3,300 so when you divide by 300 you're going to get something larger than 11 but this number right here is smaller than 3600 so when you divide it by 300 you're gonna get something a little bit smaller than 12 so the exact number of laps is going to be a little bit lower than 12 laps so 2 miles is a little bit lower than 12 laps but let's make sure we're answering their question how many complete laps how many complete laps would he need to do to run at least 2 miles so they're telling us that look you know this might be I don't know 11 point something something something laps and that would be the exact number of laps to run 2 miles but they say how many complete laps does he have to run 11 complete laps would not be enough he would have to run 12 so our answer here is 12 complete 12 complete laps that complete tells us that they want a whole number of laps we can't just divide this we divide this we're going to get some 11 points something something you can do it with the calculator or do it by hand if you're interested but we have to do at least 12 because that's our that's the the smallest whole number of laps that will get us to at least this distance right here or this number of laps or the equivalent of 2 miles