Converting units of length
- Jamir is training for a race and is running
- laps around a field.
- If the distance around the field is 300 yards, how many
- complete laps would he need to do to run at least 2 miles?
- So they tell us how far one lap is, it's 300 yards, but we
- need to figure out how many laps to go 2 miles.
- So a good starting point would be 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 2 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 can first convert the miles to
- feet, and then we know that there are 3 feet per yard, and
- then we'll have 2 miles in terms of yards.
- So 2 miles, if we want it converted to feet, we 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 I just wrote down, there's 5,280 feet per mile, or you
- say 5,280 feet for every 1 mile.
- You can write it either way, but let's just
- write it like that.
- And then we can multiply.
- So this is going to give us what?
- If we just multiply the numbers 2 times 5,280.
- So what is that going to be?
- Maybe I should get a calculator out.
- Or we could do that in our head.
- Let's think of it this way: 2 times 80 is 160.
- 2 times 200 is 400.
- So it's going to be 400 plus 160 is going to be 560.
- And then 2 times 5,000 thousand is 10,000.
- So it's 10,560.
- And then the miles cancel out, and we are
- just left with feet.
- And let me actually multiply it out.
- I did it in my head that time, but that's not always useful.
- Let me verify for you that 5,280
- times 2 is indeed 10,560.
- 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.
- So he needs to run 10,560 feet.
- Now, we want this in terms of yards.
- So 10,560 feet.
- Let's convert this to yards.
- Well, we want it in yards.
- So 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 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 feet, 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 10,560 times 1 divided by 3.
- So it's 10,560/3.
- That's that and that part.
- And then the feet cancel out, and we are
- just left with yards.
- So 2 miles is 10,560 divided by 3.
- And let's figure out what that is.
- So 3 goes into 10,560.
- It doesn't go into 1.
- It goes into 10 three times.
- 3 times 3 is 9.
- And we subtract.
- We get 1.
- Bring down this 5.
- It becomes a 15.
- 3 goes into 15 five times.
- 5 times 3 is 15.
- We have no remainder, or 0.
- You bring down the 6.
- 3 goes into 6 two times.
- Let me scroll down a little bit.
- 2 times 3 is 6.
- No remainder.
- Bring down this last 0.
- 3 goes into 0 zero times.
- 0 times 3 is 0.
- And we have no remainder.
- So 2 miles is the equivalent to 3,520 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.
- And we want laps in the numerator, right?
- Because when you multiply, the yards will cancel out, and
- we'll 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 1 lap.
- So now, multiply this right here.
- The yards will cancel out, and we will get 3,520.
- Let me do that in a different color.
- We will get 3,520, that right there, times 1/300.
- When you multiply it times 1, it just becomes
- 3,520 divided by 300.
- And in terms of the units, the yards canceled out.
- We're just left with the laps.
- So this is how many laps he needs to run.
- So 3,520 divided by 300.
- Well, we can eyeball this right here.
- What is 11 times 300?
- Let's just approximate this right here.
- So if we did 11 times 300, 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 zeroes, so it's
- equal to 3,600.
- So this is going to be 11 point something.
- It's larger than 11, right?
- 3,520 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 3,600 so when you
- divide it by 300, you're going to 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 would he need to do to
- run at least 2 miles?
- So they're telling us that, look, this might be, 11 point
- something, something, something laps.
- 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 laps.
- That complete tells us that they want a
- whole number of laps.
- We can't just divide this.
- If we divide this, we're going to get some 11 point
- something, something.
- You can do with the calculator or do it by hand if you're
- But we have to do at least 12 because that's 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.
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